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Mapping, Localization, and Trajectory
Estimation with Mobile Robots
Using Long-Range Passive RFID
Dissertation
der Mathematisch-Naturwissenschaftlichen Fakultät
der Eberhard Karls Universität Tübingen
zur Erlangung des Grades eines
Doktors der Naturwissenschaften
(Dr. rer. nat.)
vorgelegt von
Dipl.-Inform. Philipp Vorst
aus Gütersloh
Tübingen
2011
Tag der mündlichen Qualifikation: 20.05.2011
Dekan: Prof. Dr. Wolfgang Rosenstiel
1. Berichterstatter: Prof. Dr. Andreas Zell
2. Berichterstatter: Prof. Dr. Andreas Schilling
3. Berichterstatter: Prof. Dr. Horst-Michael Groß
To my parents
Abstract
This thesis addresses the use of radio-frequency identification (RFID) for three funda-mental tasks in mobile robotics: mapping, self-localization, and trajectory estimation.These topics have widely been studied in recent years, because they are regarded as keyingredients to autonomous robots. In particular, we investigate the application of long-range passive RFID in the work at hand. This RFID standard is expected to play a majorrole in the automation of identification processes in industry and commerce. We makeseveral contributions to the examined tasks and show their effectiveness in extensive ex-periments with real robots. One central guideline of our approaches is that they use onlythe given inexpensive transponder infrastructure as well as off-the-shelf RFID hardware.
An important field of application of passive transponder mapping is the continuous in-ventory of RFID-tagged goods: Compared to classical inventory, objects can be locatedrather than only enregistered. For this purpose, the robot traverses the environment andcontinuously detects transponders, using its on-board RFID reader. Localizing the RFIDtags is particularly difficult because standardized readers report detection counts, but nei-ther output distances nor bearings. Quite the contrary, labels are frequently not detecteddue to high false-negative rates. Still, by the repeated detection from different positionsof the robot, it is possible to infer transponder locations, as related works have shown.
A probabilistic sensor model, which represents detection rates depending on relativetag positions in the field of the reader antenna, establishes the basis for tag position es-timation with a particle filter. In the scope of this thesis, we have developed a methodwhich allows for the fast, semi-automatic generation of a model from training data bynonparametric regression. By learning from empirical data, it is possible to capture radiopropagation effects which are usually shielded by parametric models. We demonstrateseveral experiments with different RFID reader models. Our results show that such amodel also improves mapping accuracy if the filter is initialized by sampling likely tagposition hypotheses. Furthermore we present an iterative estimation scheme, which in-creases the efficiency of mapping. For the sake of improved accuracy, we propose a tech-nique which fuses RFID with prior spatial knowledge in the form of volumetric maps.
Self-localization denotes the case that the robot estimates its position by the detectionsof known RFID tags. RFID is beneficial for this task, because the robot’s location canquickly be resolved without ambiguity, even if one employs long-range RFID with higherposition uncertainty. We compare three methods based on Monte Carlo localization: amodel-based approach, which works in a dual fashion to model-based mapping, as well
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as two variants of location fingerprinting. Fingerprinting aims at localization by compar-ing current measurements to reference measurements which were taken at known posi-tions during a calibration stage. In this thesis, we extend the RFID snapshot approach,which computes observations likelihoods based on Bayes estimates of global detectionrates, for denser tagged environments. Moreover we introduce a new fingerprinting tech-nique which uses vector similarity measures for determining the best matching referenceobservations. We examine global localization strategies in order to generate accurateinitial belief for bootstrapping the particle filter. Based on extensive experiments, thedifferent positioning methods are compared, characterized by the variation of parame-ters, and finally probed under influences which occur in dynamic environments.
Self-localization usually requires prior mapping. This stage is not always desirable,because either human assistance is required or another localization system on board therobot which provides reference positions. For this reason we finally dedicate ourselves tothe estimation of the robot’s trajectory in previously unknown environments. This issueis a variant of simultaneous localization and mapping (SLAM), which has been one ofthe predominant topics in robotics research in recent years. Based on the reconstructedpath, which is estimated using only RFID and odometry, the robot can localize itself lateron, or it can map the newly visited environment by a second pass over the recorded data.
Our first proposed method employs a particle filter for trajectory estimation. In orderto correct particle weights, we learn likelihood functions which assess the similarity ofa measurement pair, conditioned on their relative recording distance. Second, we pursuean approach based on nonlinear sparse optimization of the graph of past robot poses. Itsedges interconnect successive positions via odometry and recognized points of a closedloop. This way inherent cumulative odometry errors can be corrected to an order ofmagnitude of RFID-based loop closure detections. The loop closure model is eitherlearned beforehand or on the data of the target environment itself. The latter case isbeneficial, since only few parameters have to be pre-specified, and trajectory estimationadapts itself to the currently chosen RFID setup. We finally analyze the accuracy ofthe approaches and demonstrate how it can even be improved by combination with laserrange data on mobile platforms which feature both RFID readers and laser range finders.
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Kurzfassung
Die vorliegende Dissertation beschäftigt sich mit dem Einsatz von Radiofrequenziden-tifikation (RFID) im Kontext dreier zentraler Navigationsgrundlagen mobiler Roboter:Kartierung, Selbstlokalisation und Trajektorienschätzung. Hierbei handelt es sich umFelder mit reger Forschungsaktivität in den letzten Jahren. Die drei Themen werden unterAnwendung passiver RFID-Technologie mit langen Reichweiten beleuchtet. Ihr wirdkünftig große Bedeutung bei der Automatisierung von Identifikationsprozessen in In-dustrie und Handel beigemessen. Diese Arbeit leistet mehrere Beiträge zu den drei Auf-gabenstellungen. Eine wesentliche Leitlinie ist, dass kosteneffizient allein die gegebeneRFID-Infrastruktur sowie handelsübliche RFID-Hardware verwendet werden kann.
Die Kartierung passiver Transponder besitzt als ein wesentliches Anwendungsfeld,Roboter zur kontinuierlichen Bestandsaufnahme in Gebäuden mit RFID-gekennzeich-neten Gütern einzusetzen. Im Vergleich zur klassischen Inventur soll nicht nur auf Vor-handensein geprüft, sondern auch eine Ortsbestimmung erkannter Objekte vorgenom-men werden, z.B. von Waren in einem Supermarkt. Dazu besitzt der Roboter ein RFID-Lesegerät und detektiert fortlaufend Transponder in der durchfahrenen Einsatzumge-bung. Die Lokalisierung der Transponder wird dadurch erschwert, dass standardisierteLesegeräte zunächst nur Detektionshäufigkeiten, nicht jedoch Distanz oder Winkel zumRFID-Tag abschätzen. Ferner unterliegen die Detektionsergebnisse hohen Falsch-Nega-tiv-Raten. Verwandte Arbeiten zeigten bereits, dass es möglich ist, durch wiederholte Er-kennung aus unterschiedlichen Positionen Aufenthaltsorte gekennzeichneter Objekte mitHilfe eines Partikelfilters zu bestimmen. Grundlage hierfür ist ein probabilistisches Sen-sormodell, welches Orten relativ zum RFID-Lesefeld Detektionswahrscheinlichkeitenzuordnet.
Im Rahmen dieser Dissertation wurde ein Verfahren zur schnellen, semiautomatischenErzeugung eines Modells aus Trainingsdaten unter Verwendung nichtparametrischer Re-gression entwickelt. Ein solches Modell verbessert auch Kartierungsergebnisse, wennder Partikelfilter durch Ziehen wahrscheinlicher Positionshypothesen initialisiert wird,wie in dieser Arbeit untersucht wird. Ferner wird eine iterative Erweiterung der Parti-kelfilter-Kartierung vorgestellt, die die Effizienz des Verfahrens verbessert. Eine größereGenauigkeit der Positionsschätzung wird hingegen durch ein Fusionsverfahren mit räum-lichem Vorwissen in Form hochauflösender volumetrischer Umgebungskarten erzielt.
Umgekehrt befähigt die Kenntnis kartierter stationärer RFID-Tags einen Roboter, sei-
ne eigene Position zu bestimmen. Es werden drei Verfahren verglichen, die auf Monte-
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Carlo-Lokalisation aufbauen: ein modellbasiertes Verfahren sowie zwei Methoden, dieauf so genanntem Fingerprinting beruhen. Fingerprinting leitet Ortsschätzungen direktaus dem Vergleich mit Messungen ab, die in einer vorherigen Kalibrierungsphase an Re-ferenzpositionen aufgenommen wurden. In dieser Doktorarbeit wird eine Erweiterungdes RFID-Snapshot-Ansatzes, welcher Positionswahrscheinlichkeiten auf Basis von De-tektionsraten im Weltkoordinatensystem bestimmt, für dicht getaggte Umgebungen vor-genommen. Ferner wird eine neue Fingerprintingtechnik vorgestellt, die Wahrschein-lichkeiten für RFID-Messungen auf Grundlage klassischer Vektorähnlichkeitsmaße be-rechnet. Für die drei Lokalisierungsvarianten werden Möglichkeiten zur geeigneten Ini-tialisierung des Partikelfilters aufgezeigt, um eine möglichst akkurate Anfangsschätzungder Roboterposition vorzunehmen. Im Rahmen umfangreicher Experimente mit realenRobotern werden die Verfahren verglichen und auf den Einfluss wesentlicher Parameteruntersucht. Dazu gehört auch die Erprobung, welche Auswirkungen auf die Position-ierungsgenauigkeit Bewegungen und Verdeckungen von Transpondern in veränderlichenUmgebungen haben.
Der Selbstlokalisation geht üblicherweise eine Kartierungsphase voraus. Diese be-darf entweder zeitintensiver Messungen mit Unterstützung eines Menschen, oder aber eswird ein weiteres Lokalisierungssystem vorausgesetzt, das für den Roboter erforderlichist, um eine RFID-Kartierung autonom durchzuführen. Aus diesem Grund beschäftigtsich die Doktorarbeit schließlich mit der Schätzung von gefahrenen Robotertrajektorien
in zuvor unbekannten Umgebungen, welche eine vorherige Trainingsphase überflüssigmacht. Das Thema ist eine Variante des simultaneous localization and mapping (SLAM),eines in den vergangenen Jahren dominierenden Forschungsthemas in der Robotik. AufBasis des nur aus Odometrie- und RFID-Daten rekonstruierten zurückgelegten Pfadeskann sich der Roboter später lokalisieren oder unter Anwendung eines Sensormodellseine Ortung der erkannten Transponder vornehmen.
Das erste entwickelte Verfahren beruht wiederum auf einem Partikelfilter. Zur Gewich-tung der Positionshypothesen wird ein Modell der ortsabhängigen Ähnlichkeit von RFID-Messungen gelernt. Demgegenüber wird in einem zweiten Ansatz die Trajektorien-schätzung als Optimierungsproblem eines Graphen formuliert. Kanten in diesem Gra-phen verbinden Roboterpositionen und entsprechen Odometriemessungen sowie wieder-erkannten korrespondierenden Enden einer befahrenen Schleife. Die inhärente, kumu-lative Ungenauigkeit der Wegstreckenmessung kann so auf einen mittleren Fehler inder Größenordnung der RFID-basierten Ortswiedererkennung beschränkt werden. DasSchleifenerkennungsmodell erlernt der Roboter auf den Daten in der Anwendungsumge-bung selbst: Hierdurch müssen nur wenige Parameter spezifiziert werden, und die Tra-jektorienschätzung selbst ist adaptiv zum aktuell gültigen RFID-Setup. Es wird die Ge-nauigkeit der Schleifenerkennung mittels RFID analysiert und schließlich unter Zuhilfe-nahme von Lasermessungen für mobile Plattformen mit RFID-Lesegeräten und Laser-scannern weiter verbessert.
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Acknowledgments
For making the thesis at hand possible and for his valuable advice I would like to thankProf. Dr. Andreas Zell cordially. I do not take for granted to write a dissertation in apleasing working environment with excellent technical equipment and a variety of dif-ferent inspiring fields of research. Furthermore, I would like to thank Prof. Dr. AndreasSchilling and Prof. Dr. Horst-Michael Groß for their valuable comments and for theirefforts in assessing the dissertation.
Vita Serbakova and Klaus Beyreuther played a major role in taking the load off us inday-to-day work. Thank you for that and for your personable way.
Sincere thanks go to all colleagues at our chair, for interesting scientific discussionsand for four wonderful years in Tübingen. I also enjoyed the cooperation with my col-leagues from AmbiSense. Several former master’s students, diploma students, and stu-dent assistents have contributed in different respects. I am thankful to them for scientificdiscussions during their theses and for enhancing the skills of our robots. Moreover, Iam grateful to Michael Becher, Marius Hofmeister, André Homeyer, Martin Meißner,Thomas Niehörster, and Sebastian Scherer for their helpful comments and proofreadingparts of this thesis.
Finally, I would like to thank Ulla, my friends, and my entire family for being thereand for being who they are; in particular, my parents, also because they taught me to becurious.
The author gratefully acknowledges the funding by the Baden-Württemberg Stiftung.The foundation has financed the research cooperation AmbiSense in the scope of theresearch program BW-FIT.
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Contents
Notation xv
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Experimental Platforms . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Methods 7
2.1 Regression Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.1 Binning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.2 Kernels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1.3 k-Nearest Neighbors . . . . . . . . . . . . . . . . . . . . . . . 92.1.4 Parameter Selection . . . . . . . . . . . . . . . . . . . . . . . 102.1.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 State Estimation with Particle Filters . . . . . . . . . . . . . . . . . . . 122.2.1 Bayes Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.2 Particle Filters . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.3 Resampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Graph Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.3.1 Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.3.2 Iterative Least-Squares Solution . . . . . . . . . . . . . . . . . 192.3.3 Stochastic Gradient Descent . . . . . . . . . . . . . . . . . . . 192.3.4 Spring-Mass Models and Relaxation Techniques . . . . . . . . 20
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Long-Range Passive RFID 21
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2 Technical Background . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.1 RFID Systems in General . . . . . . . . . . . . . . . . . . . . 223.2.2 Long-Range Passive RFID . . . . . . . . . . . . . . . . . . . . 233.2.3 Long-Range Readers . . . . . . . . . . . . . . . . . . . . . . . 253.2.4 Long-Range Passive Transponders . . . . . . . . . . . . . . . . 27
3.3 Elementary Experiments . . . . . . . . . . . . . . . . . . . . . . . . . 27
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CONTENTS
3.3.1 Detection Range . . . . . . . . . . . . . . . . . . . . . . . . . 283.3.2 Time Series of Inquiries . . . . . . . . . . . . . . . . . . . . . 293.3.3 Duration of Interrogations . . . . . . . . . . . . . . . . . . . . 32
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4 Modeling the Robot 35
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2 Modeling Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2.1 Representations . . . . . . . . . . . . . . . . . . . . . . . . . . 364.2.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3 Modeling RFID Detections . . . . . . . . . . . . . . . . . . . . . . . . 394.3.1 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.3.2 Semi-autonomous Learning Approach . . . . . . . . . . . . . . 434.3.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5 Mapping 53
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.1 Proximity-based Tag Localization Using Static Antennas . . . . 545.2.2 Finer-grained Tag Localization Using Several Static Antennas . 555.2.3 Mapping Using Mobile Antennas on Robots . . . . . . . . . . 565.2.4 Fusion and Other Approaches . . . . . . . . . . . . . . . . . . 57
5.3 Probabilistic Mapping Using Particle Filters . . . . . . . . . . . . . . . 585.3.1 Probabilistic Tag Location Estimation . . . . . . . . . . . . . . 585.3.2 Filter Initialization . . . . . . . . . . . . . . . . . . . . . . . . 605.3.3 Utilization of Negative Information . . . . . . . . . . . . . . . 605.3.4 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.4 Efficient Iterative Estimation . . . . . . . . . . . . . . . . . . . . . . . 695.4.1 Overview of the Iterative Framework . . . . . . . . . . . . . . 705.4.2 Resampling and Perturbation Approaches . . . . . . . . . . . . 715.4.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.5 Fusion with Spatial Information . . . . . . . . . . . . . . . . . . . . . 735.5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.5.2 Spatial Reconstruction and Representation . . . . . . . . . . . 745.5.3 Fusion by Sampling from Volumetric Maps . . . . . . . . . . . 745.5.4 Fusion by Subsequent Integration of Volumetric Information . . 755.5.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6 Localization 83
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
xii
CONTENTS
6.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 856.2.1 Model-based Localization Using RFID . . . . . . . . . . . . . 866.2.2 Location Fingerprinting Using Visual Appearance . . . . . . . 886.2.3 Radio Location Fingerprinting . . . . . . . . . . . . . . . . . . 89
6.3 RFID-based Localization Using Particle Filters . . . . . . . . . . . . . 906.4 Model-based Localization . . . . . . . . . . . . . . . . . . . . . . . . 92
6.4.1 Modeling Observations . . . . . . . . . . . . . . . . . . . . . . 926.4.2 Global Localization . . . . . . . . . . . . . . . . . . . . . . . . 936.4.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.5 Location Fingerprinting Using RFID Snapshots . . . . . . . . . . . . . 976.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 976.5.2 Modeling Observations . . . . . . . . . . . . . . . . . . . . . . 986.5.3 Adaptations to Densely Tagged Environments . . . . . . . . . . 1006.5.4 Global Localization . . . . . . . . . . . . . . . . . . . . . . . . 1026.5.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.6 Location Fingerprinting Using Vector Similarity Measures . . . . . . . 1056.6.1 Weighted k-Nearest Neighbors (WKNN) Fingerprinting . . . . 1056.6.2 Vector Similarity Measures for Long-Range Passive RFID . . . 1076.6.3 Filtered WKNN Fingerprinting . . . . . . . . . . . . . . . . . . 1096.6.4 Global Localization . . . . . . . . . . . . . . . . . . . . . . . . 1106.6.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.7 Experimental Comparison . . . . . . . . . . . . . . . . . . . . . . . . 1166.7.1 Tracking Accuracy . . . . . . . . . . . . . . . . . . . . . . . . 1166.7.2 Influence of Tag Density . . . . . . . . . . . . . . . . . . . . . 1176.7.3 Global Localization . . . . . . . . . . . . . . . . . . . . . . . . 1176.7.4 Robustness in Crowded and Dynamic Environments . . . . . . 1196.7.5 Comparison of Run Times . . . . . . . . . . . . . . . . . . . . 120
6.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7 Trajectory Estimation 123
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1237.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.2.1 SLAM, Trajectory Estimation, and Loop Closure in General . . 1257.2.2 RFID-based SLAM, Trajectory Estimation, and Loop Closure . 126
7.3 Trajectory Estimation Using Particle Filters . . . . . . . . . . . . . . . 1277.3.1 General Approach of Rao-Blackwellized Particle Filters . . . . 1277.3.2 Observation Modeling and Loop Closure . . . . . . . . . . . . 1287.3.3 Trajectory Estimation in the Recall Phase . . . . . . . . . . . . 1307.3.4 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.4 Trajectory Estimation Using Pose Graph Optimization . . . . . . . . . 1347.4.1 General Graph-based SLAM Approach . . . . . . . . . . . . . 1347.4.2 Observation Modeling and Loop Closure . . . . . . . . . . . . 134
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CONTENTS
7.4.3 Trajectory Estimation in the Recall Phase . . . . . . . . . . . . 1357.4.4 Automatic Interleaved Model Learning . . . . . . . . . . . . . 1367.4.5 Fusion with Laser Range Data . . . . . . . . . . . . . . . . . . 1407.4.6 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
8 Conclusion 155
8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1558.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1578.3 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
A Experimental Setup, Environments, and Data Sets 161
A.1 Robotics Laboratory and Corridor . . . . . . . . . . . . . . . . . . . . 163A.2 Corridor and Computer Museum . . . . . . . . . . . . . . . . . . . . . 164A.3 Lecture Halls and Adjacent Rooms . . . . . . . . . . . . . . . . . . . . 166A.4 Sand 1 Wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
B Measures of Similarity and Dissimilarity 171
B.1 Measures of Similarity . . . . . . . . . . . . . . . . . . . . . . . . . . 171B.2 Measures of Dissimilarity . . . . . . . . . . . . . . . . . . . . . . . . . 173B.3 Benchmark Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
C Exemplary 3D Sensor Model 175
List of Figures 177
List of Tables 179
Bibliography 181
xiv
Notation
Throughout this thesis, bold-face fonts are used for vectors (e.g., x) as well as matrices(e.g., A). Time indices are denoted by subscripts, e.g., xt for some position x at time t.Whenever additional indices are required, they may appear as superscripts in brackets,e.g., x
(i)t for the position of the ith particle at time t. Table 0.1 lists commonly used
symbols.We denote 2D positions by a tuple (x, y) of Cartesian coordinates. A pose (x, y, θ)
TABLE 0.1: Symbols for constants, variables, sets, distributions, and operators
Symbol Explanation
A Number of RFID antennas on board the robotC Number of measurement cycles in snapshot-based localizationL Number of RFID labels in the environment
t Current time index (continuous or discrete)T Index of the final point in time (end of an entire history of time steps)Lt Number of RFID tags detected in the t-th inquirya Pose of an RFID antenna (on board the robot)lj Position of RFID tag j, 1 ≤ j ≤ Lm Environment map (e.g., vector of landmark positions)x State vector/input. In localization context: pose x = (x, y, θ) of the robotz Observation in general (for RFID measurements see symbol f )
q(x) Detection rate at some position x
f RFID measurement, e.g., ft = (f(1)t , . . . , f
(A)t ), with f
(a)t = (f
(a)t,1 , . . . , f
(a)t,L ),
a = 1, . . . , A, a vector of tag countsF RFID fingerprint with pose, e.g., Ft = (ft,xt, d
Σt , rΣ
t )
R The set of real numbersN The set of natural numbers: N = 0, 1, 2, . . .N Normal distribution N (µ, σ2) with mean µ and variance σ2
U Uniform distribution U(a, b) over the interval [a, b]E[X] Expected value of a distribution X
x ∝ y Proportionality: x = αy for α ∈ R
x ∼ X Distributions: x is a sample of X
xv
NOTATION
TABLE 0.2: Abbreviations used throughout the thesis
Abbreviation Description
EIRP Equivalent isotropic radiation powerEKF Extended Kalman filterEM ElectromagneticEPE Expected squared prediction errorERP Effective radiated powerESS Effective sample sizeHF High frequencyk-NN k-nearest neighborsMCL Monte Carlo localizationPF Particle filterRF Radio frequencyRFID Radio-frequency identificationRSS Received signal strengthSIR Sampling importance resamplingUHF Ultra-high frequencyWKNN Weighted k-nearest neighborsWLAN Wireless local area network
additionally comprises an orientation θ in the xy plane. The operators ⊕ and ⊖ representthe common rigid-body transformations, which transform poses into each other whilerespecting orientations: For two poses x1 = (x1, y1, θ1) and x2 = (x2, y2, θ2), we define:
x1 ⊕ x2 =
cos(θ1) − sin(θ1) 0sin(θ1) cos(θ1) 0
0 0 1
x2
y2
θ2
+
x1
y1
θ1
x2 ⊖ x1 =
cos(θ1) sin(θ1) 0− sin(θ1) cos(θ1) 0
0 0 1
x2 − x1
y2 − y1
θ2 − θ1
Throughout the thesis, we tried to avoid abbreviations. In some places, however, weemployed common abbreviations, which are listed in Table 0.2.
xvi
Chapter 1
Introduction
1.1 Motivation
Over the last decade, radio-frequency identification (RFID) has matured as a technologyfor the identification of objects via radio waves. Particularly passive long-range RFIDhas attracted economic interest: It allows for the contactless detection of several inex-pensively labeled objects within fractions of a second. More and more identification pro-cesses in industry will be automated, such as recording incoming goods or asset tracking.In areas such as fashion or intralogistics, item-level tagging at larger scale is expectedfor the near future [5] or already practiced. This evolution will create environments withrichly tagged RFID infrastructure.
Such surroundings offer themselves for the navigation of autonomous mobile plat-forms [215]. Robots with on-board RFID readers can assist humans or help to furtherautomate inventory: The classical inventory process can be augmented by item-specificlocation information, while stocks can be taken at a higher frequency than before. Mis-placed assets can be found, which is an interesting application in dynamic warehouses,storehouses, and production sites. Humans can be guided to or be informed about desiredpositions by mobile robots in real time. At the same time, mobile robots could performother tasks by means of other on-board sensor equipment, e.g., survey the building andtransport objects. Recent scientific articles document that service robots are advancingpopulated retail environments and have assisted as guides in, for instance, home im-provement stores [92], supermarkets [80], and shopping malls [123].
From the perspective of robotics, passive long-range RFID is both a fascinating anda challenging sensor technology: On the one hand, RFID tags can serve as uniquelyidentifiable landmarks for navigation: RFID trivially solves the data association problem,i.e., the matching of sensor readings with previously observed environment features. Thisprovides high confidence about the identity of objects and locations. Moreover, dozensof transponders can be observed simultaneously without line of sight and within a radiusof several meters. On the other hand, standardized passive RFID readers only report thepresence of transponders. Neither distance nor bearing to a tag are revealed. Due tothe electromagnetic characteristics of ultra-high frequency (UHF) radio waves, detectionattempts fail frequently, even if a transponder is in theoretical read range. The arising
1
CHAPTER 1 INTRODUCTION
FIGURE 1.1: Target scenarios: Mobile robots with RFID readers assist humans in inven-
tory tasks, surveillance in logistics scenarios, or serve as shopping guides. Detected tags
– and thus also the labeled objects – can be localized. Vice versa, the dense population
of transponders provides unique landmarks for the navigation of the robot.
question is whether all these properties permit RFID to serve as an alternative or as anaddition to traditional sensors such as laser range finders.
In this thesis, we investigate RFID as a sensor technology for three elementary nav-igation capabilities of mobile service robots: mapping, self-localization, and trajectoryestimation. Our setup builds on a mobile RFID reader on board a robot and inexpensivetransponders in the environment. This way, the most expensive hardware component (thereader) is required only once. It can be delivered to any position where tags are to beread, as sketched in Figure 1.1.
For robot self-localization, we utilize the possibility to uniquely identify places bymeans of distributed transponders. Knowing its position is essential for a robot in orderto perform meaningful context-dependent tasks and to plan paths to desired target places.We evaluate different metric localization solutions which can seamlessly be integratedin metric path planning frameworks. The challenge of the large position uncertaintyof a single tag detection, without further position information, needs to be mastered.Moreover, virtually unpredictable radio propagation behavior requires to be modeled.We aim at a positioning accuracy which is clearly better than RFID read range. For thispurpose, we will also take a look at related research on mobile communication devicesand at appearance-based approaches in robotics.
Based on knowledge about its own position, the robot can further enter the locationsof tagged objects into a map. This mapping process represents robotic inventory. Deter-mining the position of a labelled object is demanding as it can only be inferred from aseries of detections and nondetections. In addition, a potentially large number of tagged
2
1.2 CONTRIBUTIONS
goods need to be located, which raises questions of efficiency. Although commerciallyhighly relevant, there has been much less research into robotic mapping using long-rangeRFID than into localization.
Third, we examine the utilization of RFID for simultaneous localization and mapping(SLAM), which has been an important research field in mobile robotics in the last years.The task is to map the environment and concurrently localize the robot without priorknowledge of the building. We reduce this problem to estimating only the trajectory ofthe robot, as often done in recent general SLAM approaches, which can be followed bya classical mapping stage. To our knowledge, SLAM based on long-range passive RFIDhas not been addressed before.
In this thesis, we present robust probabilistic algorithms for the three named buildingblocks. Our solutions exploit the high-fidelity data association and long read range ofUHF RFID while coping with the inherent uncertainty of RFID measurements. The de-veloped solutions cost-efficiently utilize a given, arbitrarily arranged RFID infrastructuresuch as in future supermarkets or storehouses. This means in particular that no furtherpreparation of the environment is required if it already contains RFID tags, e.g., on prod-ucts in shelves. If tags are artificially added as static landmarks, only the positions of fewof them need to be measured manually in order to derive a sensor model. Throughout thethesis, we foster the fingerprinting paradigm to solve variants of place recognition prob-lems such as self-localization and SLAM. Fingerprinting deduces relations in locationspace to correlations in observation space. It often outperforms positioning approachesbased on models of radio propagation, which is difficult to predict.
1.2 Contributions
This thesis features several contributions in the field of RFID-based robot navigation. Wepresent novel solutions as well as improvements and comparisons to existing approachesalong the chain from RFID modeling over mapping and localization to, finally, trajectoryestimation. In particular, the following contributions are given:
• We have developed a semi-automatic approach to learning probabilistic RFID sen-sor models with mobile robots. The main user intervention consists of providing asmall number of reference tag positions. We compare different nonparametric re-gression techniques which are then applied to automatically deduce a model. Newmodels featuring realistic detection characteristics can be (re-)trained quickly.
• We introduce two sampling techniques which both increase the efficiency and theaccuracy of RFID-based mapping: a filter initialization approach which samplesfrom the sensor model and a multi-pass, iterative estimation scheme.
• Targeted at RFID-based mapping, too, we have developed a method for fusingRFID data and spatial knowledge to improve tag position estimates. Volumetricmaps serve as prior information and bootstrap the mapping stage.
3
CHAPTER 1 INTRODUCTION
• We compare different paradigms of localizing a mobile robot using UHF RFID. Wealso present a performance comparison under dynamic environment conditions.This aspect has often been shielded in research into RFID-based positioning sofar.
• Among these paradigms, we elaborate a novel fingerprinting technique based onvector similarity measures. It is efficient and fairly easy to implement.
• We propose and compare different methods for generating initial belief over therobot’s pose during global localization. Global localization (i.e., localization with-out prior location belief) is of particular interest since RFID permits to substan-tially narrow down the search space of candidate robot locations. This propertymakes RFID outstanding in comparison with other types of robotic sensors.
• Novel trajectory estimation approaches are treated in Chapter 7. We have devel-oped a particle filter- and a graph-based technique, both of which are tailored toonly RFID and odometry. For the graph-based approach, we present an automaticcalibration mechanism which learns the observation model on the fly.
• We additionally show how laser range data can be integrated into the trajectoryestimation process to further improve the consistency of the estimated path of therobot. In contrast to laser-based SLAM, global consistency of the robot’s path isachieved by fine-grained loop closure using RFID, while laser scan matching isapplied only sparsely.
All aspects have been examined by thorough experiments and evaluation of failurecases. Various experiments were conducted in different environments and with two dif-ferent types of real robots and RFID hardware. The developed software is ready foroperation on these platforms and was written with a focus on modularity and extensibil-ity. Some of the results have been published earlier in scientific articles, which will benamed in the beginning of the concerned sections.
1.3 Outline
The remainder of this thesis is organized as follows:
• In Chapter 2 we depict the algorithms and probabilistic frameworks which arerequired to perform various types of estimation.
• The technical background of long-range passive RFID systems is explained inChapter 3. This background knowledge is important for modeling the sensorcharacteristics that are utilized for navigation tasks throughout the thesis.
4
1.4 EXPERIMENTAL PLATFORMS
• In Chapter 4 we model both RFID detections and odometry. This is done in aprobabilistic fashion, in order to account for inherent measurement noise.
• Chapter 5 treats mapping, which means that the positions of RFID tags are es-timated in a global frame of reference. A learned RFID sensor model is used tolearn maps of transponder positions from series of observations if the position ofthe robot is known.
• The dual task, self-localization, is described in Chapter 6. There, the unknownpose of the robot is inferred from a sequence of RFID measurements and priorknowledge about the places of transponders.
• In order to eliminate the prior mapping stage, the robot must be able to estimate itstrajectory without given map. Two solutions to this issue are provided in Chap-
ter 7. While they rely only on RFID and odometry, we additionally demonstratehow to integrate laser scan matching for the sake of increased accuracy.
• We summarize and discuss the results of the thesis in Chapter 8, where we alsoshow directions of future research.
Three appendices give further background information: Appendix A contains detailsabout experimental environments, setups, and the data on which the proposed techniqueshave been investigated. Vector similarity measures, which play a major role in our ap-proaches to location fingerprinting and trajectory estimation, are described in more detailin Appendix B. An exemplary supplemental 3D RFID sensor model is depicted in Ap-
pendix C, finally.In the final section of this chapter we briefly describe main hardware characteristics of
the employed robots for the understanding of subsequent chapters.
1.4 Experimental Platforms
We employed two different mobile robots with similar sensor equipment: a MetraLabsSCITOS G5 and an RWI B21, which are shown in Figure 1.2. The robots feature thefollowing hardware:
• On-board computer: Both robots possess mobile PCs with Linux operating sys-tem and at least a 2 GHz CPU.
• RFID hardware: The two robots feature off-the-shelf UHF RFID readers whichcomply to the EPC Class 1 Generation 2 standard [116, 118]. The B21 possessesan Alien Technology ALR-8780 reader (866 MHz) with four circularly polarizedantennas (type ALR-8610-AC). It transmits at 15-33 dBm (12 mW-2 W), where thepower levels are adjustable by software. The reader device is bistatic, which means
5
CHAPTER 1 INTRODUCTION
FIGURE 1.2: The mobile robots used for experiments: SCITOS G5 (left) and B21 (right)
that antennas act in pairs: One antenna transmits while the second one of a pair islistening.
A monostatic Elatec SR-113 RFID reader is mounted on the SCITOS G5. Twocircularly polarized UHF RFID antennas are connected to the reader. The trans-mission power can be configured between 15 and 30 dBm (12 mW-1 W) ERP.
• Laser range finder: On board each robot, a laser range finder provides distancemeasurements with a resolution of few millimeters (B21: SICK LD-OEM1000,SCITOS G5: SICK S300). The angular resolution is 1° over a field of view of atleast 180°.
• Motion unit: The B21 features a four-wheeled synchronous drive. In opposition,the SCITOS G5 possesses a differential drive. Both motion units supply odometry
(measurements of distance traveled) at a resolution of 1 cm or better.
Both robots additionally possess cameras, sonar sensors for ranging, and tactile sen-sors for collision detection. They were not used in our experiments. IEEE 802.11 a/b/gWLAN devices were used to interchange control commands and sensor data.
For controlling the robots we employed the Carnegie Mellon Robot Navigation Toolkit(CARMEN, version 0.6.5 beta) [1, 174]. All software required for the experiments in thisthesis was developed as additional C/C++ modules to the CARMEN framework.
6
Chapter 2
Methods
The goal of this chapter is to introduce estimation techniques and associated notationused throughout the thesis. We focus on three aspects: First, in Section 2.1, we treatregression methods which learn functions from training data. Second, in Section 2.2, wepresent particle filters, which infer state variables over time series of data. In Section 2.3we describe techniques for optimizing a graph of pairwise constraints.
2.1 Regression Methods
For several tasks in this thesis, we need to learn and predict quantitative target values yfrom vectors of input values x. This is the goal of regression. More specifically, the aimis to predict the value of y = f(x) for a new input (also called feature) x, given a setof training data (x1, y1), (x2, y2), . . . , (xN , yN) with observations xi and correspond-ing target values yi (also called responses). The functional form f(x) of the processgenerating the yi may be unknown or complex, or we do not want to restrict algorithmsto specific functional models. Additionally, training data are typically subject to noise.That is why we focus on nonparametric regression (also called smoothing) techniques,i.e., methods which are not based on a prototype function to be fitted. They are instancesof supervised learning as the target values yi stem from training stages.
To justify the presented methods, we assume the probabilistic point of view of statis-tical decision theory as in [98]. Let X ∈ R
d be a d-dimensional random input, Y ∈ R
be a response, and p(X,Y ) be their joint distribution. A function f(X) is to be approx-imated which predicts Y , given input values of X . If the squared error loss functionL(Y, f(X)) = (Y − f(X))2 is used for penalizing prediction errors, f can be found byminimizing the expected squared prediction error (EPE):
EPE(f) = E[Y − f(x)]2 =
∫
(y − f(x))2 p(dx, dy) (2.1)
The optimal solution is the conditional expectation [98, p. 18]:
f(x) = E[Y |X = x] (2.2)
7
CHAPTER 2 METHODS
-6
-5
-4
-3
-2
-1
0
1
2
3
-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5
y
x
Target functionNoisy training samples
Binningk-nearest neighbors
Gaussian kernel
FIGURE 2.1: Regression example: The function f(x) = (x − 1) sin(x2) + 0.5x is to be
approximated. Noisy observations y′(x) = y(x) + ǫ were generated with ǫ ∼ N (0, 1).The chosen parameters of all methods minimized the RMSE in 10-fold cross-validation.
So, with respect to the average squared error, the best prediction of Y at a point X = x isthe conditional mean. It is this expression that the nonparametric regression techniquesbelow aim to approximate. All methods approximate the expectation in (2.2) by aver-aging over training data, while the conditioning in (2.2) is relaxed to conditioning ondifferent notions of closeness to query points x. This perspective implicitly assumes fto be locally constant. This restriction, however, does not affect the estimation qualityif the function to be approximated only gradually changes or if the number of trainingsamples close to any point X = x is large. Finally, (2.2) also holds in case of a two-classproblem with binary-coded Y and squared error loss [98, p. 22]. This fact will be usefulfor sensor model regression with binary responses in Section 4.3.
2.1.1 Binning
Binning is a simple form of smoothing and often used for data preprocessing: The do-main is partitioned into bins, and all target values of samples falling into a specific binare replaced by their mean. Formally, the target function (2.2) is approximated by
f(x) =1
c(B(x))
∑
xi∈B(x)
yi (2.3)
where c(B) = | i |xi ∈ B | counts the number of samples in bin B. Hence, the con-ditioning in (2.2) is relaxed to a region which is defined by a bin. A natural choice ofdomain partition is a regular grid. The (usually constant) size h of a grid cell along eachdimension is the parameter which steers the degree of smoothing.
Binning has the advantage that it is computationally efficient, because assignments tobins are straightforward. The estimated target value of each bin depends only on a num-ber of training samples each of which contributes to exactly one bin. Moreover, space
8
2.1 REGRESSION METHODS
requirements are also beneficial for low-dimensional feature spaces, since the originaltraining data can be discarded once the bin values have been computed.
An example of binning is shown in Figure 2.1. The approximation does not deviatemuch if the target function only gradually changes as compared to the bin size (aroundx = 0.5). On the other hand, the function estimate is discontinuous at bin boundaries.
2.1.2 Kernels
In opposition to binning, kernel smoothing is able to achieve smooth approximations ofthe target function f . A weighting function K(x,xi), called kernel, weights the samplelocations xi based on their distances from a query point x: Training data located closeto x contribute more to the estimate f(x) than samples at greater distances. Kernelregression belongs to the class of memory-based methods: The function is approximatedat evaluation time based on memorized training data. Equation (2.2) is estimated by
f(x) =
∑Ni=1 Kh(x,xi)yi
∑Ni=1 Kh(x,xi)
(2.4)
for a training set with N samples. This is known as the Nadaraya-Watson model (cf. [21,p. 202], [98, p. 193]). Kh is the kernel function (i.e., a symmetric, positive semidefinitefunction). The bandwidth parameter h defines the degree of smoothing. With regardto (2.2), here the conditioning is relaxed to a weighted neighborhood of x.
Kernel functions used in this thesis are illustrated in Figure 2.2. Let u := ||x − xi||be the distance between x and some xi, and Kh(u) = K(u
h). Let further 1D(x) be the
indicator function, which equals one for x ∈ D and which is zero elsewhere. Then,for example, the triangle kernel is defined by K(u) = (1 − |u|)1(|u|≤1), the quartic
kernel (or biweight kernel) by K(u) = 1516
(1 − u2)21(|u|≤1) and the uniform kernel byK(u) = 1
21(|u|≤1). These three kernels are compact in that the support (the subset of
the domain with K(u) > 0) is a fixed interval. The quartic kernel distinguishes by itsdifferentiable support boundaries. Another popular choice is the Gaussian kernel:
K(u) =1√2π
exp(−1
2u2) (2.5)
It has infinite support and is continuously differentiable. The example in Figure 2.1 usinga Gaussian kernel shows that the resulting regression function is continuous and smooth.The actual function is nicely approximated in regions with moderate noise.
2.1.3 k-Nearest Neighbors
Kernel smoothing fixes the support region, and the number of training samples fallinginto different regions varies. The dual approach is k-nearest neighbors (k-NN) smooth-ing, which averages over a fixed number of training samples closest to a query input x
9
CHAPTER 2 METHODS
FIGURE 2.2: Examples of one-
dimensional kernel functions
0
0.2
0.4
0.6
0.8
1
-3 -2 -1 0 1 2 3
y
x
Gaussian kernelQuartic kernel
Triangle kernelUniform kernel
while the actual distances to x vary. Formally, the k-nearest neighbor estimate for f is
f(x) =1
k
∑
xi∈Nk(x)
yi ,
where Nk(x) is the neighborhood of the k points xi closest to x in the training set.Closeness is defined by a metric, which is often the Euclidean distance. With regardto (2.2), the conditioning is relaxed to a k-neighborhood of x. Like kernel smoothing,k-NN is memory-based. An example of k-NN smoothing is visualized in Figure 2.1.The plot is close to the kernel-based estimate, despite discontinuities. Unlike binning,the discontinuities depend on the density of training samples, not the bin resolution.Actually, it can be shown that generally for N, k → ∞ such that k/N → 0, f(x) →E[Y |X = x], assuming mild regularity conditions on the joint distribution p(X,Y ) [98].
2.1.4 Parameter Selection
Each of the presented techniques depends on a smoothing parameter. If the dimension ofthe input vectors is larger than one, there are additional bandwidth parameters for scalingin each dimension. The question is how to adjust these values optimally. Generally, acriterion is to minimize the expected prediction error (or generalization error) at a querypoint x0. Let us assume that the training data were generated according to a noisy processY = f(X) + ε with E[ε] = 0 and Var[ε] = σ2. Hasties et al. [98, p. 223] providethe following common decomposition of the error of the regression estimate f(X) atX = x0:
EPE(x0) = E[(Y − f(x0))2 |X = x0] (2.6)
= σ2 +(
E[f(x0)] − f(x0))2
+ E[f(x0) − E[f(x0)]]2 (2.7)
= σ2 + Bias2(x0) + Var[x0] (2.8)
= Irreducible error + Bias2 + Variance (2.9)
The irreducible error, σ2, is the variance of the target around the true mean f(x0). It de-pends only on the noise of measurements, not the regression quality. Bias and variance,
10
2.1 REGRESSION METHODS
however, can be influenced: The bias is the difference between the true mean and theestimated average, and the variance represents the expected squared deviation of f(x0)around its mean. In general, a low degree of smoothing will reduce the bias, but comesat the expense of increased variance. The typical curvature of test errors rises to thedirections of lowest and highest degrees of smoothing, with a minimum in between.
To find this minimum and obtain a (nearly unbiased) estimate of the approximationquality, cross-validation (CV) can be applied. It estimates the expected out-of-sampleerror Err = E[L(Y, f(X))], which is the average generalization error of f being appliedto an independent test sample from the joint distribution of X and Y . One variant – theone of our choice at several places of this thesis – is n-fold cross-validation, in whichthe training data are randomly split into n parts of equal sizes. On each of these folds,the prediction quality is tested using the training samples of the remaining n − 1 parts.Let the function m(i) ∈ 1, 2, . . . , n be the number of the fold to which sample i hasbeen assigned. Further, fj denote the function approximation for the case that fold jis used for validation and all folds except j have been used for training. The resultingcross-validation estimate of the prediction error for a loss function L then is:
CV (f) =1
N
N∑
i=1
L(yi, fm(i)(xi)) (2.10)
Typical choices are n = 5, n = 10, or n = N (the latter known as leave-one-out
CV). The parameter which minimizes the CV error will be selected, finally followed bytraining the model on the entire training set using the optimized parameter. For furtherdetails about cross-validation, we would like to refer the reader to [98, ch. 7].
2.1.5 Discussion
The presented techniques will shape up as effective tools for regression tasks in laterchapters. Still, there exist manifold extensions which can reveal even better accuracy oncertains tasks. Examples are local linear/polynomial regression or Gaussian processes.They come at the expense of increased computational complexity.
Kernel and k-nearest neighbor smoothing require the entire training set in memory atrun time. This may prevent them from real-time applicability, apart from issues of mem-ory consumption. In fact, we will elaborate a solution to this issue in Section 4.3. Theasymptotic time complexity of a single prediction f(x) is O(N) in the general case. Ifcross-validation is applied, the costs are O(N2). By contrast, binning yields predictionsin O(1) once the bins have been preprocessed, which takes O(N).
The curse of dimensionality commonly denotes the issue that the size of the trainingset would have to grow exponentially in the number of dimensions to reveal the sameapproximation quality as in a single dimension. Vice versa, let us assume that we wantto predict a response in d dimensions from a small fraction of samples. These samplesmay still cover considerable subsets of the entire range along each of the d dimensions.
11
CHAPTER 2 METHODS
Thus, the nonparametric approximations are no longer local. However, in this thesis,problems are rather low-dimensional (mostly d ≤ 3) while the training sets are relativelylarge. The only higher-dimensional example with d = 8 will be a classification task inChapter 7. For more information and solutions in particular, we refer to [21, 98].
2.2 State Estimation with Particle Filters
In the tasks treated in the subsequent chapters, it will be the goal to estimate a particular,not directly measurable, potentially dynamic state of the robot or its environment overtime. The pose of the robot or the positions of RFID transponders are two examplestates. In opposition to the regression problem in Section 2.1, here it is not the goal toapproximate a target value y = f(x) for an input x, but to estimate a state x, given atime series of observations zt which depend on the evolution of x.
First, let us define x0:t = x0, . . . ,xt to be the evolution of state vectors xt overtime up to t to be estimated. Moreover, let z1:t = z1, . . . , zt denote a sequence ofobservations which were made for the respective states and u1:t = u1, . . . ,ut be asequence of control inputs representing knowledge about the transitions between pairsof states. Without loss of generality, we make the common assumptions that time indicest ∈ N are discrete, that z1:t and u1:t start at t = 1, and that sensor and control data arrivein alternating order. We further define the – potentially nonlinear – transition function
xt = f(xt−1,ut,vt) (2.11)
of the state xt−1 and the latest control input ut, where vt is independent and identicallydistributed (i.i.d.) process noise. The measurement function
zt = h(xt,nt) (2.12)
generates observations zt for the current state xt and i.i.d. measurement noise nt. Equa-tions (2.11) and (2.12) define a first-order Markov process: It is assumed that, given theprevious state xt−1, the state xt is conditionally independent of past states xt−k, k > 1,and that observations only depend on the respective states in which they are made. Now,the estimation task is to determine xt from the set of all available data z1:t and u1:t up totime t. A graphical model of this estimation task is given in Figure 2.3.
2.2.1 Bayes Filters
The general concept of a Bayes filter provides the framework to estimate xt recursively.This recursion yields an estimate at each point in time, whenever new data arrive. Con-trary to batch algorithms, the pose of the robot, for instance, can thus be tracked in anon-line fashion. At each time step, the Bayes filter provides a posterior density of thestate to be estimated:
p(xt | z1:t,u1:t) (2.13)
12
2.2 STATE ESTIMATION WITH PARTICLE FILTERS
FIGURE 2.3: Dynamic Bayes net repre-
senting the first-order Markov process:
The xt are the hidden states which, given
the previous state xt−1, are independent
of all other states xt−j, j > 1. Transi-
tions between states depend on control
inputs ut. The zt nodes are observations
made in the corresponding states.
...States
Observations
Control inputs
x0 x1 x2
u1 u2
z1 z2
The distribution p(x0 | z0,u0) := p(x0) of the initial state x0 may be known exactly,or p(x0) may be the uniform distribution over the entire state space in case of lackingprior knowledge. z0 and u0 are empty measurements. Now, one can estimate the stateat time t recursively if the posterior p(xt−1 | z1:t−1,u1:t−1) of the previous time step isgiven. In each iteration, the state is predicted using the system dynamics in (2.11):
p(xt | z1:t−1,u1:t) =
∫
p(xt |ut,xt−1) p(xt−1 | z1:t−1,u1:t−1) dxt−1 (2.14)
The density p(xt |ut,xt−1) corresponds to the transition function (2.11) and is calledtransition model or system model [9]. In the context of robot localization, it is widelyknown as motion model, because the control data u1:t correspond to movements of therobot. After the prediction step, the latest measurement zt is incorporated to correct theestimate. The resulting posterior density is:
p(xt | z1:t,u1:t) =p(zt |xt) p(xt | z1:t−1,u1:t)
p(zt | z1:t−1,u1:t)(2.15)
with
p(zt | z1:t−1,u1:t) =
∫
p(zt |xt)p(xt | z1:t−1,u1:t)dxt (2.16)
The likelihood p(zt |xt) represents the measurement function (2.12). It is called sensor
model, observation model, or measurement model. In Chapters 5 through 7, we willdesign various such models for dealing with RFID measurements.
Equations (2.14) and (2.15) provide the framework for recursively estimating xt byBayesian filtering. The integrals, however, cannot be solved analytically in the generalcase. Thus, there are a number of different Bayes filter types which are suited for spe-cific problem instances. A well-studied instance is the extended Kalman filter (EKF).The EKF builds upon linearized transition and observation models with white Gauss-ian noise. In the linear case, the Kalman filter can be shown to be optimal in that itminimizes the mean squared error (e.g., [41, p. 95f]). In many applications, includ-ing the scenarios investigated in this thesis, transitions (movements) are nonlinear andnoise distributions are not Gaussian. An effective technique under these circumstancesare nonparametric filters. Histogram filters are one possible instance: They discretize
13
CHAPTER 2 METHODS
the entire state space into a finite number of regions and represent the posterior of eachregion by a single probability [237]. Popular examples in robotics are occupancy grid
maps [177], which represent occupied space by a posterior over cells and which can beacquired via laser-based grid mapping. Another variant of histogram filters are particlefilters, as detailed below. They reveal larger flexibility because they can adaptively (andtherefore efficiently) focus on likely subsets of the state space.
2.2.2 Particle Filters
A particle filter [84] is a nonparametric Bayes filter which makes use of Monte Carlosimulation. The posterior density (2.13) at time t is approximated by a set (x(i)
t , w(i)t )Ns
i=1
of Ns samples (or particles). This way, its shape can be, for instance, non-Gaussian andpotentially multimodal. Each particle (x
(i)t , w
(i)t ) comprises a state hypothesis x
(i)t and
an associated importance weight w(i)t . With all weights normalized, i.e.,
∑Ns
i=1 w(i)t = 1,
the posterior density can be approximated as:
p(xt | z1:t,u1:t) ≈Ns∑
i=1
w(i)t δ(xt − x
(i)t ) (2.17)
δ denotes the Dirac delta function1. It can be shown that for Ns → ∞ the approximationconverges to the true posterior, that is, to the optimal Bayes estimate (cf. [9]).
Now, the choice of weights relies on importance sampling, which is applicable if itis difficult to sample from the density p(xt | z1:t,u1:t), but if this density p(·) can be
evaluated up to proportionality. Let us assume that samples x(i)t can be drawn from a
proposal distribution q(xt | z1:t,u1:t) (also called importance density) of shape:
q(xt | z1:t,u1:t) = q(xt |xt−1, z1:t,u1:t)q(xt−1 | z1:t−1,u1:t−1) (2.18)
Then, it is possible to approximate p(·) if the samples drawn from q(·) are subsequentlyreweighted to account for the discrepancy between p(·) and q(·). This is the principlebehind the basic filtering scheme of sequential importance sampling (SIS): Given the setof samples approximating p(xt−1 | z1:t−1,u1:t−1) at time t−1, the sample states are prop-
agated according to q(xt |xt−1, z1:t,u1:t). The result is a sample x(i)t ∼ q(xt | z1:t,u1:t),
which is finally reweighted by [9]
w(i)t ∝ w
(i)t−1
p(zt |x(i)t )p(x
(i)t |ut,x
(i)t−1)
q(x(i)t | z1:t,u1:t)
(2.19)
The described steps are summarized in Algorithm 1. In all equations in this section wehave already used the Markov process property. That is, we have exploited the condi-tional independence of states and only regarded filtered estimates of xt rather than x0:t.
1The Dirac delta function is defined by δ(0) = ∞, δ(x) = 0∀x 6= 0 and satisfies∫
∞
−∞δ(x)dx = 1.
14
2.2 STATE ESTIMATION WITH PARTICLE FILTERS
ALGORITHM 1: Sequential importance sampling (SIS) particle filter
Input: Sample set (x(i)t−1, w
(i)t−1)Ns
i=1, control input ut, observation zt
Output: New sample set (x(i)t , w
(i)t )Ns
i=1
1 for i = 1 to Ns do
2 Draw x(i)t ∼ q(xt |x(i)
t−1, zt,ut)
3 Compute the sample weight w(i)t according to (2.19)
4 return (x(i)t , w
(i)t )Ns
i=1
Filter Degeneracy and Effective Sample Size
The SIS particle filter suffers from the problem of degeneracy: Due to the repeated sam-pling and weighting steps most of the particles will end up with low weights; the varianceof sample weights provably increases over time. Samples with low weights will hardlycontribute to the approximated density and thus waste computational resources.
As a measure of degeneracy, the effective sample size (ESS) [161] indicates how manysamples effectively contribute to the approximated density. It can be estimated by:
Neff =
(
Ns∑
i=1
(
w(i)t
)2)−1
∈ [0, Ns] (2.20)
The w(i)t are the normalized sample weights. In later chapters, we will come back to
the effective sample size in order to assess filter performance. A small value of Neff isevidence that most of the particle weights are degenerated. Generally, only a sufficientlylarge number of samples with nonnegligible weights can help to produce accurate esti-mates and to maintain the consistency of the filter. Therefore, Neff should be kept aslarge as possible. One option is to increase the number of samples, Ns, but this onlypostpones degeneracy rather than solves the problem.
A better mechanism is to design “good” importance densities which maximize Neff
and minimize the variance among importance weights. The importance density q∗ whichis optimal in that it minimizes the variance of the true particle weights is given by [56]:
q∗(xt |x(i)t−1, zt,ut) = p(xt |x(i)
t−1, zt,ut) =p(zt |xt,ut,x
(i)t−1) p(xt |ut,x
(i)t−1)
p(zt |ut,x(i)t−1)
(2.21)
Unfortunately, it is often not possible to sample from p(xt |x(i)t−1, zt,ut) or to compute
the integral p(zt |ut,x(i)t−1) =
∫
p(zt |x′t)p(x′
t |ut,x(i)t−1)dx
′t. Exceptions are the cases
that the domain of xt is finite or that p(xt |x(i)t−1, zt,ut) is Gaussian [9]. Generally, it is
beneficial to incorporate the latest observation zt in the proposal (e.g., see [176]).
15
CHAPTER 2 METHODS
ALGORITHM 2: Residual resampling
Input: Sample set (x(i)t , w
(i)t )Ns
i=1
Output: New sample set (x(i)t , w
(i)t )Ns
i=1, replacing the former one1 for i = 1 to Ns do // compute deterministic number of copies per sample
2 ci := ⌊Nsw(i)t ⌋ // round down to integer
3 C :=∑Ns
i=1 ci
4 for i = 1 to Ns do // determine remainder weights
5 w(i)t =
w(i)t Ns−ci
Ns−C
6 for i = 1 to Ns do // draw remaining samples from multinomial distribution
7 Draw ri ∼ Mult(Ns − C; w(1)t , . . . , w
(Ns)t ) // e.g., systematic resampling
8 ci := ci + ri
9 S := ∅
10 for i = 1 to Ns do // assemble new sample set
11 Add ci copies of (x(i)t , Ns
−1) to the new sample set S
12 return S
A convenient, often used proposal distribution is the prior density (which is subopti-mal, since it ignores the latest observation zt):
q(xt |x(i)t−1, zt,ut) = p(xt |ut,x
(i)t−1) (2.22)
In this case, plugging (2.22) into (2.19) gives the reweighting formula:
w(i)t ∝ w
(i)t−1p(zt |x(i)
t ) (2.23)
However, as pointed out in literature, the design of the importance density is crucial withregard to filter performance [9] and convergence speed of the filter [238, p.12].
2.2.3 Resampling
Another solution to filter degeneracy is resampling: The idea is to promote samples withlarger weights and to remove samples with small weights. This way, particle filters focusonly on regions of the state space where the likelihood is high. Resampling is performedprobabilistically by sampling with replacement. The probability of drawing a particledepends on its importance weight. After the step, weights are set to w
(i)t = Ns
−1 ∀i.While particle degeneracy is reduced, one should still resample with care: Resampling
leads to particle impoverishment, a loss of diversity among the sample set, since particleswith large weights are statistically selected many times. Impoverishment is especiallyan issue if one is interested in the path that a particle has taken up to a certain time step.
16
2.3 GRAPH OPTIMIZATION
ALGORITHM 3: Generic particle filter
Input: Sample set (x(i)t−1, w
(i)t−1)Ns
i=1, control input ut, observation zt
Output: New sample set (x(i)t , w
(i)t )Ns
i=1
1 η := 02 for i = 1 to Ns do
3 Draw x(i)t ∼ q(xt |x(i)
t−1,ut, zt)
4 Compute the sample weight w(i)t according to (2.19)
5 η := η + w(i)t
6 for i = 1 to Ns do // normalization
7 w(i)t := η−1w
(i)t
8 if Neff < ϑN then // effective sample size dropped below threshold?9 Resample (e.g., using Algorithm 2)
10 return (x(i)t , w
(i)t )Ns
i=1
Methods to overcome this issue generalize the filtering task to a smoothing problem [81].They will be discussed in the context of trajectory estimation in Chapter 7.
There exist a number of resampling techniques: Multinomial resampling samplesfrom the cumulative importance weights of the particles using Ns i.i.d. random numbers(U [0, 1]). Stratified resampling works similar besides that random numbers are drawnin a stratified fashion by splitting the interval [0, 1] into Ns subintervals. For systematic
resampling it suffices to draw a single random number. Then, the sample set will betraversed deterministically in order to copy particles. The method of our choice is resid-
ual resampling, described in Algorithm 2. It reveals low variance, and is independent ofthe order of samples in the sample set. Moreover, the deterministic choice of survivingparticles guarantees that particles with larger weights are not erased accidentally. Ourchoice is based on the analysis of resampling schemes by Douc et al. [54]. We refer totheir paper for details also about the other resampling algorithms.
The resampling step accomplishes the general particle filtering framework. The gen-eral filtering procedure is summarized in Algorithm 3.
2.3 Graph Optimization
Some estimation problems require to find a globally consistent, maximum likelihoodconfiguration of a set of hidden variables by processing all observations at once. Thisperspective is natural in simultaneous localization and mapping (SLAM), which we willaddress in Chapter 7. There, the task will be to infer the entire trajectory of the robotas well as the shape of the environment from a series of observations, with known noisedistributions, but without further prior information. One such class of batch estimation
17
CHAPTER 2 METHODS
landmark
true pose
true transition
odometry
accumulated odometric
uncertainty
observation
(a)
xi
xj
θi
θj
Σij
δij
∆xij
∆yij
∆θij
(b)
FIGURE 2.4: Graph optimization: (a) Constraint network of hidden states, transitions,
and observations to be optimized. (b) Modeling edges in pose graph optimization
methods are graph optimization techniques. Unobserved states – robot and landmarkslocations – are modeled as nodes in a graph. Observations and odometry yield edgesbetween nodes and can be regarded as “soft constraints” [239]. Graph-based techniquesaim at relaxing these constraints and finding a maximum-likelihood configuration of theconstraint graph. The graph is often sparse and permits efficient optimization.
2.3.1 Formalism
Let x0:T = (x0, . . . ,xT ) be a sequence of robot poses, which are again hidden states. Letfurther u1:T = (u1, . . . ,uT ) be the sequence of observed transitions between the statessuch that xt+1 = xt ⊕ ut+1 is a (corrupted) initial estimate of the robot pose at time t.
A sequence of observations be given by z1:T = (z1, . . . , zT ). The xi are the nodes of agraph, consecutively connected by edges that are determined by the movements ui. Ob-servations zi represent additional edges constraining pairs of nodes. All these edges arenoisy constraints, since odometry and sensor readings are inherently uncertain. Whileodometric errors accumulate over time, however, observation edges allow to correctposes along the path: Distant nodes are related to each other, where the noise of anobservation is typically much smaller than accumulated pose errors. The task of graphoptimization now is to find a globally consistent layout of that graph. The typical opti-mization criterion is to maximize the log-posterior
log p(x0:T | z1:T ) = const +T
∑
t=1
log p(xt |xt−1,ut) +T
∑
t=1
log p(zt |xt) (2.24)
18
2.3 GRAPH OPTIMIZATION
if constraints are considered conditionally independent (cf. [239]).A uniform treatment of movements and observations is possible if the nodes are 2D
poses xi = (xi, yi, θi) with Cartesian coordinates (xi, yi) and heading θi and if edges rep-resent noisy estimates of displacements between nodes. Acting upon a Gaussian noiseassumption, a constraint between two nodes i and j is then modeled by a full-rank rigid-body transformation with expected value δij = (∆xij, ∆yij, ∆θij) (2D translation plusrotation). Σij is the associated error covariance matrix. Let fij(x) generate zero-noiseobservations according to the current configuration of the nodes i and j in the graph,where x be the concatenation of x0, . . . ,xt. Then maximizing (2.24) turns into minimiz-ing the negative log-likelihood (cf. [91, 193])
∑
1≤i,j≤T
(fij(x) − δij)TΣ−1
ij (fij(x) − δij) (2.25)
If there is no constraint between nodes i and j, the information matrix Σ−1ij is set to the
zero matrix 0.
2.3.2 Iterative Least-Squares Solution
Formulated as a maximum-likelihood problem with constraints of zero-mean Gaussiannoise, (2.25) can be rewritten in matrix form. One linearizes f(x) = F (x) + J∆x,where J is the Jacobian of the constraints with respect to x [193]. Let δ be the vector ofconstraints, r = δ − F (x) the residual and d = ∆x a small change in x. Then, (2.25)becomes [193]
(F (x) + Jd − δ)TΣ−1(F (x) + Jd − δ) = (Jd − r)TΣ−1(Jd − r), (2.26)
which is minimal if (JTΣ−1J)d = JTΣ−1r. Solving for d repeatedly in order to in-crementally correct x represents a typical nonlinear least-squares solution. This solutionof graph-based SLAM was first proposed in a similar manner by Lu and Milios [163].The involved matrices are usually sparse. Consequently, as pointed out by Takeuchiet al. [231], the utilization of sparse-matrix software packages and the reordering ofnodes yield reasonably fast solutions even for larger numbers of constraints.
2.3.3 Stochastic Gradient Descent
The least-squares method is computationally expensive due to its matrix operations, evenwhen utilizing sparseness. Moreover, the solution is still a linear approximation to a non-linear problem. These insights motivated Olson et al. [193] to apply stochastic gradient
descent (SGD) to graph optimization. SGD iteratively chooses a single constraint andcorrects the state vector in direction of greatest gradient descent. In Olson’s solution thecorrection vector for a constraint cij = (i, j, δij,Σij) is chosen to be [193]
d = 2αM−1JT
ijΣ−1ij rij, (2.27)
19
CHAPTER 2 METHODS
where rij is the residual of cij and Σ−1ij its information matrix. The Jacobian Jij maps
the scaled residual to the state space, and M−1 = diag(JTΣ−1J) is the Jacobi pre-conditioner. The learning rate α is set α = 1/(γτ); it decreases over the number ofiterations, τ , where γ = mini,j Σ−1
ij [193]. One major factor of efficiency results fromOlson’s formulation of the state space: Rather than the vector of global poses x, an in-cremental pose space was employed, in which x was transformed to x′ with x′
0 = 0 andx′
i = xi − xi−1 ∀i > 0. Note that x′ is the vector of pose differences (by simple subtrac-tion) instead of relative poses. The resulting Jacobian matrix simply consists of ones andzeros and need neither be computed nor be stored explicitly. Later, Grisetti et al. [91]proposed an even more efficient state parametrization, in which a spanning tree of posedifferences is constructed from robot poses. As a consequence, a single constraint opti-mization requires fewer updates of nodes in the tree. Grisetti et al. also showed fasterconvergence of their method. To be able to update the graph while the robot is exploringits environment, both techniques were later enhanced by on-line versions [87, 194].
2.3.4 Spring-Mass Models and Relaxation Techniques
Spring-mass models regard the network of constraints as a network of masses upon whichobserved displacements between poses act as forces [58, 59, 82, 112]. The stiffness ofthese “springs” is inversely proportional to the covariances of the corresponding obser-vations. Until convergence to a (local) minimum, node positions (rather than constraints)are iteratively corrected via gradient descent according to the sum of forces acting uponthem. This kind of relaxation approaches were observed to be slow when the graph con-tains large cycles [77]. Frese et al. [77] therefore extended it to multi-level relaxation,which performs relaxation on multiple scale levels of the pose graph. Overviews ofother graph-based approaches can be found in [90]. An earlier discussion of graph-basedapproaches and comparison to other estimation techniques can be found in [76].
2.4 Conclusion
In this chapter, we were concerned with three forms of estimation problems: First, non-parametric regression was introduced as a means to predict function values based ontraining data in a supervised fashion. Then, we described particle filtering as a nonpara-metric Bayesian filtering technique to infer the time-varying hidden state of a dynamicsystem from series of noisy control inputs and observations. Last, we treated graph op-timization, which aims at finding a globally consistent solution for a sequence of stateswith pairwise constraints. All estimation methods are probabilistic and are able to dealwith the uncertainty of sensor readings that is inherent in most robotic applications.
So far we have introduced the methodical background of this thesis. The next chapteris about radio-frequency identification and clarifies the technical background.
20
Chapter 3
Long-Range Passive RFID
In this chapter, we treat theoretical and practical aspects of RFID as a sensor technology.After a brief general introduction, technical information about passive long-range RFIDis given in Section 3.2. In Section 3.3 we conduct elementary experiments to characterizeRFID for the navigation tasks of this thesis. Finally we draw conclusions in Section 3.4.
3.1 Introduction
Radio-frequency identification (RFID) is a technology which allows for the contactlessidentification of tagged objects. An interrogator, called RFID reader, requests the iden-tity of one or several RFID tags via radio waves. Originally developed by the militaryin 1948, RFID is nowadays used for the automatic recognition of goods in an increasingnumber of production and logistics scenarios. It subsumes an entire family of identifica-tion standards which mainly differ in radio frequency and read range. Correspondingly,the spectrum of applications is manifold. Short-range RFID systems, with a read radiusof usually less than one meter, have often been employed for access control, paymentsystems, libraries, and animal marking, for instance. Long-range systems, on the otherhand, permit object identification from a distance of several meters, even without line ofsight. This saves labor, since a person is not required to scan an object at close range,minimizes the risk of errors, and allows for automation. Long-range RFID has conse-quently attracted considerable economic interest. It can be used for inventory control,positioning, asset tracking along the supply chain, theft control, toll collection, or anti-counterfeiting, to name a few applications.
Compared to classical barcodes [114, 257], long-range RFID distinguishes by the factthat a bulk of tags can be read quasi-simultaneously in fractions of a second, even ifobjects are moving. Another property is important, which also reveals superiority toclassical barcodes: Each tagged object can be identified uniquely. That is, every itemof a product type – or more generally object class – has its own identification number,since an RFID tag can be programmed unambiguously. This characteristic makes RFIDa valuable sensor in robotics: With other types of sensors, such as laser range findersor cameras, it is often difficult to recognize distinguishable features of the environment(landmarks) that have been observed earlier. This challenge is known as the data asso-
21
CHAPTER 3 LONG-RANGE PASSIVE RFID
Host PC or
enterprise system
Data
Antenna RFID tagRFID Reader
Energy, data, commands
FIGURE 3.1: LEFT: Components of RFID systems and communication between them.
RIGHT: Bird’s eye view of a robot with (hidden) on-board RFID reader and two con-
nected RFID antennas scanning to the sides.
ciation problem. While posing physically founded challenges, RFID trivially solves thisproblem in that identified RFID tags serve as uniquely identifiable landmarks.
In the following, we will elaborate the technical background of RFID systems anddiscover implications for the utilization of RFID as a sensor for mobile robot navigation.
3.2 Technical Background
3.2.1 RFID Systems in General
RFID systems consist of at least one RFID reader and a number of tags. The reader as-sumes the role of an interrogator and communicates with the RFID tags via radio waves.Since the interrogation is initiated by a host PC connected to the RFID reader, the PCis often regarded as the third essential element of an RFID system [206]. The inquiryresults will also be reported to the host.
These components of an RFID system are illustrated in Figure 3.1. The RFID readerreceives high-level commands from the host application, which can be the request to scanfor tags. Commands and data addressed to some tag will be encoded, transmitted via theconnected reader antennas, and responded by the RFID tag. The tag itself consists of anantenna receiving the coded signal and transmitting the reply, a microchip which controlsthe communication with the reader, and a small memory containing the stored data. RFIDtags are also called transponders because of their role to transmit and respond.
Besides other criteria, RFID systems distinguish by transmission frequencies and thepower supply of the tags. With respect to the latter, transponders can be active or passive.A passive transponder gathers the energy to run its microchip and to communicate fromthe electromagnetic field of the RFID reader. An active RFID tag possesses a battery forboth purposes. Its battery life time is up to ten years and allows for larger read ranges.
22
3.2 TECHNICAL BACKGROUND
TABLE 3.1: RFID frequency bands and typical read ranges of passive transponders
Frequency band Typical frequencies Read range
Low frequency (LF) 134.2 kHz <1.5 mHigh frequency (HF) 13.56 MHz <1 mUltra-high frequency (UHF) 868 MHz (Europe)/915 MHz (USA) 3-7 mMicrowaves 2.45/5.8 GHz 3-7 m
On the other hand, size and price of the transponder increase.With regard to transmission frequencies, there are several frequency bands, as listed
in Table 3.1. Low-frequency (LF) systems achieve data transfer by inductive coupling ofreader and tag. Although its read range can reach 1.5 m [150], the typical range is usuallya few centimeters due to reasons of security. High-frequency RFID also transmits byinductive coupling. Typical read ranges are larger, up to approx. 1 m.
UHF and microwave RFID achieve transmissions via the emission and reflection ofelectromagnetic waves in the far-field of the reader. They feature read ranges of 3 mand more. Since the higher the radio frequency, the better are the data rates that can beachieved, UHF RFID is the favorable technology when large populations of tags are tobe inventoried.
A recent extension in the list of radio frequencies is ulta-wideband (UWB) technology.UWB transmits on a wide spectrum of microwave frequencies with low power simulta-neously. This makes communication robust and applicable in sensitive settings such ashospitals [253]. Localization is possible at an accuracy of few centimeters, depending onthe placement of the UWB nodes [79]. Current commercial solutions, however, requirebattery-powered nodes.
Overviews of and details on RFID technology in general are given in [150, 206, 252].
3.2.2 Long-Range Passive RFID
In this section we detail the characteristics of passive long-range RFID, as employed inthis thesis. Above all, we describe the most important standard known as EPC Class 1Generation 2 (C1G2) [116, 118]. It specifies physical and logical requirements for RFIDin the UHF band in the range 860-960 MHz and was originally published in 2005. TheEPC specifications were later also standardized with minor modifications as ISO 18000-6C [71, 72]. The UHF RFID band features worldwide admission, but at different fre-quencies: While in the USA readers operate at 915 MHz, the regulated frequencies inEurope and Japan are 868 MHz and 950 MHz, respectively.
Tag Interrogation: A long-range RFID reader emits an electromagnetic (EM) fieldwhich temporarily activates a passive tag. By modulating the emitted EM wave, com-mands can be transmitted to the tag. A tag responds by means of backscattering: It
23
CHAPTER 3 LONG-RANGE PASSIVE RFID
changes a resistor parallel to its antenna, by which the continuous wave of the reader isreflected. The modulated signal can be measured and decoded by the RFID reader. Var-ious commands enable the RFID reader to select a subset of tags which should respondto queries, to inventory tags, and to access their memory banks [69]. Memory accessinvolves read, write, lock, and kill operations. For example, reading allows for access tothe tag identifier (ID) and thus the actual identification. By locking, tag contents can besecured, and killing refers to the deactivation of a tag.
The EPC Class 1 Generation 2 (EPC C1G2) specifications permit to query the sametransponder with up to four RFID readers thanks to sessions. Session numbers alwaysaccompany commands, as well as desired data rates for the backwards link. Vice versa,a reader can inventory an entire population (bulk) of tags in read range. The reader usesa singulation mechanism to query all tags in read range and to detect collisions. ISO18000-6C relies on a variant of the ALOHA algorithm which singulates by means of timeslots and 16-bit random numbers rather than the full electronic product code (EPC). Bymeans of this method and check sums on data transfer, transmission errors and collisionsare detected by the RFID reader. Consequently, it is virtually impossible that the RFIDreader reports an incorrect transponder ID. This aspect is important, because it is one ofthe great benefits of RFID to rely on perfect data association1.
Apart from checksums and protocol information, the memory contains four types ofdata: kill/access passwords, the electronic product code (EPC), a memory bank withread-only information about manufacturer and serial number of the tag (called TID), anduser memory, if available. Both TID and EPC are unique, but the standard reply of aninventoried tag includes the EPC only, if not requested for access to its memory. TheEPC is a 96-bit (or longer) number which apportions the producer as well as the articleand serial number of an item. The SGTIN-96 standard [117] reserves 38 bits for singleitems. In this vein, more than 274 billion instances of the same article can be enumeratedunambiguously. In later chapters, we will utilize the stored EPC as a tag identifier. Forcompact overviews of ISO 18000-6C, we refer to the literature [53, 69].
Read Range: An important characteristic of an RFID system is its read range. Con-forming to the described ISO/EPC standard, passive UHF systems feature read ranges ofseveral meters. The actual maximum read range of an RFID system depends on:
• Frequency of the transmitted signal: As shown in [66], the read range is directlyproportional to the wave length of the transmitted signal. For a given power, readranges differ across the world, but only by 10 % for the frequencies listed above.
• Transponder characteristics: Size and shape of a tag as well as the quality ofits antenna, the power consumption of its microchip, and the connection betweenthem influence the maximal detection radius.
1Actually, the only errors observed during the preparation of this thesis traced back to problems with theserial connection between RFID reader and PC.
24
3.2 TECHNICAL BACKGROUND
• Reader characteristics: The reader influences the read range by its transmissionpower, its sensitivity, and the design and polarization of the connected antennas.The maximum transmission power is 4 W in the USA and 2 W in Europe. Readersare either monostatic or multistatic, which means that transmission and receptionrequire either one or multiple (typically two) antennas, respectively. The separa-tion of transmit and receive channels has impact on the read range [185].
• Environmental factors: Depending on objects in the vicinity of reader and tag,electromagnetic waves can be absorbed, reflected, or diffracted. Especially objectscontaining metal or water are problematic: Water absorbs energy from the EMfield and prevents the successful reading of proximate transponders. Metal reflectselectromagnetic waves; by interference, signals may amplify or cancel each other,which renders the propagation of EM signals unpredictable.
• Active sources of noise: Other radio devices may disturb the interaction betweenreaders and tags. Medical equipment in a hospital is an example.
The write range of a tag depends on the same factors. It is typically by 30 % smaller,because the tag chip requires more power to perform write operations [185].
While the listed criteria affect the maximum read range, the actual chance of success-fully reading a transponder largely depends on distance and angle between reader antennaand tag antenna. We will take this aspect on in later sections, especially in Chapter 4.In the remainder of this thesis, we will refer to failed detection attempts of transpondersin read range as false negatives. They occur frequently. By false positives, we will de-note detections of tags which are outside theoretical read range. They occur when signalreflections in the environment increase the antenna read range. False positives due toincorrectly decoded transponder IDs, however, appear virtually never.
3.2.3 Long-Range Readers
Today, a variety of long-range RFID readers are available in the market. Apart from anumber of technical aspects, they differ in size, transmission power (and thus read range),ways of connecting antennas, and communication with the application/host PC.
Size Classes and Prices: As of 2010, handheld and compact desktop UHF readers canbe purchased coarsely from 500 EUR to 3000 EUR. They typically have read ranges ofless than 1 m [242] and provide only one integrated antenna. Standard-size readers witha read range of several meters and 1-4 antenna ports for fixed mounting or fork lifterscost 1500-4000 EUR. This is the class of readers that we investigate in this thesis: Theirhousings are slightly larger (approx. 20 cm × 30 cm × 5 cm), and far-field antennas canbe connected flexibly. By this, they can easily be carried by service robots. Moreover,their prices are expected to decline. RFID gates for the control of incoming and outgoing
25
CHAPTER 3 LONG-RANGE PASSIVE RFID
Configuration
InventoryRequest
Tag List
Configuration
Request forAutonomous
Tag List
Interactive Mode Autonomous Mode
Inventories
Application Reader Tag Application Reader Tag
Tag List
Tag List
FIGURE 3.2: Interactive vs. autonomous inquiries in the style of [68]. LEFT: The
application waits until the reader has finished its interactions with tags. RIGHT: After
subscription, the reader frequently supplies the list of recent tag detections.
goods cost several thousands of dollars/euros and represent the largest size class. Theirantennas feature heights of 1-2 m.
Synchrony of Inquiries: With regard to the communication between reader and appli-cation, ISO 18000-6C-compliant readers can be classified by the mode of synchrony inwhich they report tag detections. As depicted in Figure 3.2, communication can be eithersynchronous or asynchronous. In synchronous communication, the application requestsan RFID inquiry and waits for the reply by the reader. This mode is called interactive
or application-triggered [68]. In this case, the application exactly knows how many readattempts have been requested.
On the other hand, in asynchronous communication the reader inventories tags contin-uously. It frequently reports the inquiry results to the application. This mode is knownas autonomous or event-driven mode. It appears in two very similar variants: The firstvariant is exactly like in Figure 3.2 (right), where the reader provides tag lists accordingto predefined rules (e.g., after specified time intervals or whenever a tag is detected).In the second variant the application still requests every single tag list, but the readerautonomously performs inventories in the background. In autonomous mode, the appli-cation may not know how often the reader has actually queried tags in read range. Thedistinction between the two modes will be important for the probabilistic modeling ofRFID detection rates in Chapter 6.
Type of Information Provided about Inquiries: The described standards specify thatonly the EPC of a tag is obtained and reported to the target application by the RFID
26
3.3 ELEMENTARY EXPERIMENTS
FIGURE 3.3: Transponders at full scale: Alien Squiggle (top) and Impinj Propeller (bot-
tom left) labels; solid Omni-ID Mini tag (bottom right) with a thickness of approx. 2 mm
reader. Generally, beyond this mere detection information, the RFID interrogator couldadditionally measure the strength or the angle of arrival of the signal backscattered bya tag. These additional pieces of information are not (yet) provided by the majorityof readers. Most readers, however, offer commands to adjust the transmission power.Thereby, signal strength information can be compensated for to some extent.
3.2.4 Long-Range Passive Transponders
Passive UHF RFID tags are available in manifold shapes (Figure 3.3) and for differ-ent purposes. There are force-resistant transponders for harsh environments which costseveral dollars/euros. But the vast majority of transponders are inexpensive inlays andflexible smart labels. A single tag can cost less than 10 ¢, depending on how manytransponders are purchased.
Most transponders are linearly polarized. Yet, invariance to their linearization can beachieved by the circular polarization of reader antennas.
3.3 Elementary Experiments
In this section we describe elementary experiments which we performed with EPC-compliant RFID readers. The goal is to learn about their detection characteristics. Thegained knowledge will enable us to deduce algorithm designs and it will help to betterunderstand the outcomes of experiments in later chapters.
All experiments were conducted with two UHF RFID readers, an Elatec SR-113 andan Alien Technology ALR-8780. With regard to the abovementioned technical back-ground, readers conform to the EPC C1G2 standard. The ALR-8780 has a bistaticantenna setup; the SR-113 follows a monostatic configuration. Moreover, the SR-113features a maximum transmission power of 1 W (30 dBm) EIRP (equivalent isotropicradiation power), while the ALR-8780 transmits 2 W (33 dBm).
27
CHAPTER 3 LONG-RANGE PASSIVE RFID
y (
m)
x (m)
Reader: ALR-8780. Tag: Squiggle (Higgs 3)
-4
-3
-2
-1
0
1
2
3
4
-1 0 1 2 3 4 5 6 7
y (
m)
x (m)
Reader: ALR-8780. Tag: Impinj Propeller
-4
-3
-2
-1
0
1
2
3
4
-1 0 1 2 3 4 5 6 7
y (
m)
x (m)
Reader: ALR-8780. Tag: Omni-ID Mini
-4
-3
-2
-1
0
1
2
3
4
-1 0 1 2 3 4 5 6 7
FIGURE 3.4: Read range experiments with the ALR-8780 reader and three types of tags
attached to a wooden pole. The reader antenna is depicted by the small orange rectangle.
Gray dots symbolize failed detection attempts, blue (dark) dots successful tag readings.
3.3.1 Detection Range
We conducted a series of experiments to determine the detection range of the employedRFID systems. During the experiments, we moved the antenna (on board the robot) on aplane parallel to the ground surface, while the tag under investigation remained fixed ona pole. Because the position of the antenna was known at each time step, we were able torecord a large number of samples of detection attempts for various relative displacementsbetween reader antenna and transponder.
In the first experiment, we logged detection attempts for the two readers and differenttypes of tags. They were configured to scan at full transmission power. The resultsare shown in Figure 3.4. The left subfigure shows positions where a transponder of typeAlien Technology Squiggle (ALL-9440 with Higgs 3 chip) was or was not detected. Thistype of tag is widely used in common industrial RFID applications. The plot certifiesthat tags can be read at distances of several meters. Some successful detections wereperformed at distances of up to 7 m. The directional, rather than isotropic, character ofthe antenna along the positive x axis can also be observed. Note that in all figures wepresumed symmetry around the x axis. On the other hand, detections behind the antenna,i.e., x < 0, occur rarely and only at close distance. One further observes that the detectionrange is not a strictly confined area: There is a transition from farther regions to an areaof high detection rates closely in front of the reader antenna.
The analysis of detections of the Impinj Propeller tag (Figure 3.4, middle) reveals thatdetections have focussed to an area close to the reader antenna. The detection statistics ofthe transponder type Omni-ID Mini (right hand side of Figure 3.4) were different: Evenat full power level (2 W), the reader was unable to detect the transponder at distancesof significantly longer than 1.5 m. The reason is that this type of tag is optimized formetal surfaces. This property can also be seen in Figure 3.5, which depicts detectionrange experiments with the SR-113 reader operating at a power level of 1 W: While theSquiggle tag was detected over several meters when attached to a wooden pole, it could
28
3.3 ELEMENTARY EXPERIMENTS
y (
m)
x (m)
Reader: SR-113. Tag: Squiggle (Higgs 3) on wood
-4
-3
-2
-1
0
1
2
3
4
-1 0 1 2 3 4 5 6 7
y (
m)
x (m)
Reader: SR-113. Tag: Squiggle (Higgs 3) on metal
-4
-3
-2
-1
0
1
2
3
4
-1 0 1 2 3 4 5 6 7
y (
m)
x (m)
Reader: SR-113. Tag: Omni-ID Mini on wood
-4
-3
-2
-1
0
1
2
3
4
-1 0 1 2 3 4 5 6 7
y (
m)
x (m)
Reader: SR-113. Tag: Omni-ID Mini on metal
-4
-3
-2
-1
0
1
2
3
4
-1 0 1 2 3 4 5 6 7
FIGURE 3.5: Read range experiments with the SR-113 reader and two types of tags on
two undergrounds (left column: wooden pole, right column: metal pole). The reader
antenna is depicted by the small orange rectangle. Gray dots symbolize failed detection
attempts, blue dots successful tag readings.
not be detected when attached to metal. The Omni-ID Mini transponder, however, waseven detected at longer distances when fixed on the metal pole. This can be explained bythat the transponder utilizes the metallic surface for transmission purposes.
These experiments illustrate that RFID reader, transponder type, and underground ma-terial have major impact on size and shape of the detection field.
3.3.2 Time Series of Inquiries
In a second series of experiments, we fixed the type of transponder and chose a static tagplacement. We compared the performance of successful read attempts over time, similarto the benchmark by Ramakrishnan and Deavours [201]. They characterized an RFIDsystem by the time to first read, i.e., the time that is required to read the nth tag for thefirst time. For each reader, we placed the RFID antenna 1 m in front of a metal shelfwhich contained 287 labeled items at different heights. The reader was configured formaximum performance (largest power level and number of ALOHA slots).
Figure 3.6 depicts the numbers of different tags accumulated over time by the two in-
29
CHAPTER 3 LONG-RANGE PASSIVE RFID
Cu
mu
lative
nu
mb
er
of
diffe
ren
t ta
gs
Time (s)
ALR-8780SR-113
0
20
40
60
80
100
120
140
160
180
50 100 150 200 250 300 350 400 450 500
(a)
Cu
mu
lative
nu
mb
er
of
diffe
ren
t ta
gs
Time (s)
ALR-8780SR-113
0
20
40
60
80
100
120
140
160
180
5 10 15 20 25 30
(b)
FIGURE 3.6: Cumulative numbers of different detected tags for both platforms. The right
column contains closeups of the first 30 seconds of the plots in the left column.
vestigated readers. The graphs show that a considerable number of inquiries is requiredto read large portions of the population of RFID tags. Even after several minutes, thereaders observe some transponders for the first time. The Alien ALR-8780 takes ap-prox. 18 s to read 50 % of the final number of detected tags (184). The Elatec SR-113requires less than 5 s to read 50 % of the final number of detected tags (138), but it takesmore than 15 s to reach approximately the final level. Both readers do not manage toscan the entire shelf. The likely reason is that some transponders were located closeto or shielded by the metal of the shelf. Besides, the Elatec reader also detected fewertransponders because of its lower transmission power.
Figure 3.7 analyses how many tags were read in each inquiry. The ALR-8780 mostlyidentified two or even fewer tags per inquiry. On the contrary, the SR-113 detectedapprox. 16 labels on average, although it was configured to scan for tags only 0.5 s ascompared to the approx. 0.7 s inquiry duration of the ALR-8780. One reason of the su-perior performance of the newer SR-113 reader is probably that it handles tag collisionsbetter. This is an important aspect in environments which are densely populated by tags.
First, these experiments illustrate that it takes time to resolve a large population oftags. Although the EPC standard specifies up to a few hundreds of tags can be singulatedin a single interrogation and within less than a second, at least our off-the-shelf readerswere unable to achieve this performance level. Consequently, a fast driving mobile robotwill simply miss some transponders when inventorying. However, the newer SR-113reader showed promising performance, which justifies some confidence that future RFIDreaders will perform better. Moreover, by placing more antennas at different heights,the robot would be able to identify more products. Despite the disillusioning result thattransponders were missed, our second observation is that both robots could detect severaldozens of tags within a few inquiries. Here we see that localization-related techniquescan extract several pieces of information from RFID measurements in order to recognizeplaces in reasonable time – even though just detections of tags in a radius of several
30
3.3 ELEMENTARY EXPERIMENTS
Fre
quency o
f occurr
ence
Number of tags per inquiry
ALR-8780
0
50
100
150
200
250
300
350
400
450
500
0 5 10 15 20 25
Fre
quency o
f occurr
ence
Number of tags per inquiry
SR-113
0
50
100
150
200
250
300
350
0 5 10 15 20 25
FIGURE 3.7: Frequency of occurrence of the detected numbers of transponders in the
static setup. LEFT: ALR-8780 reader mounted on the B21. RIGHT: SR-113 reader
attached to the SCITOS.
meters are given, no distances or bearings.
Figure 3.7 showed how many tags were detected in a static configuration. An impor-tant question is how similar these inquiries are as compared to each other. Therefore,we computed similarity matrices S = (sij), where sij states to what extent the measure-ments i and j are similar. We compared the lists of individual tag counts at a single readerantenna, using the cosine similarity measure (see Appendix B). Again, we contrasted theALR-8780 with the SR-113, and we examined two different settings: A location withlow tag density (<10 transponders), and the setting from above with more than 200transponders in a distance of 1 m. In case of perfectly reproducible RFID scans compris-ing all transponders in read range, one would expect sij = 1 ∀i, j. The actual outcomesof 32 exemplary consecutive RFID inquiries are visualized in Figure 3.8. Each squaredot in one of the four subfigures represents an entry sij of the matrix. White correspondsto sij = 0 (no similarity or no tags detected), whereas black indicates sij = 1 (mea-surements i and j are identical). Of course, the diagonal elements show that sii = 1 ingeneral. Note that we defined the cosine similarity to be zero for empty measurements;that is why some diagonal elements are white.
The ALR-8780 reveals that in the setting with high tag density (Figure 3.8(a)) mea-surements are not very similar most of the time. Consequently, the tag lists of pairsof measurements are often entirely or almost disjoint. In the case of the lower tagdensity (Figure 3.8(b)), larger fractions of tags were re-detected, but still quite oftena pair of measurements shared little information. With respect to the SR-113 reader(Figures 3.8(c) and 3.8(d)), pairs of measurements seem to have more tags in common.Again, on average the amount of information shared is smaller in case of the higher tagdensity, as compared to the lower tag density setting. These observations are compati-ble with the earlier Figure 3.6: It illustrated that even after long time, some tags wereidentified for the first time.
31
CHAPTER 3 LONG-RANGE PASSIVE RFID
(a) ALR-8780, higher tag density (b) ALR-8780, lower tag density
(c) SR-113, higher tag density (d) SR-113, lower tag density
FIGURE 3.8: Visualization of similarity matrices for 32 consecutive RFID inquiries in
a static setting. Each entry represents a comparison of two RFID measurements. Dark
and light correspond to high and low similarity, respectively.
3.3.3 Duration of Interrogations
The ISO 18000-6C standard specifies that up to 100 tags in read range can be read within200 ms [69]. Our previous experiments suggested that this upper bound is not achievedin practice by our readers: The SR-113 was configured to scan for 0.5 s and detectedapprox. 15 tags per inquiry.
In another experiment, we investigated the time that the ALR-8780 reader requires tointerrogate populations of tags in interactive mode. Therefor, we connected four antennasto the reader and moved it through the laboratory. More than 400 tags were placedat different heights and densities inside an area of approx. 50 m². Table 3.2 lists themean inquiry times which were required to scan with all antennas once or several times.The reader was configured to perform the given number of scans before reporting theinquiry result. The listed values were derived from 11422 interrogations in total. It tookapprox. 0.7 s to query all antennas once and approx. 2.6 s for four inquiries at each ofthe antennas. That is, one interrogation with a single antenna lasts approx. 0.17 s onaverage. Relating this value to Figure 3.7, one can see that the ALR-8780 reader doesnot attain the specified best-possible performance level after ISO standard by far, either.The number of tag counts in an inquiry and its duration were weakly correlated (Pearson:approx. 0.35; Kendall: approx. 0.26). Correlation is plausible, as transponders need to besingulated when occurring in bulks, but the variance remains unexplained in large part.
The results show that during one interrogation of all its antennas, the robot may havemoved significantly. This makes it difficult to determine the exact position from which a
32
3.4 CONCLUSION
TABLE 3.2: Mean durations and standard deviations (in seconds) of reading all 4 an-
tennas of the ALR-8780 reader k times
k 1 2 3 4
Duration (s) 0.77± 0.09 1.46± 0.18 1.99± 0.26 2.66± 0.29
detected transponder was actually observed.
3.4 Conclusion
Summary
In this chapter, we have presented different RFID standards for the identification of tagsby readers via radio waves. The standards above all differ in the radio frequency bandsused and the power supply of tags. Passive UHF RFID allows for the detection of inex-pensive tags over several meters and in principle without the requirement of line-of-sight.It provides reading of tags in bulks, and high-fidelity, unambiguous data association.
Yet, long-range RFID poses some challenges: Physical phenomena such as reflections(e.g., by metal), diffraction, and absorption (e.g., by water) represent sources of consid-erable noise. Thus a single transponder detection comes with large position uncertainty.Range and bearing are typically unknown, because signal strength or direction of arrivalare mostly not reported by UHF RFID readers.
We conducted experiments in which we studied the detection behavior of differentreader and tag types: Detection range, tag counts, inquiry times, and the similarity ofmeasurements over time were investigated.
Discussion and Outlook
We have shielded RFID privacy and security issues [254], which have caused compre-hensible skepticism by the public and also prevented to use RFID in some commercialdomains. Such issues, however, are technically not relevant for this thesis. Besides,measures have been and are being developed to solve those issues.
At the moment, it is unlikely that every product will be labeled in the very near future,mostly for financial reasons. Yet, already today passive UHF RFID is successfully em-ployed in areas such as intralogistics and for certains types of products such as clothes.The ability to print polymer circuits or to manufacture labels from organic materials inthe medium run can be expected to boost the distribution of RFID, especially in lowerprice segments.
Other research groups conducted similar experiments in order to examine RFID per-formance. For instance, Brusey et al. [32] presented an early study on interference ofseveral readers. Buettner and Wetheral [33] examined read rates and cycle times with
33
CHAPTER 3 LONG-RANGE PASSIVE RFID
a software radio. Welbourne et al. [255] recorded detection statistics for a building-wide RFID deployment. Several researchers recorded detection statistics for differ-ent kinds of labeled objects or various displacements between reader and transpon-der [49, 52, 108, 164, 201, 204]. Others finally measured tag counts depending ondistances, movements [205, 258], and on attenuation [258].
Taking all experimental studies together, we conclude that
• navigation techniques using UHF RFID must be able to cope with the positionuncertainty, the noisiness, and the high false-negative rate of RFID detections, and
• it is difficult to simulate RFID detections, because various conditions and param-eters exert influence. For this reason, we decided against testing our algorithms insimulation, even though there is software which simulates parts of RFID charac-teristics [69, 145].
Still, from the perspective of robotics, RFID is a valuable sensor technology:
• RFID tags uniquely identify landmarks and hence solve data association issues.Erroneous association is virtually impossible. A number of tags can be read quasi-simultaneously. In opposition to other sensors, exhaustive feature matching is notrequired, which lowers computational demands.
• Identification is possible even when the robot is moving. Motion blur is an issuewhen cameras are used, and time-of-flight 3D cameras reveal nonnegligible noiseat the borders of moving objects.
• Estimation using other sensors may be difficult if the environment contains sym-metries (laser range finders) or similar visual features (cameras).
In the subsequent chapters, we will utilize exactly these properties and derive robustnavigation methods for mobile robots using UHF RFID.
34
Chapter 4
Modeling the Robot
In this chapter we probabilistically model robot motion (Section 4.2) and RFID detec-tions (Section 4.3). Such models will be required in later chapters for robust localizationand mapping. In Section 4.4 we summarize this chapter and draw conclusions.
4.1 Introduction
For RFID-based navigation, two essential sensors need to be characterized: We first ded-icate ourselves to odometry, which represents estimates of the robot’s motion. Its inher-ent noise is quantified by means of a motion model. Then we present a semi-automaticlearning technique for models describing location-dependent detection probabilities oftransponders inside the electromagnetic field of an RFID reader. This way, a single tagdetection provides more information than just the reported tag identifier.
Both motion and RFID sensor model require the fixation of coordinate systems, asdepicted in Figure 4.1: One for the world coordinate system W , which is the globalframe of reference, as well as one for the robot, one for each of its antennas, and one foreach tag. Whenever possible, we will omit the index W , if it is clear from the context thatsome vector is given in global coordinates. W is given by the origin of the map of theenvironment in which the robot resides. R is the frame of the robot and fixed where theground and the rotation axis of the robot intersect. Its xR axis follows the global headingof the robot, parallel to the global xy plane. zR points upwards, yR follows because ofright-handedness. Ai is the frame of the ith RFID antenna onboard the robot, and Lj
the frame of RFID label j. The x axes of tag and antenna frames follow the direction ofmaximum antenna gain, which is orthogonal to the antenna planes. Since tag antennasare symmetric, ambiguity is resolved by choosing the direction towards the visible sideof the tag. The yLj
axis of the tag follows the major axis of the rectangular label. The yAi
axis of a reader antenna lies in the plane of the antenna and parallel to the global groundsurface; this way, zA typically points upwards.
With respect to these frames, we will typically denote the global pose of the robot byx := Wx. The pose of its ith antenna is given by ai := Wai, while lj := W lj symbolizesthe position and orientation of RFID tag j. The transformation matrix RTAi
betweenrobot and reader antenna i is known and fixed during all of our experiments. x changes as
35
CHAPTER 4 MODELING THE ROBOT
W
R
Ai Lj
xR
yR
zR
xAi
yAi
zAi
xLj
yLj
zLj
xW
yW
zW
FIGURE 4.1: Coordinate frames for robots (red), RFID antennas (yellow), and RFID
tags (blue)
the robot moves; estimating its value is the localization or trajectory estimation problem.In opposition, estimating the transponder positions lj is the goal of mapping.
4.2 Modeling Motion
Most wheeled indoor mobile robots move in two dimensions. Consequently, it sufficesto describe robot locations by a vector Wxt = xt = (xt, yt, θt). xt and yt are the time-dependent global coordinates of the robot on the ground plane, relative to the frame ofreference. θt denotes the global heading of the robot. Nonholonomic robots (e.g., withdifferential drive or synchronous drive, as in our case) have two degrees of freedom:They can rotate and move forward in direction of their current heading, where rotationand translation can be performed simultaneously. By means of encoders attached to thewheels, the path traveled can be measured.
4.2.1 Representations
Movements are understood as transformations between two consecutive poses xt andxt+1, as visualized in Figure 4.2. We assume that the robot’s motion unit reports (noisy)movements (∆x, ∆y, ∆θ). This is the shape of a rigid-body transformation, where ∆xand ∆y are forward and sideward translation relative to xt, and ∆θ is a final rotationby ∆θ. Then, xt+1 can be written as:
xt+1
yt+1
θt+1
=
xt
yt
θt
+
cos θt − sin θt 0sin θt cos θt 0
0 0 1
∆X∆Y∆Θ
(4.1)
36
4.2 MODELING MOTION
∆x∆y
∆θ
dφ1
φ2
t
t + 1
FIGURE 4.2: Two ways of modeling the 2D movement of the robot from xt to xt+1:
(1) Rigid-body transformation (∆x, ∆y, ∆θ) with respect to the frame at time t. (2) First
a rotation by φ1, followed by a straight translation by d and a final rotation φ2.
∆X ∼ fX(∆x), ∆Y ∼ fY (∆y) and ∆Θ ∼ fΘ(∆θ) are distributions of the true motionvalues, depending on the reported odometric numbers. Modeling movements this way iscommon in graph-based SLAM, as seen in Section 2.3.
Another often used option is to model movements by two rotations and one transla-tion [237]: Between two time steps, the robot is assumed to first rotate by the angle Φ1
towards the target pose xt+1. Then, it moves forward by a distance D on a straight line.Finally, the robot assumes its final orientation, turning by the angle Φ2. Again, D and theΦi are distributions of the actual movement, depending on the measured traveled distanced and rotations φi, respectively:
xt+1
yt+1
θt+1
=
xt
yt
θt
+
0 cos(θt + Φ1) 00 sin(θt + Φ1) 01 0 1
Φ1
DΦ2
(4.2)
Both models are equivalent in the deterministic case. Odometry is affected by differ-ent sources of errors, however, such as wheel slippage, limitations by the resolution ofencoders, or unequally worn-out wheels, to mention only some. In order to accountfor uncertainties, the transformations are treated as random variables. It is commonto assume Gaussian distributions for each rotational and each translational argumentin both models. For example, if φ1 is the first rotation derived from odometry, thenΦ1 ∼ N (µrφ1, σ
2rφ
21) is the distribution which expects the mean of the true rotation to
scale linearly with φ1 and its variance to scale with φ21.
Eliazar and Parr [63] argued that a more realistic representation should not only dependon the start and end angle of the robot. Speed variations and side shifts may also occurbetween two time steps. Therefore, they proposed a motion model which combineselements of the other two presented models (4.1) and (4.2):
xt+1
yt+1
θt+1
=
xt
yt
θt
+
cos(θt + R/2) − sin(θt + R/2) 0sin(θt + R/2) cos(θt + R/2) 0
0 0 1
DCR
(4.3)
37
CHAPTER 4 MODELING THE ROBOT
The idea is that the robot moves D units along a major axis at a global angle of θt+∆θ/2(down-range), while C expresses a potential simultaneous movement in perpendiculardirection (cross-range). R is the actual rotation that the robot has performed. Then,down-range D, cross-range C and rotation R are distributed according to (with r := ∆θ):
D ∼ N (dµDd+ ∆θµDr
, d2σ2Dd
+ (∆θ)2σ2Dr
) (4.4)
C ∼ N (dµCd+ ∆θµCr
, d2σ2Cd
+ (∆θ)2σ2Cr
) (4.5)
R ∼ N (dµRd+ ∆θµRr
, d2σ2Rd
+ (∆θ)2σ2Rr
) (4.6)
Here, µAbis the coefficient for the contribution of term b to the mean of the distribution
over A [63]. Analogously, σ2Ab
stands for the contribution of b to the variance of A.
4.2.2 Calibration
The probabilistic frameworks employed in this thesis require to calibrate model param-eters. The inappropriate estimation of motion model parameters would result in inferiorperformance when localizing the robot: Underestimating motion noise can lead to incon-sistent pose estimates and filter divergence. If motion noise is overestimated, this willdecrease accuracy or require more particles to achieve comparable precision.
Calibration can be performed manually by collecting a series of measurements, com-paring measured and actual movements. This procedure can be cumbersome. In lit-erature, one often finds heuristic choices of parameter values, too (e.g., [158, 219]).They often work surprisingly well. As pointed out in Section 2.2.2, however, the per-formance of particle filters depends on the proposal distribution. Thus, finding realisticparameter values justifies the efforts. Eliazar and Parr [63] developed an expectation-maximization (EM) method for calibrating the motion model automatically: The E-stepapplies DP-SLAM 2.0 [62], a particle filter-based grid mapping algorithm, and computestrajectory hypotheses for a given set of motion model parameters. In the M-step, the mo-tion model parameters are derived in a least-squares fashion, assuming the Gaussian dis-tributions (4.4)-(4.6). This EM procedure is started with a coarse estimate of parametersand is iterated until approximate convergence.
In this thesis, we follow the approach by Eliazar and Parr [63]. Figure 4.3 visualizesthe motion model that was learned for the B21 robot. We simulated the propagation of200 particles. As can be seen, position uncertainty – without exteroception – increasesover time. Especially noisy rotations reveal major impact on the final odometric position.The motion model learning technique seems to slightly overestimate odometric errors.But in some experiments we actually observed rare outliers in the reported odometric ro-tation, which are then captured better by the learned large variance of the motion model.
38
4.3 MODELING RFID DETECTIONS
y (
m)
x (m)
SamplesSimulated path
-2
0
2
4
6
8
10
-8 -6 -4 -2 0 2 4 6 8
FIGURE 4.3: Learned motion model for the B21 robot
4.3 Modeling RFID Detections
Many applications building upon RFID systems require models which describe RFIDdetection behavior. By such an RFID sensor model, we mean a qualitative or, better,quantitative description of tag detection rates (also called read rates) or radio signalstrength. Detection rates are defined by the ratio of successful reads by the numberof read attempts or by the inquiry duration, depending on the type of RFID reader (cf.Section 3.2.2).
As concluded in Chapter 3, the most relevant model parameters are the relative dis-
placement between reader antenna and transponder as well as the transmission power orother reader parameters. A sensor model will be required for mapping and localizationapproaches with mobile robots such as the ones presented in Chapters 5 and 6. But itis also useful for applications beyond robotics: For example, the placement of readerscan be optimized for maximal coverage of a stock, or the placement of transponders ongoods can be improved with regard to detectability [108].
In Section 4.3.1, we classify related modeling approaches. Thereafter, starting in Sec-tion 4.3.2, we present our approach which permits to learn an RFID sensor model auto-matically with a mobile robot and with little user intervention.
Let us first fix some notations and show how the smoothing methods from Section 2.1can be applied to learning RFID sensor models: Let a and l be the global poses of anRFID antenna on board the robot and of an RFID label, respectively, with respect to aglobal frame of reference. Let x = lj ⊖ ai ∈ R
d be the relative pose of some tag withrespect to some reader antenna. Then, an RFID sensor model is a function
q(x, ω) : Rd × Ω → R
m (4.7)
which relates an m-dimensional target value to the d-dimensional relative displacementbetween tag and reader antenna and further non-geometric model parameters ω in some
39
CHAPTER 4 MODELING THE ROBOT
parameter space Ω. Typical detection rate models (e.g., [96, 247]) assign a detectionrate to a 2D relative position such that m = 1 and d = 2. Signal strength models oftencomprise mean and variance of the predicted power for a 2D position, so m = d = 2.This probabilistic perspective leads to a useful alternative view: Detection characteristicscan also be represented by a likelihood function
p(q |x, ω) (4.8)
which models the conditional probability of a measurement q ∈ Rm given position x
and other parameters ω.If q(x, ω) : R
d×Ω → [0, 1] models detection probabilities, then µ := p(q = 1 |x0, ω0)represents the probability of detecting some tag (at all) in an inquiry, for some fixed x0
and ω0. In this case a is Bernoulli-distributed:
p(q |x0, ω0) ∼ Bern(q |µ) = µq(1 − µ)1−q, q ∈ 0, 1 (4.9)
Given N0 observations y1, . . . , yN0 with yi ∈ 0, 1, i = 1, . . . , N0, the maximumlikelihood estimator for µ is:
µ = E[q] =1
N0
N0∑
i=1
yi (4.10)
Consequently, the methods from Section 2.1 (cf. Equation (2.2) on p. 7) can be appliedto estimate µ locally.
In the more general case that q(x, ω) models signal strength or detection frequen-cies per time interval (which means that observations yi are real-valued rather than bi-nary), the regression techniques from Section 2.1 can be utilized to learn q(x, ω). Then,p(q |x, ω) is often modeled by a Gaussian distribution with mean E[q |x, ω] and corre-sponding variance of the observations.
4.3.1 Related Work
In order to structure RFID modeling approaches, we have collected the classificationcriteria listed in Table 4.1. Rather than forming a taxonomy, the criteria describe differentaspects of related techniques. The presented survey covers passive UHF RFID quiteexhaustively, but we also refer to related research into active UHF RFID.
The most important aspect of an RFID sensor model is the modeled variable. A modelcan either capture tag detection events or signal strength, depending on the type of RFIDstandards and RFID reader. Active RFID (WiFi, Bluetooth, ZigBee etc.) and some newerpassive RFID readers supply signal strength data for transponder detections. ISO 18000-6C standard passive readers report only detection events. They can be represented on thebasis of either single inquiries (such that the model captures tag detection probabilities)or time intervals (such that detections per time are measured).
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4.3 MODELING RFID DETECTIONS
TABLE 4.1: Classification of RFID modeling approaches
Criterion Instances and references of examples
Modeled variable
• Detection rate per time [249]• Detection probability per inquiry [6, 14, 16, 47, 96,
119, 164, 170, 195, 198, 258]• Signal strength [50, 119, 125, 132, 200]
Frame of reference • Reader antenna [16, 47, 96, 119, 200]• Global coordinate system [11, 119, 217, 249]
Model derivation• Based on physical theory [47, 132, 164]• Empirically learned [16, 61, 78, 96, 119, 200, 247]• Heuristic [169, 170, 172, 195]
Representation of themodeled variable
• Discrete [6, 96, 195, 264]• Continuous [47, 78, 119, 200, 247]
Treatment of uncer-tainty
• Deterministic model [167]• Probabilistic model [78, 96, 119, 200]
Calibration efforts • Manual measurements [61, 247, 258]• Automation [108, 119, 247]
Dimensionality• 1D (distance [258] or bearing [78, 127, 128, 263])• 2D, i.e. planar (virtually all other related works)• 3D, i.e., all three room dimensions [108, 132, 164]
Next, the geometric parameters of the model (usually the location of an RFID tag)can be represented relative either to a global frame of reference or to a reader antenna.Distributions of the modeled variable over a global coordinate frame are forms of loca-
tion fingerprinting. We will pick up this perspective in Chapters 6 and 7. Here we focusrather on sensor-centric models, i.e., the variable is modeled relative to an RFID antenna.
RFID models in literature considerably differ in how the model is derived. Somearticles aim at analytically modeling the propagation of the radio signal (e.g., [47, 164]).They typically dispose variants of the radar equation or of the Friis free space equation:
Pr =PtGtGrλ
2
(4π)2d2(4.11)
The received power Pr depends on the transmitted power Pt, the antenna gains Gt, Gr
of transmitter and receiver, as well as on wave length, λ, and – of capital importance forlocalization purposes – on the distance d between transmitter and receiver. One has tonote that (4.11) is valid for ideal radio propagation. It does not account for real-worldinfluences such as multi-path effects, diffraction, absorption etc. and breaks down forsmall d. Moreover, the formula is only applicable if the detection range of current RFIDsystems is mainly limited by the power reaching the transponder. According to Nikitin
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et al. [185], however, this assumption is reasonable. In RFID reader-limited systems, theradar equation has to be used (see e.g., [164]), which also includes the propagation of thereflected signal back to the reader antenna such that Pr ∝ 1/d4. For technical details, werefer the reader to [66, 185]. An overview of propagation models is given in [145].
Other approaches, such as ours, learn a model empirically from reference measure-ments. Employed estimation methods range from binning [119, 247] to Gaussian pro-cesses [119, 200].
Finally, some researchers heuristically model tag detections based on known techni-cal/physical properties or prior experiments. Examples are the fuzzy logic models byMilella et al. [169, 170, 172] or the attenuation scaling by Ota et al. [195].
Physically founded models have two major advantages: They can be described com-pactly and stored efficiently, using few formulas and constants. The second advantageis that the constants – if not known from technical specifications – can usually be cal-ibrated by fitting the general model to a small number of measured samples. On theother hand, it is virtually impossible to analytically model all relevant aspects of radiopropagation. That is why it is often easier and more effective to record measurementsand empirically learn the models. Entirely learned models can adequately capture real-world properties of the sensor, including observed noise. Yet, they may require a largenumber of prior measurements. According to literature, even the simple heuristic modelsyield surprisingly accurate mapping or localization results [96, 172]. They are, however,oversimplified or lack a prescription how to choose decisive parameters.
Sensor models further distinguish by whether the modeled variable is represented in adiscrete or a continuous fashion. Discrete representations mostly occur if the model hasbeen derived empirically. For instance, Hähnel et al. [96] described the probability ofdetecting an RFID tag by three areas for which the probability was assumed constant. Inopposition, continuous representations stem from analytic forms or typically Gaussianapproximation of detection behavior. For example, Germa et al. [78] presumed a 1DGaussian distribution of detection likelihood depending on the bearing towards a detectedtag.
An often chosen variant of discrete representation – mostly with short-range RFID –is proximity: The read range of a transponder is described by a circle or other sharplyconfined region representing a close area inside which the tag can (always) be detected.This model is particularly reasonable if transponders on the floor explicitly mark places.Proximity is also a classical example of a deterministic sensor model. As documented inChapter 3, however, passive long-range RFID is subject to various sources of noise. Con-sequently, probabilistic models are more promising. In the style of (4.8), they incorporateprobability distributions of the target variable, conditioned on the model parameters.
Robots permit to automate the calibration/learning step. The degree of automationranges from complete human intervention (e.g., [247]) via semi-automation [96, 247] tofully automatic nonparametric learning [119]. Besides these examples from the field ofmobile robotics, Hodges et al. [108] decided in favor of a robotic manipulator, whichprecisely positioned a tag with respect to an RFID antenna.
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4.3 MODELING RFID DETECTIONS
The last major classification criterion is the dimensionality of the model, i.e., thenumber of model parameters. In most cases, the sensor model is learned for a num-ber of Cartesian room dimensions or angles. Examples are 1D models depending ondistances [258] or the bearing [78, 171] to transponders. 2D models, which constitutethe majority of models, typically cover the displacement between reader antenna and tagalong the x and y axes. In other cases, the model can also include nongeometric factorssuch as the reader configuration. In the work by Ota [195], for instance, the specifiedattenuation of the transmission power is taken into consideration.
4.3.2 Semi-autonomous Learning Approach
Our approach to modeling RFID detections is to learn a detection rate function q(x)from empirical data. This view is very similar to [96, 164], but our approach is able toquickly acquire a model with a mobile robot by means of nonparametric regression. Theproposed method is supposed to operate on RFID detection counts, but the extension tosignal strength values is straightforward. We published an earlier version of our modelingtechnique in 2008 [247].
The robot traverses the environment during some kind of exploration stage, eithercompletely autonomously or manually steered. During exploration, the robot recordsRFID detection statistics for several RFID labels simultaneously, as indicated in Fig-ure 4.4. Additionally, it logs reference locations. From these recorded data, the sensormodel function is derived in the steps as detailed below. During exploration, laser-basedMonte Carlo localization [74] provides accurate positioning at an error of few centime-ters (< 10 cm on average).
The robot must be equipped with a handmade list of transponder positions. The de-tection characteristics are learned for and averaged over these tags. Any kind of tagarrangement can be chosen, which should be similar to the way in which transpondersare installed also in the target scenario. It is this list of tag locations which makes the pre-sented approach only semi-autonomous. However, the positions of a few tags distributedin a small area can be measured quickly.
Data Preprocessing: Suppose a sensor model is to be learned for d-dimensional inputsrepresenting the relative positions of tags with respect to a reader antenna. For thesedimensions, coarse bounds (i.e., the domain) X ⊂ R
d for which the model is to belearned, have to be pre-specified. For example, if D is the coarse maximum read rangeof the reader in meters and a 2D sensor model is to be learned along the x and y axes, itis reasonable to set X = [−0.5, D]× [−D/2, D/2]: The choice of the x range is becausethe antenna scans along the x axis and is sometimes able to detect some transponderseven behind the antenna (although shielded). The choice of the y range follows from thesymmetry of the detection field. For each time step t, for which sensor data have beencollected, for all antennas a = 1, . . . , A and for all tags l = 1, . . . , L with known global
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ExplorationRFID measurementsand referencepositions
Tag map
Model generation
Sensormodel
look−uptable
Preprocessing Parameteroptimization
Regression on entire dataset
h
RM
SE
FIGURE 4.4: Overview of the stages for learning a sensor-centric RFID model
position, we compute xt,a,l = ll ⊖ at,a. This is a tag position relative to an antenna attime t. If xt,a,l ∈ X , we accept the training sample (xt,a,l, yt,a,l), where yt,a,l states howoften tag l was detected with antenna a at time step t when recording the data. This setof accepted raw samples only contains relative detection positions and (integer-valued)detection counts. From now on, we will ignore the identities of tags and antennas; wewill model by averaging over tags of the same type.
Thereafter, we – optionally – apply binning as described in Section 2.1.1: This leads toa considerable reduction of the number of samples and speeds up further computations.Moreover, other regression techniques not described in this thesis would benefit from thefact that the new set of training data are unambiguous for each bin. A suitable bin sizeis found adaptively: We optimize for approximation quality and the number of trainingsamples to be obtained:
1. For w = 0, 1, . . . , wmax, we set the grid cell size b := 2−w. Samples are assigned tothe resulting grid cells. The number of grid cells Nρ
b is counted which approximatea bin value with a predefined resolution ρ (or, equivalently, each grid cell containsat least ⌈1/ρ⌉ raw detection samples).
2. The grid cell size b∗ is chosen such that the number of grid cells with sufficientnumber of samples is maximal, that is, b∗ = argmax
bNρ
b .
Finally, binning is applied with bin size b∗. The result of the preprocessing stage is aset of training data (xi, yi)1≤i≤N ⊂ X × R. The xi are the centers of bins, and the yi
are the (real-valued) binning estimates for each corresponding bin, provided that the bincontains enough (≥⌈1/ρ⌉) raw detection samples.
Model Regression: The model regression step takes the preprocessed samples (xi, yi),i = 1, . . . , N , as training data and applies one of the regression techniques from Sec-tion 2.1. In order to optimize the corresponding smoothing parameters, cross-validationis performed as described in Section 2.1.4. Note that if the model is learned for d > 1
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4.3 MODELING RFID DETECTIONS
dimensions, it suffices to tune only one bandwidth for Cartesian position dimensionsand only one bandwidth for orientations. The reason for this is that the sensor modelfunction can be assumed to behave similarly for x, y and z directions as well as for allrotations. Once the error-minimizing smoothing parameters have been found, regressionis repeated using the entire training data in order to approximate q(x).
Additionally, we compute an estimate q0 of the chance of accidentally detecting anRFID tag beyond the assumed effective read range X . All samples discarded during thepreprocessing step contribute to the estimate
q0 =
∑
xt,a,l 6∈X yt,a,l∑
xt,a,l 6∈X 1. (4.12)
Model Storage: The approximated function q(x) is evaluated at fixed positions of afine-grained grid and stored as a look-up table. By this, q(x) is only approximated, butthe efficiency of evaluating the sensor model function on-line is increased. The predic-tion complexity is O(1) rather than a complexity of O(N) linear in the number N oftraining samples. The grid resolution is chosen fine enough such that the neighboringsubsampled target values do not deviate too much. As of our experiences, one percent ofthe maximum read range D of the RFID antenna is a well-justified choice.
For the case that the sensor model q(x) represents the expected number of tag detec-tions per time and p(q |x) is modeled by a Gaussian, we further compute the variance ofthe training data at x.
4.3.3 Experiments
We applied our approach from Section 4.3.2 to various configurations. The goal wasto acquire models for the two RFID readers from Section 3.3, based on raw detectiondata. The experiments were conducted in our robotics lab (see Section A.1). There weattached RFID tags to walls and furniture around a traversable area of approx. 50 m².
Learning Detection Probability Models
The first series of experiments concerns modeling detection probabilities and was con-ducted using the ALR-8780 RFID reader. Recall that this reader receives inventory re-quests and returns a list of tags which have been detected during the inquiry. A sensormodel for this reader is a function q(x) : x → [0, 1], where q(x) = p(1 |x) and x is therelative displacement of a transponder w.r.t. to an RFID antenna.
As a reference, we first recorded a model manually and placed a carton pole at dif-ferent positions relative to a static RFID antenna. For each of 195 grid points (6× 7 m,0.5 m resolution) in the room and four different heights (0-1.2 m) and four orientations
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FIGURE 4.5: LEFT: Manually recorded sensor model. RIGHT: Learned model using
k-nearest neighbors regression. (ALR-8780, 2 W transmission power)
in 45° steps, 100 measurements were taken. The result is shown in Figure 4.5 (left). Val-ues between grid points were interpolated linearly. Preparing and recording this modelrequired approx. 50 hours.
In opposition, we examined the semi-autonomous approach. As a first dataset, we re-corded 3783 inquiries in 2915 s, while the robot was travelling 355.6 m through the labat an average velocity of 0.12 m. In this case, 15 transponder positions were provided.These tags had been attached to room equipment coarsely at the height of the upperRFID antennas of the robot. For the ranges x ∈ [−0.5, 7], y ∈ [−4, 4], this configurationresulted in 322,266 raw training samples, where symmetry around the x axis was as-sumed. The preprocessing step with a specified binning precision of ρ = 0.1 (wmax = 7)automatically selected a bin size of 0.0625 m. This yielded 8424 preprocessed trainingsamples after binning.
The preprocessed samples were smoothed using k-nearest neighbors (k-NN) and ker-nel regression. The k-NN result is shown in Figure 4.5 (right). Note the obvious dif-ferences to the manually recorded model in Figure 4.5 (left), in which RFID labels aredetected more often. Reasons for these discrepancies are: (1) The hand-crafted modelwas recorded subject to almost ideal free-space conditions. The tags were attached to car-ton, which is electromagnetically neutral to UHF radio waves. In the semi-autonomousexperiment, transponders were mounted close to different materials, including metallicpipes. (2) The tag density was higher during the semi-autonomous experiment. Thisdecreases detection rates, as shown in Section 3.3. (3) The semi-autonomously learnedmodel uses a quite, but not perfectly accurate reference positioning system. This intro-duces minor aliasing (uncertainties in the relative tag locations of the training data).
Figure 4.6 shows the models which were learned for the ALR-8780 reader on boardthe B21 at full transmission power level, using different kernel types. The bandwidth h ofeach kernel was automatically selected using cross-validation, where the h was chosenfrom 0.1, 0.2, 0.3, 0.4, 0.5, 0.6. As can be seen, the results reveal slight deviations.The best visible differences can be observed beyond x ≥ 5.5 m, although there detection
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4.3 MODELING RFID DETECTIONS
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FIGURE 4.6: Comparison of 2D detection probability models using four different kernel
types. (ALR-8780, 2 W transmission power)
rates are approximately 5 % and rather negligible. Small deviations occur also close tothe antenna origin, at y = 0, x ≤ 0. This area, however, is inside the contours of therobot, right behind the modeled antenna, where it is virtually impossible to find an RFIDtag. So, apparently the choice of kernel type is not crucial in kernel regression.
All four plots feature a core mode of detection right in front of the reader antenna.Up to distances of approx. 1.5 m, a transponder can be detected at a probability of 0.5,given that it is located coarsely at the height of the upper RFID antenna of the robot.At a distance of 2.5 m, there is still a chance of 25 % of successfully reading a tag. Asecond mode of increased detection rates, although less pronounced, can be observed ata 3.5 m radius in front of the reader antenna. This belt-shaped region can be explainedby reflections of the radio waves at the ground. Note that using the Friis free spaceequation (4.11) would fail in predicting this second mode. A nonparametric regressionapproach can simply learn the actual detection characteristics.
The cross-validation errors depending on the choice of bandwidth are plotted in Fig-ure 4.7 (left). Each kernel reveals its individual bandwidth which minimizes the meansquared error of predicting new sensor model values on test folds. The RMSE valuesdo not differ much, though. Partly this is owed to the prior binning step, which alreadysmoothes the training data.
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CHAPTER 4 MODELING THE ROBOT
0.224
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tion tim
e (
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FIGURE 4.7: Cross-validation: LEFT: Errors depending on the bandwidths of investi-
gated kernel types. RIGHT: Prediction times per target value of all regression methods.
Figure 4.7 (right) depicts the time required for predicting a single target value. Ascan be seen, kernel type and bandwidth considerably affect prediction times, since thesmoothing methods are memory-based. For each query, a neighborhood search needs tobe performed. Regression with Gaussian kernels is significantly slower than the otherkernels because they have theoretically infinite support. In our implementation, we al-ready restricted the support region to ±3h.
Although a KD-tree keeps the training data (based on the ANN library [178]), kernel-based and k-NN predictions take one or several milliseconds (PC with Pentium D 3 GHz,one of two cores used, 2 GB RAM). This performance is acceptable for offline regression.For real-time regression, when several hundreds or thousands of predictions per secondare required, memory-based smoothing is too inefficient. This analysis illustrates theusefulness of the look-up table described above, with constant time look-up duration,independent of kernel type, bandwidths, and the number of training samples. This alsoholds for regression only by binning, which takes less than 1/50 of a ms, but can still bespeeded by the look-up table.
Influence of the Attachment Height of Transponders
The models so far were fed with the positions of transponders at the height (z coordinate)of the upper RFID antennas. This setting can be regarded as the special case of anenvironment which has been prepared with artificial landmarks in order to support thelocalization and navigation of the robot. In the general case, the robot may face RFIDtags which are located at entirely different heights. That is why in another experiment weextended the above setup to 64 tags at heights between 0.2 m and 2.1 m. These values canbe expected when objects in human environments are tagged (e.g., products in a shelf).
The resulting model is shown in Figure 4.9(b). It was approximated using a Gaussiankernel and cross-validation for determining the smoothing bandwidth. When compared
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4.3 MODELING RFID DETECTIONS
0.33
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FIGURE 4.9: Comparison of 2D detection probability models using transponders spread
over different height ranges: (a) Model based only on 15 transponders coarsely at the
height of the upper antennas of the RFID reader. (b) Model based on 64 transponders at
different heights between 0.2 and 2.1 m. (ALR-8780, 2 W transmission power)
to Figure 4.9(a), the detection rates decrease at every potential tag location. This isbecause the model averages over all detections; since more tags are situated further awayfrom the antenna scan axis, they are less likely to be read successfully. The second modeof increased detection rates due to reflections is less dominant. Apart from the reduceddetection rates, the shape of the model has not changed entirely. Still, we can see thatknowledge about the z coordinate may be required in order to adequately predict thefrequency at which a transponder will be read.
Table 4.2 lists statistics of the preprocessing step. Less than one hour of recordingRFID detections resulted in up to approx. two million training samples. The preprocess-ing step then considerably reduced the number of training samples, by more than 97 %with ρ = 0.1, in favor of faster regression thereafter, while preserving the underlyinginformation by binning. The involved adjustment of bin sizes took between 1.8 s for 2D
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TABLE 4.2: Preprocessing statistics and durations of cross-validations.
2D model, 2D model, 3D model,15 tags 64 tags 64 tags
Number of raw samples 322,266 1,410,226 2,242,582Number of preprocessed samples 8,424 36,462 32,860Optimized bin size 6.25 cm 1.56 cm 12.5 cmDuration of bin size optimization 1.8 s 5.5 s 17.4 s
Method Tested param- Duration of cross-validationeter range [hours:]minutes:seconds
Gaussian kernel h = 0.1, 0.2, 1:36 1:22:34 2:55:47Quartic kernel 0.3, . . . , 0.7 0:06 2:11 1:50Triangular kernel 0:08 2:08 2:12Uniform kernel 0:06 2:09 2:10k-NN k = 20, 21, . . . , 210 0:27 2:17 5:48Binning (no h = 0.05, 0.10, 1:20 14:35 19:39preprocessing) 0.15, . . . , 1.50
modeling with 15 tags and 17.4 s for 3D modeling with 64 tags.If we compare the bin sizes which maximize the number of samples, the optimal size
in 3D modeling is 12.5 cm, which is much larger than in the 2D case. So, despite thelarge amount of training samples, one can notice the curse of dimensionality in that thedensity of preprocessed samples decreases. In terms of uniformly spaced raw trainingdata, the density corresponded to one sample every 5 mm in 2D and only every 3.5 cm in3D. For adding another real-valued dimension/parameter to the sensor model, one wouldprobably have to measure longer, to increase the number of known RFID tags, or toexploit further assumed symmetries in the detection field. Another circumvention wouldbe to integrate the additional model parameter heuristically or analytically.
Table 4.2 also contains the durations required to perform parameter selection by meansof cross-validation (PC with Pentium D 3 GHz, one of two cores used, 2 GB RAM). Gen-erally, it is possible to adjust the smoothing parameters within seconds or few minutes,depending on the method. Due to the different types of smoothing parameters and reso-lutions of the grid search, not all regression times can be compared directly. Yet, againone can generalize that using the Gaussian kernel is too inefficient in presence of a largenumber of samples. Furthermore, all other approaches are fast, as compared to the num-ber of tested parameters and training samples, although not truly real-time capable.
Learning Detection Count Models
In the general case of an EPC-compliant RFID reader, detection counts per time interval
can be modeled. General detection count models comprise mean and variance of the
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4.4 CONCLUSION
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FIGURE 4.10: A model featuring mean (left) and standard deviation (right) of detection
counts, computed via k-NN regression (k = 256). (SR-113, 1 W transmission power)
observed rates. A 3D model, beyond the scope of 2D self-localization, is shown inAppendix C. Figure 4.10 illustrates the 2D result for the SR-113 reader, based on k-nearest neighbors regression (with k = 256). It was computed from 2975 RFID inquiriesand 15 known tag locations coarsely at the same height, which yielded 106,461 trainingsamples inside the detection area. The corresponding likelihood function for this case isa Gaussian distribution with expected mean and standard deviation as looked up in thelearned model at some query position.
4.4 Conclusion
Summary
In this chapter, we have modeled the robot. For odometry and RFID reader, we focussedon techniques which reduce human intervention.
The uncertainty of the robot’s locomotion was calibrated based on the automatic learn-ing approach by Eliazar and Parr. Their technique utilizes laser range data and odometryto iteratively deduce an environment map and refine the odometry parameters.
For modeling RFID detection rates, we pursued a nonparametric modeling approach.During an exploration stage, the robot records RFID measurements and reference po-sitions. Provided a manually recorded list of global transponder positions, the robotcan compute a model of RFID detection probabilities (or RFID detection counts). Aftera preprocessing step, regression techniques such as binning, k-NN regression or kernelsmoothing are applied to recover the mean (and the variance, if required) of the detectionbehavior. Our experiments showed that:
• The learned models were able to reveal insights to RFID detection characteristicswhich are difficult to predict analytically. Particularly, reflections at the ground
51
CHAPTER 4 MODELING THE ROBOT
plane and the impact of transponder placement (density/attached material) wereobserved.
• The regression methods differ significantly with regard to run time and degree ofsmoothness. Aside from the regression technique, the smoothness degree mainlydepends on prior binning and the selected smoothing parameter. Binning alone andk-NN regression are fast, while additional kernel regression provides smooth sen-sor models. Gaussian kernel regression was slow and yielded models very similarto the more efficient quartic kernel.
• Large numbers of training samples were easily generated for 2D and 3D modeling.The addition of further parameters may be subject to the curse of dimensionality.
Discussion and Outlook
We aimed at minimizing the necessity of human/heuristic interventions in order to obtaina mathematically sound machine learning method based on empirical data. Based on ourproposed approach [247], Joho et al. [119] showed that the transponder positions canalso be inferred automatically. They observed the convergence of tag location estimatesand the RFID sensor model when both were iteratively refined in alternating steps, givena very coarse, manually supplied sensor model.
As we observed, the addition of further (real-valued) model parameters might be dif-ficult and might require significantly longer training or analytic/heuristic interventions.For example, a reducible transmission power of the RFID reader could be modeled bydownscaling the expected detection rates learned at full power level. But adjustments ofthis kind can only coarsely approximate RF signal propagation and detection behavior.An alternative is to avoid sensor modeling where possible. This is one motivation for thefingerprinting approaches in subsequent chapters.
The primary reason of the time consumption of regression is the parameter selectionbased on cross-validation. An efficient kernel, however, permits to compute a modelwithin few minutes. The presented approach requires no human intervention during themodel computations. Human intervention is reduced to measuring a number of transpon-der positions and, if the robot does not provide a random walk or exploration behavior,steering the robot for a number of minutes.
Compared to manual calibration measurements, the utilization of a mobile robot in-troduces a few sources of uncertainties. However, we showed [247] that the quality ofmanually calibrated and autonomously learned models are comparable, measured by lo-calization accuracy in that case.
The proposed framework seamlessly integrates with the modeling of signal strength,which an increasing number of future RFID readers will be able to supply.
In the next chapter, we show how the learned tag detection likelihoods enable robotsto estimate the positions of detected transponders.
52
Chapter 5
Mapping
In this chapter, we present methods to map the positions of RFID tags, that is, to deter-mine the locations of transponders by means of the RFID reader on board the robot. Thedual case of locating the mobile RFID reader itself will be treated as self-localizationin Chapter 6. After an introduction in Section 5.1, we survey related literature in Sec-tion 5.2. Section 5.3 treats the general particle filtering framework for mapping. Ex-tensions by iterative estimation and by the fusion with spatial information are presentedin Section 5.4 and Section 5.5, respectively. In Section 5.6 we finally summarize anddiscuss this chapter.
5.1 Introduction
RFID-based mapping denotes the task of acquiring a spatial model of the transponderarrangement in the environment. This definition follows the classical view of roboticmapping using other types of sensors [236]. Beyond robotics, the issue is more generallytermed localizing RFID tags, with the understanding that this is achieved by means ofone or several RFID readers whose antenna positions are known.
We treat the case that the positions of RFID labels are inferred from a series of RFIDdetections as observed by the on-board antennas of a mobile robot. By detecting tagsfrom different positions and headings of the robot, it is possible to determine tag locationsin some fixed frame of reference. The resulting map can serve as a reference for RFID-based localization, which we deal with in Chapter 6. Besides, transponder locationsaugment the pure information of the presence of tagged objects by location information.Mobile robots can be used to inventory buildings with tagged products, supermarkets forinstance, and maintain an up-to-date database of object positions. Other purposes are wayfinding, based on RFID tags as navigation stimuli, or user guidance to labelled targets.Of course, it is also possible to run mapping on other types of vehicles such as forklifters.This would permit to locate palettes in real time using commercially available platforms(see [4, 120]). Inventory applications demand accurate position estimates, efficiency, andthe possibility to process a large number of transponders.
In this chapter, we assume that the robot is equipped with an RFID sensor model(cf. Section 4.3). Moreover, the robot must know its position while mapping. Therefore,
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CHAPTER 5 MAPPING
we further presume that accurate pose estimates are contributed either by a referencelocalization system (e.g., laser-based Monte Carlo localization [74]), by some SLAMapproach (e.g., FastSLAM [97]), or by trajectory estimation as described in Chapter 7.
In particular, we can classify the RFID mapping problem as follows: We understandit as an instance of landmark-based, geometric mapping: The result is a list of transpon-der positions in metric coordinates, where transponders can be regarded as landmarks
(distinguishable environment features). The mapping process itself is passive: It merelyobserves and does not define targets where to record measurements in the environment.Furthermore, one can distinguish between online and offline mapping: Online mappingapproaches provide tag position estimates instantly at any desired point in time while re-ceiving sensor data, offline mapping approaches only after completing the measurementsby batch-processing the entire collected data set. Our proposed techniques presentedsubsequently are mostly capable of real-time estimation with any-time estimates, but of-ten process the entire data of a single tag at once. We finally focus our attention to thestatic mapping case, assuming that transponders are not relocated while being detectedby the robot.
Robotic mapping in general is a long-studied and important field: Truly autonomousoperation requires the robot to explore and understand its environment on various levels,which extends from pure geometric representations to semantic labeling. For overviewsof robotic mapping in general, we refer to [236, 239]. In the context of mapping, thecommon estimation techniques rely on particle filters and Kalman filters, combined withsophisticated feature matching methods. The classical sensors for mapping are laserrange finders and ultrasonic sensors as well as stereoscopic, monocular, or omnidirec-tional cameras. In opposition to passive RFID, these sensors require feature extractiontechniques to recognize single objects, but usually provide rich geometric data in theform of distances or bearings.
5.2 Related Work
Mapping stationary tags by means of mobile antennas on a robot, as pursued in this the-sis, is one special case of localizing RFID transponders by means of RFID readers withknown positions. An often chosen, yet more expensive setup is to locate transpondersby a number of distributed RFID readers in the environment. One example is the oftencited “smart shelves”, which are equipped with readers to determine the set of currentlycontained tags, as proposed by, for instance, Gryazin and Tuominen [93].
5.2.1 Proximity-based Tag Localization Using Static Antennas
The simplest and coarsest solution to determine the position of a tag is based on proxim-ity: The tagged near object is associated with the known position of the detecting RFIDantenna. Typical examples are activity recognition systems such as the one by Hong
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5.2 RELATED WORK
et al. [110] at room-level accuracy or by Ohsawa et al. [188] by means of shelves withRFID readers. Chou et al. [40] presented an object locator which helps to find misplacedobjects using RFID interrogators spread in a building. They achieved an accuracy of2-3 m, the range of the interrogators. The SixthSense system by Ravindranath et al. [204]inferred object ownerships and interactions by observing movements of RFID tags alongseveral read points. They described places qualitatively, i.e., by the antenna which isdetecting the transponder. Related works by Kleiner et al. [130, 131] and Tanaka [233],who mapped the positions of proximate transponders only by estimating relative dis-placements between them, will be described in Chapter 7.
Since ISO-compliant readers do not necessarily report signal strength, a single tagdetection with a static antenna typically does not provide much more information thanproximity1. If signal strength information is available, if detections are counted per timeinterval, or if the power level of the RFID antenna can be adjusted, then the distanceto the stationary RFID antenna can be estimated. An example is the work by Wilsonet al. [258], who related distances to antenna attenuation. Ravindranath et al. [204] alsodetected movements within read range by means of signal strength.
5.2.2 Finer-grained Tag Localization Using Several Static Antennas
Several RFID antennas whose detection areas intersect permit to refine the position es-timate of a transponder. Alippi et al. [6], for instance, used multiple static UHF readerswhose antennas were rotated and whose power levels were varied. The authors reportedmean errors of approx. 0.65 m in an environment of size 5 m × 4 m and with four readerstransmitting at 0.1-3 W.
Other researchers proposed to improve position estimates by calibration against refer-ence tags at known locations [38, 240, 251]. This strategy allows for mapping withoutexplicit, a priori acquired sensor model and compensates for variations in detection be-havior due to the propagation of electromagnetic fields. The resulting accuracy, however,depends basically on the density of reference transponders, which need to have been lo-cated precisely beforehand. Chawla et al. [38] reported errors of 0.15 m. In the LAND-MARC system by Ni et al. [184], several tags were localized by a number of readersand a grid of surrounding reference tags. They investigated the influence of the numberof readers, the influence of the environment, and the influence of number and placementof reference tags. Wang et al. [251] presented simulation results for localizing tags in3D using several static antennas: They built upon a grid of reference tags in the ceilingwhose detections were compared to the detection of the target tag to be localized. Thetransmission power of the readers was gradually increased until the target tag could bedetected. The target location was estimated in a least squares fashion.
Hekimian-Williams et al. [100] mounted UHF antennas on a pan-tilt unit. With a soft-
1Besides the uncertainty distribution which is given by a probabilistic sensor model as introduced in theprevious chapter, of course.
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CHAPTER 5 MAPPING
ware-defined radio, they predicted the phase difference of the reflected tag signal at anaccuracy of better than 3. Zhang et al. [263] obtained similar simulation results.
An entirely different approach was taken by Lieckfeldt et al. [156]: They compareddifferent techniques to estimate the position of a person based on the noise (“RF scatter”)that was observed due to obstructed transponders. A signal strength model of the roomwithout user presence served as reference.
By means of a grid pattern of five movable short-range antennas, Hinske et al. [105,106] determined position and orientation of objects with multiple HF tags in a tabletopgame. They achieved an accuracy of a few millimeters.
Bouet and Pujolle [30] localized tags in 3D by intersecting read ranges. They reportedaccuracies of 0.15-1.6 m, simulating four surrounding readers at distances of 2-6 m.
Another option for locating RFID tags is to use several more distant, static readerswhose read ranges do not intersect. This way, it is possible to track mobile tags overtime. Kanda et al. [124], for instance, localized people wearing RFID tags along severalread points in a museum by trajectory filtering. They relied on 20 RFID readers, variedthe attenuation of the readers, and integrated the measurements with a human motionmodel in a particle filter. The resulting mean error was 2.8 m.
5.2.3 Mapping Using Mobile Antennas on Robots
Instead of placing multiple RFID antennas in different fixed positions, mobile robotspermit to map transponder locations by moving antennas to different measurement posi-tions. By integrating several observations over time, tag positions can be refined.
A group of RFID mapping approaches using robots assumes UHF transponders to belocated to the sides of free space, attached to walls and assets. This setup is the onepursued in this thesis, since it is the least special one and can be expected in futurestorehouses and supermarkets. To this end, researchers often rely on variants of particlefiltering [47, 96, 119, 169, 170, 171, 172] or probability grids [111, 162, 195]. Theirsolutions mainly differ in how RFID detections are modeled (for details see Chapter 4.3)and how reference positions are obtained (typically laser-based SLAM or Monte Carlolocalization). Accuracies range approx. from 0.3 m to 0.8 m, but the certainly relevanttransmission power level has not always been reported.
Among these approaches, Hori et al. improved the mapping accuracy in simulationby lowering the transmission power once a tag had been detected [111]. Using an HFRFID reader in a library scenario, Ehrenberg et al. [61] achieved an accuracy of 1 cm andwere able to correctly determine the book order for books of a minimum width of 2 cm.Germa et al. [78] combined RFID measurements and visual people detection in a particlefilter: Their robot was equipped with eight RFID antennas for omnidirectional scanning.The fused detections enabled the robot to follow the tracked person, using customizedmotion control laws.
Liu et al. [162] located a transponder from a resource-constrained mobile device usinga heuristic, conservative detection rate model: They compared probability grids and the
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5.2 RELATED WORK
deterministic intersection of read coverage regions. They were able to detect objectswhich had been shifted by more than 0.2 m. An extension of this system with stationary,but rotatable antennas was presented in [182].
Patil et al. [198] mapped passive UHF tags using an upwards-pointing directed an-tenna on a robotic vacuum cleaner. Tags were fixed at a height of 1.5 m, for which a90 % detection probability within a circular region was known. The locations of the tagswere computed deterministically by averaging or bounding the places from where thetransponders were detected. Reference locations were obtained by a WLAN positioningsystem (mean error 2.5 m or worse). The mapping accuracy was 1.2-3.3 m.
Despite the non-Gaussian character of a passive-RFID detection field, Miller et al.
[173] applied Kalman filtering to mapping passive transponders with a mobile robot.Attached to card board boxes and plastic bins, UHF tags were located with mean errorsof 0.65-0.87 m.
A number of articles deal with localizing active RFID tags by means of nonparametricfilters or Kalman filters [50, 51, 125, 133, 146]. This class of approaches are instancesof range-only mapping, since distances can be estimated from signal strength informa-tion. Kloos et al. [133] attached multiple active transceivers, which were connected toa server, to a mining truck and tracked persons with transceivers using particle filters.Gräfenstein et al. [85] exploited the anisotropy of a rotating antenna on a robot. Angle-dependent signal strength values allowed them to localize static nodes at an accuracy ofapprox. 0.15 m. Note that in the context of active RFID mapping and localization arerarely distinguishable, as the communication of active nodes is symmetric.
5.2.4 Fusion and Other Approaches
Milella et al. [171] fused RFID and vision to determine the bearing of RFID tags withoptical marker patterns. They used a fuzzy sensor model, estimated tag positions via afuzzy variant of particle filtering, and achieved a mean error of 5.4. Deyle et al. [48]generated image-alike signal strength maps by means of a robot-mounted rotatable UHFantenna. This representation was supposed to allow for fusion with laser or especiallymonocular camera images. Tagged objects could be found at spots of high likelihood inthe fused images. Raskar et al. [203] proposed to locate RFID tags by emitting struc-tured light. The sensed light pattern was to be decoded and replied by a photosensingtransponder to determine its bearing with respect to the light source. A fusion of RFIDand stereovision for transponder mapping was proposed by Zhou et al. [266]. They de-signed special transponders which had to be activated via a laser beam. Finally, Schulzet al. [220] combined different types of sensors to track people indoors. They fusedthe observations of several static laser range finders, ultrasonic receivers and ID-codinginfrared badges in a Rao-Blackwellized particle filter.
Roh et al. [207, 208] proposed to estimate the pose of an object by several orthogonallyaligned transponders. Cerradar et al. [36] optically localized objects in the camera image.Prior RFID detections allowed them to narrow down the search space of visual features
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CHAPTER 5 MAPPING
to identify objects in the scene. Schönegger et al. [218] proposed to compute the positionof an RFID tag relative to two antennas: They intersected the read ranges of the antennaand evaluated the measured RSS values. Bohn [24] mapped HF tags on the floor: Heused a reference positioning service on a mobile device to write the positions to tags.Positions were averaged and rewritten whenever the mobile device revisited a tag.
Other relevant works are those in which transponders are mapped and the robot islocalized simultaneously. These approaches will be detailed later in Chapter 7.
5.3 Probabilistic Mapping Using Particle Filters
5.3.1 Probabilistic Tag Location Estimation
Because of the inherent noisiness and position uncertainty of RFID measurements, weadopt a probabilistic perspective in order to determine the locations of transponders.Formally, let us denote the number of RFID labels in the environment by L. The datarecorded during the mapping stage consist of a sequence f1:t = f1, . . . , ft of RFID
detections up to time t. Each measurement ft = (f(1)t , . . . , f
(A)t ) at a time step t comprises
the readings at the A reader antennas. For each antenna a, the measurement representsa vector f
(a)t = (f
(a)t,1 , . . . , f
(a)t,L ), where f
(a)t,j ∈ N counts how often tag j was detected by
antenna a at time step t. The history of locations x1:t = x1, . . . ,xt where the robotread the RFID tags be given, too. Furthermore, aa(xt) be the global antenna pose ofRFID antenna a, given a pose xt of the robot.
Estimating the location lj ∈ Rd of some tag j requires to compute the conditional
density p(lj |x1:t, f1:t). Typically d = 2 and lj = (xj, yj). We rewrite this density by:
p(lj |x1:t, f1:t) =p(ft |x1:t, f1:t−1, lj)p(lj |x1:t, f1:t−1)
p(x1:t, f1:t)(5.1)
=p(ft |xt, lj)p(lj |x1:t−1, f1:t−1)
p(x1:t, f1:t)(5.2)
= ηp(lj |x1:t−1, f1:t−1)A
∏
a=1
p(f(a)t | aa(xt), lj) (5.3)
= ηp(lj |x1:t−1, f1:t−1)A
∏
a=1
p(f(a)t,j | lj ⊖ aa(xt)) (5.4)
In (5.1) we utilized Bayes’s theorem and in (5.2) the Markov assumption. In (5.3) wereplaced the denominator by a normalizer η−1 and split the measurement ft into read-ings for each antenna, assuming independence. Finally, in (5.4) we made the furtherassumption that detecting tag j is independent of all other tag detections. The ⊖ operatorcomputes the position of the tag relative to the antenna pose. Note that the three inde-pendence assumptions are strict. Technically, RFID detections can be correlated over
58
5.3 PROBABILISTIC MAPPING USING PARTICLE FILTERS
Area of high
likelihood
-4
-2
0
2
4
6
8
10
6 8 10 12 14 16 18 20
y (
m)
x (m)
True tag position
-4
-2
0
2
4
6
8
10
6 8 10 12 14 16 18 20
y (
m)
x (m)
True tag position
FIGURE 5.1: Filter initialization approaches. LEFT: Simplified illustration of the sam-
pling idea: In each distinct detection position, samples are drawn according to the rates
predicted by the RFID sensor model and transformed to the coordinates of the detect-
ing RFID antenna. Samples finally cluster in areas of high likelihood, where detection
ranges intersect. MIDDLE+RIGHT: Example results for 100 particles, once obtained
using uniform sampling around the first detection position (middle) and once by sam-
pling based on a series of tag detections (right). The actual tag position is marked with
a cross. The circles are the uniformly weighted initial particles.
time, among each other (due to effects of transponder density), and antenna ranges mayoverlap. We expect, however, that these correlations have minor impact and are partlycompensated by the sensor model p(f
(a)t,j | lj ⊖ at), which was learned under similar pre-
conditions.
The resulting formula (5.4) allows for the recursive estimation of tag positions by therepeated application of the sensor model. We employ particle filtering for this purpose.Model-based mapping with a particle filter was first realized by Hähnel et al. [96]. Webuild upon their seminal work. Besides the often proven properties of robustness andaccuracy, our filter choice is predicated on the applicability of arbitrarily shaped sensormodels, the possibility to also incorporate motion if desired, and efficiency by filteringonly in likely areas of the location space. We will make use of the latter two aspectswhen we devise significant performance improvements in the next sections.
Each transponder position is estimated by an individual particle filter. In the staticmapping case, there is no transition model (and hence no resampling), but it can beintegrated for tracking in a straightforward manner (examples are [78, 220]). The taglocation prior p0(lj) := p(lj |x1:0, f1:0) is the initial distribution according to which theparticle filter is initialized. In the next section, we will compare possible priors.
To extract the pose lj from the sample set, there are different options [151], among
which we favor the common weighted mean of sample positions: lj =∑Ns
i=1 w(i)x(i).Our choice is based on the statistical soundness of this estimator against particle filteringas introduced above. Moreover, one can typically expect a unimodal distribution of thetag location belief after few filter iterations, as can be seen in [96, 119].
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CHAPTER 5 MAPPING
5.3.2 Filter Initialization
The most common strategy is to initialize the particle filter upon the first detection of theRFID tag [96, 119]. Due to the uncertainty of a single observation, a large number ofparticles are sampled uniformly from a disk around the position of the detecting antenna.Its radius equals the maximum read range. Hähnel et al. [96] even chose the center ofthe circle to be the center of the robot, because they sometimes observed false-positivedetections in that the wrong, opposite antenna detected a tag. This kind of initializationapplies to online filtering, is efficient to implement, and fails only in the usually rarecases that the maximum read range was underestimated. The drawback is that obviouslythe vast majority of samples are placed at locations where the tag is actually not located.
We propose an alternative, shown in Figure 5.1, in which one randomly creates par-ticles in areas of high likelihood, given a series of detections rather than only the firsttag detection. We first prepare sampling from the RFID sensor model function q(·): Weevaluate q at Q discrete positions xj (on a regular grid, for instance) and assign these po-sitions a probability wxj
:= ηq(xj), where η = (∑Q
j=1 q(xj))−1 is a normalization factor.
Let a1, . . . , ak be the set of antenna poses from where the transponder was detected.We select a subset of poses aπ1 , . . . , aπk′
which differ significantly with regard to pair-wise distances or difference in heading. Then we sample from the RFID sensor modelaccording to the previously chosen positions and normalized weights. These samples aretransformed to the coordinate frames defined by the antenna poses aπi
, i = 1, . . . , k′.k′ is variable. For each of the k′ selected positions, we draw equally many initializationpoints until the desired total number of particles Ns is reached.
This approach is sketched in Algorithm 4. The evaluation of the sensor model function(lines 1-7) depends on the number of grid points and is practically done only once whenthe mapping software is started. The subset selection of antenna poses (lines 8-10) runsin O(k2), but a single comparison of antenna poses is fast, and typically k is relativelysmall. Adding Ns particles (lines 11-14) finally runs in O(Ns log G) if G is the numberof sampled grid cells of the sensor model function.
Because the depicted strategy relies on several tag detections, it is feasible in batch-processing or delayed initialization of a tag particle filter. That the described approach ismore effective than uniform sampling, however, is underlined by Figure 5.1, in which anexemplary initialization based on real RFID data is shown. The model sampling-basedinitialization concentrates samples close to the true transponder location; fewer particlesare placed in unlikely positions. Detailed experiments follow in Section 5.3.4.
5.3.3 Utilization of Negative Information
In a single inquiry, only the few tags which are reached by the RFID reader have non-zerodetection counts. When the robot traverses an environment, most tags are not detectedmost of the time (formally, f
(a)t,l = 0 for many tag IDs l and many time steps t). More-
over, as argued before, even within theoretical read range, transponders are frequently
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5.3 PROBABILISTIC MAPPING USING PARTICLE FILTERS
ALGORITHM 4: Particle filter initialization by sampling from the sensor model
Input: Antenna positions a1, . . . ,ak from where the tag was detected, anddesired number of samples Ns
Output: New sample set (x(i), w(i))Ns
i=1
1 M = ∅; η = 0; S = ∅2 // Evaluate sensor model function q on a grid of positions of the model range X3 foreach x ∈ GRID(X) ⊆ X do
4 wx ← q(x)5 M ← M∪ (x, wx)6 η ← η + wx
7 foreach (x, wx) ∈ M do wx ← wx · 1η // Normalize the weights of samples in M
8 Select aπ1 , . . . ,aπk′, k′ ≤ k where ∀1 ≤ i < j ≤ k′:
9 ||aπi⊖ aπj
||x,y ≥ θcart or // 2D positions differ by at least θcart
10 ||aπi⊖ aπj
||θ ≥ θrot // Antenna orientations differ by at least θrot
11 for i = 1 to k′ do
12 for n = 1 to ⌊Ns
k′ ⌋ do
13 Sample (x, wx) from M with probability wx
14 S ← S ∪(
x,(
k′⌊Ns
k′ ⌋)−1
)
// Add sample with uniform weight
15 return S
not detected (false negatives). The related RFID literature is divided with respect to thedecision if negative information should be utilized. Often, it remains unclear if nonde-tections of tags are evaluated. Hähnel et al. [96] and Joho et al. [119] apparently builtonly on successful detections. By contrast, Liu et al. reported that negative informationimproved their location estimates [162]. They employed a very conservative, discretesensor model (5 % detection probability within read range, 0 % outside).
There are two more reasons for ignoring nondetections: Mapping is faster, as lesssensor data need to be processed. In addition, most nondetections occur far away fromthe true tag location; they reveal no influence on the spatially focussed sample set.
Since negative information has proven useful in other localization contexts (e.g., [109,135]), we investigated its usefulness for passive RFID-based mapping. We propose thefollowing careful restrictions, based on the above concerns and earlier experiments:
• Non-detections are evaluated only after evaluating all or sufficiently many detec-
tion events.
• Only those nondetections will then be considered which are closer to the current
tag location estimate than some threshold (e.g., RFID read range). This way, irrel-evant nondetections are ignored, and fewer estimation steps are required. To speedup computations, the current position estimate can be approximated by selectingonly the most likely particle.
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CHAPTER 5 MAPPING
5.3.4 Experiments
We examined the different aspects of the described mapping approach through a numberof experiments with our two mobile robots. To do so, we recorded RFID measurementson several trajectories in different environments, as detailed in Appendix A. The RFIDdata were annotated with accurate reference positions, which were estimated by MonteCarlo localization using the laser scanners of the robots. In each of the environments,RFID tags were attached to the sides of the traversable areas. Mostly, the transponderswere fixed on walls, doors, and furniture at varying heights. The density of RFID labelswas varied in some experiments to deal with density-dependent impacts on detectionrates, too. To be able to investigate the accuracy of estimated transponder positions, wemanually determined the true positions of a subset of tags in each dataset.
RFID measurements and reference positions were then fed as observations to the map-ping algorithm. We experimented with different parameters and compared the mappingoptions as elaborated in Sections 5.3.1-5.3.3. As particle filtering is randomized, thefilter was run at least five times for each configuration (i.e., for each log file and param-eter constellation). In the following, we present the results of the different experiments.Note that in all cases we ignored a tag in the assessment of the results if it had not beendetected at least three times. Moreover, the minimum detection rate that the respectivesensor model would return was set to 10-3.
In order to quantify 2D position estimation errors, we subsequently provide the meansand standard deviations over all tag estimates. Additionally, we provide plots of cumula-tive error distributions. As the main characteristic to compare the mapping accuracy ofan inventory run of the robot, we use the mean 2D estimation error of each experimenttrial, i.e., of a run on a single log file, averaged over all estimated tag positions. In cor-responding plots, we compare the mean mapping error per experiment trial for differentestimation techniques and parameter sets, averaged over all experiment trials (repeatedruns of the particle filters on all log files in a dataset).2 These plots therefore contain themeans and standard deviations of mean errors per log file. This way, the standard devia-tions also reflect the repeatability of mean errors in different runs of the robot. In order todistinguish the (typically smaller) standard deviations of means over all experiment tri-als, the standard deviations in corresponding figures are marked by standard deviations
(of trial means).
Mapping Accuracy Depending on the Number of Particles
The SCITOS G5 with on-board SR-113 reader was steered on 20 different paths throughthe Sand 1 wing (see Section A.4, p. 167). The reader was configured to scan at a trans-mission power of 1 W (30 dBm) on ten recorded paths and to scan at 0.18 W (22.5 dBm)
2We verified that log file sizes were sufficiently balanced such that averaging at once over all tags and logfiles on the one hand and averaging over the means of errors for each log file on the other hand yieldedequivalent means with negligible deviations.
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5.3 PROBABILISTIC MAPPING USING PARTICLE FILTERS
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FIGURE 5.2: Mean absolute mapping errors and standard deviations (of trial means) de-
pending on the number of particles (logarithmic axis scale) and the transmission power
level for the SR-113 reader on board the SCITOS G5.
on ten other trajectories. In each case, for five log files, 83 transponders of known lo-cations were spread along the corridor, and for the other five logs, the tag density wasincreased to 303 labels in total. Thereof, 81 true tag positions were known. Additionally,the B21 with on-board ALR-8780 reader was steered on 15 paths through the roboticslab (Section A.1, p. 163: LAB.LD.M* datasets). The tag density was constant; up to287 tags could be observed, of which 15 locations were evaluated. The transmissionpower level was 2 W (33 dBm). For details about the experimental environments and thedatasets, see Section A.1 and Section A.4.
The ALR-8780 reader was configured to interactively report which tag was detected.In each cycle, each tag could be detected at most once by one of the four antennas.Therefore, a Bernoulli-distributed sensor model (cf. Section 4.3) was learned by meansof quartic kernel regression.
The SR-113 reader, by contrast, scanned continuously and was configured to countthe detections of nearby tags for 0.25 s with each of its two antennas, yielding one entireRFID measurement every 0.5 s. We compared two different types of sensor models:First, we learned a model based on quartic kernel regression which represents means andvariances of detection counts per time by a Gaussian distribution. Second, we derived amodel based on quartic kernel regression which represents the probability of detecting a
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CHAPTER 5 MAPPING
FIGURE 5.3: Mean absolute mapping
errors and standard deviations (of trial
means) depending on the number of
particles (logarithmic axis scale) and
the filter initialization approach for the
ALR-8780 reader on board the B21
(33 dBm)
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tag at least once, following a Bernoulli distribution (cf. Section 4.3). That is, we modeledthe likelihood p(q ≥ 1 |x), where q is the detection count of a tag and x is the relativedisplacement of the tag with respect to the detecting RFID antenna. The goal was tobenchmark the Gaussian model against a Bernoulli-distributed model, the latter of whichignores potentially noisy detection counts. We underline that the model learning datasetswere separate from the mapping datasets.
Figure 5.2 and Figure 5.3 show the mapping errors for the two robots and readers,depending on the chosen number of particles. The mapping error is denoted by the meanabsolute 2D Cartesian distance between estimated and actual tag position, averaged overall observed transponders with known true locations and over all trajectories and repeatedruns of the particle filter. By estimated tag position we mean the estimate after applyingall detections of a log file. The top row of Figure 5.2 and the left part of Figure 5.3visualize the errors if the filter is initialized uniformly upon the first detection of a tag.The bottom row and the right part, respectively, illustrate the effects of initialization bysampling from the sensor model as described in Section 5.3.2.
For now, we focus on the former initialization method, the uniform initialization. InFigure 5.2, we further distinguish between the two transmission power levels of the RFIDreader and the two sensor model types. The quality of the tag position estimate followsthe expected trend to improve with the number of samples. At full power level and using1000 samples, the SR-113 achieved a mean error of 0.56± 0.44 m with the Gaussiansensor model and 0.63± 0.58 m with the Bernoulli model. Decreasing the power level ofthe SR-113 reader reduced the error to 0.53± 0.30 (Gaussian model) and 0.54± 0.27 m(Bernoulli model).
Interestingly, with the Bernoulli model, more than 175 samples did not significantlyimprove the results. This model also seemed to better exploit the reduced uncertainty ofan RFID detection when the read range is smaller due to a lower power level.
By comparison, the ALR-8780 achieved a comparable accuracy of 0.56± 0.53 m, al-though transmitting at twice the power. Increasing the number of particles beyond 1000(not shown) did not further improve the estimation results considerably.
The small standard deviations in Figure 5.2 and Figure 5.3 are evidence of the repeat-ability of mean mapping errors for different paths of the robot. Recall that here the
64
5.3 PROBABILISTIC MAPPING USING PARTICLE FILTERS
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22.5 dBm30.0 dBm
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22.5 dBm30.0 dBm
FIGURE 5.4: Mapping accuracy vs. cumulative frequency for 2000 particles and uniform
initialization (SR-113 on board the SCITOS G5)
FIGURE 5.5: Means and
standard deviations of
particle reweighting run
times, depending on the
number of particles
0.0005
0.001
0.0015
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depicted standard deviations represent the deviations of mean errors as averaged overeach mapping run (i.e., inventory) on a single log file.
The cumulative frequencies with which specific mapping errors are achieved are plot-ted in Figure 5.4. The results are based on the errors of all mapped tags for ten differentrobot trajectories and five repeated runs of the particle filter (2000 samples). In our ex-periments with the Bernoulli model the median errors, for instance, were approx. 0.55 mat full power level and approx. 0.45 m at reduced power level. An error of less than 1 mwas obtained in approx. 90 % of the cases for full power level and 95 % at reduced power.
Example mapping results are visualized in Figure 5.14 on p. 81.
The time required for a single filtering step is illustrated in Figure 5.5. On a 3 GHzCPU, evaluating the likelihood function on 1000 samples lasts less than 1.5 ms on av-erage. This is fast enough to process several hundreds of RFID tags per second, asspecified by the current EPC RFID standard. Still, it is desirable to increase run-timeefficiency in order to disburden the CPU for other demanding navigation tasks (e.g., pathplanning). Alternatively, RFID-based mapping could be implemented on embedded sys-tems of lower computational power. The next experimental results show how efficiencyis improved.
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CHAPTER 5 MAPPING
TABLE 5.1: Comparison of mean effective sample sizes (ESS), relative to the total num-
ber of samples (Ns = 1000), for the two types of sensor models and the two initialization
methods. (SR-113 at 30 dBm, SCITOS G5)
Mean relative ESS (%)Initialization method Gaussian sensor model Bernoulli sensor model
Uniform initialization 0.43 ± 0.05 0.42 ± 0.04Sampling from sensor model 5.42 ± 0.81 8.28 ± 0.77
Comparison of Initialization Methods
Figures 5.2 (bottom row) and 5.3 (right) depict the mapping results for the case that thefilter was initialized by sampling from the sensor model at distant detection positionsof the same tag (θcart = 0.5 m, θrot = 20). Two effects can be observed in all cases:First, the number of particles revealed smaller influence on the estimation errors thanfor uniform initialization. In the case of the ALR-8780, as few as 50 samples sufficedto achieve almost the same accuracy as 1000 samples. This result permits by far moreefficient mapping. The only expense is a minor overhead in efforts during initializationof batch estimation. Second, documented for the case of the Gaussian sensor model ofthe SR-113 reader, the estimation accuracy was improved: The mean mapping error with1000 samples was reduced to 0.48± 0.32 m at 30 dBm and to 0.43± 0.25 m at 22.5 dBm.
These results can be explained by Table 5.1. It lists the mean relative effective samplesize (ESS), averaged over all mapped tags and all repeated runs of the particle filter, afterevaluating all tag detections. Recall that the ESS estimates how many samples effectivelycontribute to the position estimate (cf. Section 2.2.2). The table shows that by samplingfrom the sensor model, the final ESS after estimation was 10 to 20 times larger in our ex-periments. That is, the initialization method actually generates samples more effectivelyin areas of high likelihood. Consequently, more particles contribute to the position esti-mate close to the true tag location. This improves the position approximation via samplepositions. Vice versa, fewer samples still achieve a comparable approximation quality asthe standard initialization.
An example of a filter evolution is illustrated in Figure 5.6. The tag was mapped withan error of 0.20 m, using 100 samples and initialization by model sampling. Althoughmodel sampling was shown to increase the effective sample size, the plot reveals that af-ter processing several observations, many particle weights are degenerated. This insightwas one motivation for the further enhancements in Section 5.4 and Section 5.5.
Impact of the Number of Tag Detections
It is usually desirable to assess the estimation quality even in absence of ground truth.The number of tag observations might be a suitable indicator: Intuitively, the more oftena tag is observed from different locations, the better should be its position estimate. We
66
5.3 PROBABILISTIC MAPPING USING PARTICLE FILTERS
initially
98
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0
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0 5 10 15 20 25 30
rel. E
SS
observation
FIGURE 5.6: Particle filter evolution: TOP: Distribution of 100 samples after initial-
ization and after processing 1, 5, and 20 observations (coordinates in meters). Radii
are proportional to importance weights, relative to the best sample. BOTTOM: Effective
sample size, relative to the filter size, after evaluating the given number of observations.
hence investigated this hypothesis. In Figure 5.7 the mapping errors of all tags and allexperiment trials are plotted against the number of measurements in which the tags weredetected at least once. For this statistic, we evaluated the mapping results of the SR-113at full power level (30 dBm), using a particle filter with 2000 samples and a Bernoullidetection model.
The mapping error was not a decreasing function of the number of tag observations.This outcome holds for all experiments that we conducted, including also the ALR-8780reader, different sensor models, and power levels. So, unfortunately, our experimentsindicate that one cannot simply explain or predict the mapping error by the number oftransponder observations. We also investigated whether the variance of detection posi-tions is correlated with mapping accuracy, which turned out not to be the case.
Impact of Negative Information
We incorporated nondetections as described with both RFID readers (full RF transmis-sion power, PF with 1000 samples, initialization by sensor model sampling) as describedin Section 5.3.3. The datasets were the same as before (ALR-8780 in the lab, SR-113in the Sand 1 wing). The distance threshold to the position prior, as estimated from suc-cessful detection attempts, above which nondetections were rejected was set to 2 m. Theresults are summarized in Table 5.2, where the mean errors of ignoring nondetections(as in the previous experiments) and of evaluating nondetections are compared. For thesituation that we did evaluate nondetections, we distinguished two cases: In the bounded
case, we did not use more nondetections than there were regular detections of the respec-
67
CHAPTER 5 MAPPING
0
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3
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
mappin
g e
rror
(m)
number of detections
FIGURE 5.7: Mapping error per tag depending on the number of detections. Each dot is
a single estimation result of one tag and one trial for ten different log files. (SR-113 on
board the SCITOS G5)
TABLE 5.2: Comparison of mean absolute mapping errors and standard deviations (m)
with and without the incorporation of nondetections. Values with asterisks indicate re-
sults of experiments including negative information which are significantly better (t-test;
*= significance level p < 0.1, **= significance level p < 0.05).
Reader and model Treatment of nondetectionsWithout Unbounded number Bounded number
ALR-8780, Bernoulli 0.57 ± 0.54 0.61 ± 0.54 0.59 ± 0.55SR-113, Bernoulli 0.62 ± 0.35 0.56 ± 0.33 ** 0.61 ± 0.35SR-113, Gaussian 0.49 ± 0.32 1.30 ± 0.66 1.10 ± 0.55SR-113, Gaussian, 0.49 ± 0.32 0.46 ± 0.31 ** 0.48 ± 0.32 *fixed variance
tive tag, and in the unbounded case, we evaluated all observed nondetections within thedistance threshold.
Modeling detections by a Bernoulli distribution, nondetections slightly improved themapping error in our experiments, although only the unbounded case with the SR-113yielded a significant error reduction. Applying the Gaussian sensor model to mappingwith the SR-113 reader worsened the results rigorously. The inspection of the reasonsrevealed that the sensor model is overly confident in regions of low detection rates (seeFigure 4.10 on p. 51, for example): There, the modeled variance of the signal is alsosmall. Consequently, samples which had been assigned large weights after evaluatingall detection events were still easily devaluated due to noisy nondetection events. Tocompensate for this effect, in another experiment series we fixed the variance of thesensor model to its maximum variance (approx. 9) for all nondetections. As Table 5.2
68
5.4 EFFICIENT ITERATIVE ESTIMATION
FIGURE 5.8: Mapping errors
(means and standard deviations
(of trial means)) after adding
artificial noise to the robot ori-
entation. The horizontal axis
denotes the standard deviation
of rotational Gaussian noise (in
radians).
(SR-113/SCITOS G5, 30 dBm)
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Gaussian modelBernoulli model
shows, this significantly improved the mapping accuracy, as compared to not treatingnondetection events.
On balance, however, incorporating failed detection attempts do not seem to yieldmajor improvements. In our experiments, we obtained error reductions of 1-4 cm (< 7 %)at the expense of higher computational demands: The bounded case roughly doubled theprocessing time, the unbounded case required approximately three times as much time.
Mapping with Varying Noise Levels
So far we have relied on mapping with accurate reference positions: The laser-basedMonte Carlo localization of our robots has an average Cartesian position error of lessthan 0.1 m and orientation errors of less than 5. To explore the limitations of mappingaccuracy, we conducted experiments in which we added zero-mean Gaussian noise withdifferent variances to the orientations of the RFID antennas. The results for the SR-113reader at 30 dBm in the Sand 1 wing and a particle filter with 1000 samples (initializationby sensor model sampling) are visualized in Figure 5.8. With regard to the Gaussian sen-sor model, adding moderate rotational noise of up to 0.25 radians (approx. 15°) increasedthe error slightly, by less than 5 cm. Artificial noise with a large standard deviation of0.8 radians (approx. 45°), however, raised the error by approx. 0.25 m, which representsan increase of roughly 50 %.
5.4 Efficient Iterative Estimation
In this section we present techniques to considerably reduce the number of particlesrequired to map a single tag. They further complement the robustness of the filter ini-tialization method which we presented above. The central idea is to pass over the sensordata several times, while each pass requires a small number of particles only.
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CHAPTER 5 MAPPING
ALGORITHM 5: Multi-pass tag position estimation
Input: Observations f1:t and robot poses x1:t
Output: Tag position l
1 Initialize particle filter S with few particles2 while stop condition not met do
3 Apply standard filtering to S, using f1:t and x1:t // see Section 5.3.1
4 if stop condition not met then Resample and perturb the particles // see Section 5.4.2
5 return extracted pose l from S
5.4.1 Overview of the Iterative Framework
Accurate, robust mapping is usually guaranteed by a large number of particles. Themaintenance of large numbers of particles, however, is computationally demanding inenvironments where many transponders have to be processed every second. Moreover,particle filtering with many samples does not scale with regard to space complexity,either: In supermarkets with tagged products, for instance, one can expect hundredsof transponders per linear meter. Mapping environments of this kind hence poses highmemory demands.
Why think about a further increase of efficiency, now that the initialization by sam-pling from the sensor model seems to work well with small particle numbers? The fewersamples are initialized, the more likely they can still miss the location of highest likeli-hood. In addition, few samples may still poorly approximate the belief and may thereforeresult in lower accuracy. That is why we propose to process the same recorded sensordata several times, where in each iteration (i.e., pass over the entire data) the tag positionestimate is refined. By iterative optimization, inaccuracies of one pass over the sensordata are tolerated and corrected in a later pass over the recorded observation.
The general framework for the iterative optimization of the tag position is summarizedin Algorithm 5. Lines 1 and 3 embody filtering as described before. The stop conditionin line 2 could be a convergence test, but in our experiments it proved effective to simplyiterate a fixed, small number of times (2-4 passes). The central part of the multi-passestimation approach is summarized in line 4 and detailed in the next section: After eachpass over the sensor data, resampling is first performed and then followed by the dis-turbance of particle states. This perturbation achieves a finer-grained exploration of thestate space in the next iteration, close to locations of high likelihood. Besides, particlediversity is recovered, since most imprtance weights will be almost zero after step 3. Itcan also be seen as a kind of artificial evolution of sample locations – despite the staticmapping case treated here – which resembles diffusion-alike motion.
70
5.4 EFFICIENT ITERATIVE ESTIMATION
5.4.2 Resampling and Perturbation Approaches
Final Resampling and Non-Adaptive Perturbation
One technique is to resample the particle filter after each pass over the sequence of sensordata, using any of the resampling schemes from Section 2.2.3. Thereafter, the particlelocations are perturbed according to a zero-mean Gaussian distribution N (0,W), whereW is a diagonal covariance matrix of predefined values. This way, diversity amongsample positions is guaranteed to increase. The current distribution of particle weightssteers the resampling, but is then ignored when samples are disturbed at the same degreeafter each pass over the sensor data. Error values obtained in prior experiments permit todetermine W.
Resampling and Covariance-based Perturbation
Another perturbation technique was proposed by Liu and West [160], originally in thecontext of combined parameter and state estimation. For our application, it adds Gauss-ian noise depending on the covariance of the sample set. Joho et al. [119] also chosethe approach for RFID-based mapping with interleaved model learning. The best resultswere obtained with at least 500 particles.
Formally, let x be the mean position of all samples and x(i) be the position of the ithparticle. Then a particle index j is sampled Ns times corresponding to the distribution ofimportance weights. The new location x′(i) of particle i is sampled according to:
x′(i) ∼ N (ax(j) + (1 − a)x, h2V) (5.5)
The matrix V is the covariance of all particles. The coefficients a and h depend on adiscount factor δ ∈ (0, 1], which controls the degree of perturbation, via:
h2 = 1 −(
3δ − 1
2δ
)2
and a =√
1 − h2 (5.6)
Larger values of δ cause samples to be disturbed at a lower degree. Liu and West recom-mended values between 0.95 and 0.99.
5.4.3 Experiments
We applied the resampling/perturbation methods to mapping using the SR-113 readerat 30 dBm transmission power. The results were evaluated on the Sand 1 wing dataset(SAND1.HD.30dBm). We compared four variants of the techniques: (1) Constant-levelGaussian noise, as above, where the particles were resampled once after each pass usingresidual resampling; (2) resampling after Liu/West, where resampling was performedonly once after each pass over the sensor data; (3) resampling after Liu/West, whereresampling was performed whenever the effective sample size dropped below Ns/2; and
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CHAPTER 5 MAPPING
0.4
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Liu/West, frequent resampling (3)Liu/West, frequent res. + noise (4)
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Constant-noise res. after pass (1)Liu/West, res. only after pass (2)
Liu/West, frequent resampling (3)Liu/West, frequent res. + noise (4)
FIGURE 5.9: Mapping accuracy of iterative estimation: means and standard deviations
(of trial means) (SR-113/SCITOS G5, 30 dBm)
(4) the same as (3), but with adding noise after each resampling. Several noise levels wereinvestigated, but in Figure 5.9 we present the results of noise with a standard deviationof 0.25, i.e., W = diag(0.25, 0.25). As in [119], we set δ = 0.95. The filter wasinitialized by sampling from the sensor model (Gaussian distribution, learned via quartickernel regression as above).
According to Figure 5.9, the variants 1, 2, and 4 achieved comparably good results inour experiment. Resampling after Liu/West with frequent resampling performed slightly,but significantly worse for small particle numbers. Our explanation, which is basedon the earlier presented studies of the effective sample size, is the problem of particledepletion: The sample set converges too quickly to a confined area of highest likelihood,where few particles are not sufficient to approximate the tag position distribution well.By adding noise frequently or resampling only after an entire pass over the data, particledepletion is circumvented.
The results show that applying the same sensor data to n particles in k passes is moreeffective than a single pass with Ns ≥ nk particles. For example, two passes with 100particles yielded better accuracy than a single pass with 500-2000 particles (cf. Figure 5.2on p. 63). This is also underlined by Table 5.3, in which filtering with a single pass overthe recorded observations, using 1000 samples, is compared to two-pass estimation with100 samples. As can be seen, we achieved coarsely the same accuracy in 35-60 % of thetime that was required to map a tag on average. Variants (1) and (2), where resamplingtook place only once after each pass, were most efficient. Moreover, our experimentsindicate that already two passes over the data seem to be sufficient in iterative estimation.The third and fourth passes did not further improve accuracy.
As a conclusion, the batch estimation of transponders can considerably be acceler-ated by the presented resampling/perturbation techniques. Although two passes over therecorded sensor are required, the iterative estimation was more efficient, because the re-quired number of particles was reduced significantly. At the same time, the mappingerrors were equivalent or even improved slightly.
72
5.5 FUSION WITH SPATIAL INFORMATION
TABLE 5.3: Mean estimation errors (± standard deviations) and mean processing times
per tag for different resampling/perturbation techniques in iterative estimation
Estimation method Pas
ses
Par
ticl
es
Accuracy (m)
Processingtime pertag (ms)
Without resampling 1 1000 0.46± 0.33 30.3(1) Constant level Gaussian noise 2 100 0.46± 0.31 10.7(2) Liu/West, resampling after each pass 2 100 0.47± 0.31 11.0(3) Liu/West, frequent resampling 2 100 0.47± 0.33 15.8(4) Liu/West, frequent resampl. + noise 2 100 0.47± 0.41 17.9
5.5 Fusion with Spatial Information
In this section we present a generic approach which fuses RFID detections with volu-metric maps for the sake of increased accuracy. The section is based on our publica-tion [210], which we presented at ECMR 2009. The original sampling algorithm wasdeveloped by Karsten Rohweder in the scope of his diploma thesis [209].
5.5.1 Overview
The previous sections showed that tagged objects can be mapped at an accuracy of clearlybetter than the read range of an RFID reader. Still, estimation errors are nonnegligible.The central issue remains that valuable knowledge about bearing and distance to a tag isnot provided.
The fusion approach presented subsequently is motivated by the fact that the positionof an RFID tag is coupled with the position of some object to which it is attached. Thespatial structure of an object can be detected by sensors like stereoscopic/depth cam-eras, 2D/3D laser scanners, and sonar. Combining such a sensor with RFID exploits thegeometric accuracy of the former with the identification mechanism of the latter.
Our approach is generic insofar as we decouple the spatial reconstruction from thestage of tag position estimation. Thus, various types of sensors can be employed to gaina-priori knowledge about the structure of the environment. Here, in particular, we usea 2D laser range finder. Similar kinds of fusion with prior map knowledge have provensuccessful in localizing people on streets [187] and robots near buildings [23].
Occupancy grid
(prior over
tag positions)
Mapping with
spatially accurate
sensor
Particle filter
initialization
Particle filter
updates with RFID
measurements
Tag positions
(posterior over
tag positions)
FIGURE 5.10: Overview of fusion stages
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CHAPTER 5 MAPPING
As shown in Figure 5.10, a spatial model of the environment is derived first, storedin a volumetric map such as an occupancy grid. The spatial model represents a priordistribution over possible tag locations. It is used to initialize a particle filter. This secondstage effectively focuses the particle positions on the areas of interest. Afterwards, RFIDmeasurements are evaluated, which finally results in a map of transponder positions.
5.5.2 Spatial Reconstruction and Representation
The first step of our approach is to generate an occupancy grid map [177] from thereadings of a spatially accurate sensor. By accurate, we mean estimation errors of fewcentimeters, far below the errors of purely RFID-based mapping. An occupancy grid m
divides the space into a 2D array of grid cells, where each cell mij has an associatedprobability p(mij) of its volume of space to contain solid matter. Note that most spatiallyaccurate sensors can yield maps in the shape of occupancy grids: Both for laser-based(e.g., [62, 89]) and vision-based mapping approaches, grid maps can be obtained by ray-tracing to observed features in order to reweight free space and occupied cells. Ideally,such a grid already exists for self-localization purposes, which means that the grid comesfor free for RFID mapping.
We can formally integrate spatial knowledge into the estimation framework as follows:We extend (5.1) by the given grid map m, omit the robot poses x0:t for convenience, andapply Bayes’s theorem twice to obtain:
p(l |m, f1:t) =p(f1:t | l,m)p(l |m)
p(f1:t |m)(5.7)
= µ p(f1:t | l)p(l |m) (5.8)
The normalization factor subsumes the division by p(f1:t |m). In (5.8) the RFID mea-surements f1:t are independent of the grid map m, given the pose l of the transponder, asthe sensor model itself does not depend on the grid map m. Now, the distribution p(l |m)can be regarded either as a prior over tag locations or as an additional constraint in im-portance weighting. The former perspective permits us to sample from the distributionand initialize the particle filter this way. It requires, however, that m is known upon filterinitialization, at least roughly in the region where the transponder to be mapped can beexpected. The latter perspective allows for applying p(l |m) whenever desired, but doesnot contribute spatial knowledge upon filter initialization. The density p(l |m) itself candirectly be modeled using the normalized occupancy weights of the grid cells of m. Inthe following, we show how to incorporate the two fusion perspectives during mapping.
5.5.3 Fusion by Sampling from Volumetric Maps
The particle filter initialization is realized by sampling from the occupancy grid withinRFID read range from a detection position and relative occupancy probability. Particlesare then randomly placed in the drawn cells as shown in Figure 5.11.
74
5.5 FUSION WITH SPATIAL INFORMATION
FIGURE 5.11: Illustration of the structural initialization approach. TOP LEFT: The
occupancy grid representing the spatial structure of our lab. BOTTOM LEFT: Contour
detection for the optional case that tags are expected to lie on the outer sides of objects.
RIGHT: Close-up showing a random initial assignment of particles to occupied cells.
The particles are represented by small circles, where darkness corresponds to weights.
First, we collect the set of antenna poses from which a particular tag has been detected.For each of the antenna poses, we then select the subset of grid cells C which are suffi-ciently close to the antenna pose to be in RFID read range. From these cells, a smallersubset C ⊂ C is selected whose weights exceed a minimum occupancy threshold. Nor-malizing the cell weights in C so that
∑
c∈C wc = 1 yields the final set of candidate cellsfrom which we sample.
In a preprocessing step, contour detection can optionally be performed on the occu-pancy grid if one favors object contours over solid mass. Contour detection is valuableif tags are expected not to be hidden deeply inside matter. To extract object contoursfrom the occupancy grid, we first determine the cells whose occupancy probabilities fallbelow a threshold pempty and are thus considered empty, but have non-empty neighbors.For these cells, the magnitude of the occupancy gradient is computed and stored sep-arately. Centered on cells with a gradient magnitude greater than a threshold mthresh,a circular region is created with a radius of the contour strength and a probability ofpcontour = 1.0. The contour radius is adjustable to compensate for noise in the chosenspatial reconstruction method.
For each sampled cell, a tag position hypothesis is created, weighted with the celloccupancy probability, and added to the particle filter. After processing all detection po-sitions, particle densities are such that structure contours are densely populated, structureinteriors less so, and overlapping detection areas from different detection positions againdensely populated. Afterwards, the common RFID filtering steps are applied, but nowobviously only in the areas that conceivably matter most.
5.5.4 Fusion by Subsequent Integration of Volumetric Information
The second perspective on fusing RFID measurements with structural data is to integratethe structural knowledge only after evaluating all RFID inquiries. This procedure would
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CHAPTER 5 MAPPING
also potentially allow for interleaving camera- or laser-based SLAM with the localizationof the transponders. The final weight of the ith particle in this alternative approach is:
w(i)final = η · w(i)
t · poccupied(x(i)t ) (5.9)
Thereby, η is again a normalizer, t is the final time step, and poccupied(x(i)t ) is the occu-
pancy probability at the particle’s position. Visually, this method constrains the sampleset to occupied positions of the occupancy grid after purely RFID-based mapping. Theweights of particles with implausible positions will be decreased or even set zero if par-ticles are located on free space.
5.5.5 Experiments
In order to assess the accuracy of the fusion approach, we conducted several experimentswith the B21 robot and its on-board ALR-8780 UHF reader.
The experimental environment was the laboratory (see Section A.1) with a free spaceof approx. 50 m². More than 400 passive UHF tags at different heights and orientationswere attached to walls, furniture, and empty product packages in a metal shelf. We re-corded 34 datasets on manually steered, arbitrary paths through the lab (Section A.1:LAB.* datasets with cycle count C = 2). In the scope of the experiments the robot trav-eled a distance of 3.0 km over a duration of 3.9 h. Approximately 20,000 RFID readingswere performed at 2 W. Additionally, we built a 2D laser occupancy grid of the lab asdepicted in Figure 5.11, using the laser-based grid SLAM module GMapping [88].
On these data, we compared the performances of the three mapping techniques: aparticle filter which is initialized uniformly and does not take spatial knowledge intoaccount (subsequently referred to by “UNI”); the particle filter which is initialized withstructural knowledge (“STR”) as described in Section 5.5.3; and a particle filter withuniform initialization, but fusion with spatial knowledge after the evaluation of all RFIDmeasurements (“SUB”) as described in Section 5.5.4.
Mapping Accuracy in Arbitrary Locations
For a particle filter with 1000 particles, we compared the mean absolute errors of tagposition estimates. The comparison is based on 40 transponders whose true positionswere determined manually. These tags were located both on the exteriors of objects andinside shelves, and their heights varied from 0.28 m to 1.38 m over ground. For eachdataset, the particle filter was run ten times. The results are shown in Table 5.4. A meanerror of approx. 0.95 m was obtained for the standard approach without fusion (UNI).Integrating knowledge about structure by the initialization strategy (STR) reduced theerror to approx. 0.86 m. This is an improvement of 9.7 %. The subsequent fusion withspatial knowledge (SUB) also reduced the error, but only by 3.3 % to a value of 0.93 m.The improvements show that taking knowledge about spatial structure into account is
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5.5 FUSION WITH SPATIAL INFORMATION
FIGURE 5.12: Example of a generated map with tag position estimates (orange/light
gray dots) and associated ground truth (dark dots). Most tag positions were estimated
accurately. Larger errors occur where metallic reflections at radiators frequently yielded
ghost detections of tags (bottom part of the image).
TABLE 5.4: Results of uniform and structural initialization: Mean absolute mapping
errors and mean effective sample size relative to the size of the particle filter (ESS)
Initialization Mean error (m) Mean ESS (%)
UNI (no fusion) 0.9497 0.95STR (fusion by initializ.) 0.8579 1.32SUB (subsequent fusion) 0.9275 0.43
beneficial with regard to lower mapping errors. An example mapping result is illustratedin Figure 5.12.
To assess why the initialization approach performs better than the subsequent fusionwith occupancy information, we estimated the ESS relatively to the size of the sample set.By initializing the particles in occupied positions, more particles effectively contributeto the position estimates: almost 40 % more (STR) than in the case of the uninformedinitialization (UNI). That is, using the occupancy grid as a prior distribution, the samplesare guided to regions of higher likelihood. The subsequent fusion (SUB), by contrast,improves the position estimate, but at the cost of an even smaller ESS: Applying (5.9)naturally leads to a larger variance of particle weights. Because of these insights, weincreased the number of particles. Even with 10,000 samples, however, the uniforminitialization did not yield better results.
Figure 5.13 (left) illustrates the mapping error, averaged over all experiments, for dif-ferent fractions of investigated tags. For the best 75 % of the tag estimates, the fusionapproaches yielded better results. The structural initialization (STR) roughly halves theerror for the best third of the estimates. Rather surprising at first glance is that the worst20 % of the tag estimates are better if no fusion takes place. The example in Figure 5.12,however, indicates that the effect is caused by outliers: Structural initialization can gener-ate particles on even more unlikely positions in case of false positives caused by metallicreflections. Outlier rejection should deserve further attention in RFID-based mapping,
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CHAPTER 5 MAPPING
0.03125
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mean m
appin
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rror
(m)
contour radius (m)
uniform initialization
FIGURE 5.13: LEFT: Accuracy vs. precision: The x-axis denotes the fraction of tags that
have a mean mapping error of less than the value on the (logarithmic) y-axis. RIGHT:
Mean errors and standard deviations (of trial means) for different contour radii, com-
pared to a uniform initialization of particles without spatial knowledge. “ncd” means
that contour detection was not performed.
but is beyond the scope of this work.
Tags on Exteriors of Objects
Typically, tags will be attached to the exteriors of objects. If the special case holds thatobjects are not placed one after another and transponders are not hidden deeply insidematter, our fusion approach can utilize these conditions. A typical scenario in which thisspecial case holds is when RFID tags are used as manually installed navigation stimuli,e.g., attached to walls as artificial landmarks.
Figure 5.13 (right) shows the results which we obtained for this special case, using1000 particles. The evaluation is based on 15 tags, attached to walls roughly at the heightof the upper RFID antennas. The mean estimation error was reduced to approx. 0.35 m inthis case. This is an improvement of about 33 %, as compared to 0.52 m without fusion.
Comparable improvements were also achieved with the SR-113 reader on board theSCITOS G5 on the Sand 1 logs, where almost all tags were located on exteriors. Fusionby structural initialization reduced the mapping error by approx. 25 % to 0.38± 0.30 mat full RF power (30 dBm). In this case 1000 samples, a Bernoulli model, and a contourradius of 5 cm were used, 90 known tag positions were evaluated.
5.6 Conclusion
Summary
In this chapter, we have shown how to probabilistically map the positions of passive UHFtransponders by means of a mobile robot with on-board RFID reader. Particle filtering
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5.6 CONCLUSION
was employed in combination with learned RFID models. We have introduced severalmechanisms which improved either efficiency or accuracy, or both:
• Filter initialization by sensor model sampling effectively placed particles in areasof high likelihood. This improved accuracy, even using few samples.
• The iterative estimation scheme allowed for mapping with small numbers of parti-cles and few iterations. This reduced the time required for mapping a transponderposition while still maintaining the same accuracy.
• The fusion with spatial information, based on a laser-generated occupancy gridmap, reduced estimation errors, too. It was implemented by sampling from a gridmap as a prior over tag locations before processing RFID measurements.
The mean estimation errors obtained depend on the placement of tags. On mixed sets oftransponders close to challenging metal shelves, quite large mean errors of up to 0.95 mcould be observed. On the other hand, tags on walls and exteriors of objects were mappedat accuracies of approx. 0.35-0.45 m on average.
Discussion and Outlook
We primarily focused on batch-processing the entire recorded sensor data. This appearsto prevent them from online-applicability. The processing, however, was so efficientsuch that the methods can be performed in a quasi-online fashion on demand. Moreover,it paves the way for detecting the relocation of tagged objects: One could split the tagdetections at candidate pivot elements and compare if the location estimates of parts ofthe data differ. If on-line processing is desired, KLD-sampling [73] helps to reduce thesample size.
An interesting extension is to locally characterize radio signal propagation by the mea-surement statistics of sparsely distributed reference tags. Several researchers proposedthis idea in the contexts both of passive [38, 240, 251] and of active RFID [18]. Staticreference transponders might help to localize unknown, not yet mapped transpondersmore accurately.
As our experiments with different power levels indicate, mapping could be improvedby switching between different transmission powers, as pursued by Hori et al. [111]. Ininventory, however, there is a general tradeoff between minimal mapping uncertainty andmaximal count of detected goods.
Our fusion experiments with a 2D RFID sensor model and a 2D laser range finderresulted in significant reductions of estimation errors: These improvements justify theextra efforts of the fusion: In robotic inventory, for instance, one will be interested inposition estimates which are as accurate as possible. Note that our structural fusion rep-resents matter anonymously. When using cameras, the fusion accuracy could further beimproved by registering precisely localizable visual features of object classes with RFIDdetections.
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CHAPTER 5 MAPPING
While in this chapter we localized RFID tags, based on RFID detections in knownpositions, the next chapter will treat the dual case: The pose of the robot will be inferredfrom detections of transponders whose locations are known.
80
5.6 CONCLUSION
Estimated tag positionsTrue positions
20
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(d)
FIGURE 5.14: Example mapping results with estimated (red/filled dots) and true (black
rectangles) tag positions, axes in meters. (a) Sand 1 wing (dataset SAND1.HD.30dBm).
50 particles, mean error 0.54 m, median 0.44 m, maximum 1.74 m. (b) Tags on walls and
desks in the robotics lab. (c) Tags on products in the lower half of a shelf in the middle
of the room (gray area). 100 particles, mean error 0.93 m, median 0.73 m, maximum
3.09 m. (d) As before, but now using prior structural knowledge. 100 particles, mean
error 0.70 m, median 0.39 m, maximum 3.19 m.
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CHAPTER 5 MAPPING
82
Chapter 6
Localization
In this chapter we show how a mobile robot can robustly localize itself, using its on-board RFID reader. After an introduction in Section 6.1, we review related work in Sec-tion 6.2. The general Monte Carlo localization framework is described in Section 6.3.Then, self-localization using a sensor model as in the previous two chapters is describedin Section 6.4. In contrast, two probabilistic location fingerprinting techniques are pre-sented in Section 6.5 and Section 6.6. The performance of all methods is experimentallyinvestigated and compared in Section 6.7, before we conclude in Section 6.8.
6.1 Introduction
The goal of localization is to estimate the pose of a robot with respect to a given mapof the environment. Often found synonyms are self-localization, which underlines thatthe robot determines its pose autonomously by means of on-board sensors, or more gen-erally position estimation [237]. Localization is a key ability because it enables a robotto understand its local context, to infer meaningful actions, and to plan paths to targetpoints. Note that the position of a robot cannot be “measured” directly. It has to beinferred from uncertain sensor data and an adequate description of the surroundings. Inparticular, global positioning systems such as GPS do not work indoors.
Self-localization in general is a well-understood problem in robotics. It can be re-garded as solved, at least for structured, static environments. Classical sensors involvedcomprise laser range finders (LRFs), ultrasonic sensors, and cameras. Laser provideshigh localization accuracy: Using their on-board LRFs, our robots can estimate their po-sitions with errors of below 10 cm. Despite the success of the named sensors, robots canbenefit from passive RFID as a technology for localization in manifold respects. RFIDtags on walls and objects serve as uniquely identifiable reference landmarks for naviga-tion which can be observed by the on-board RFID reader (Figure 6.1). If the positionsof transponders are known, the detection of a tag gives a clue about the current positionof the RFID reader. From a localization perspective, passive UHF RFID is an excit-ing alternative to the classical sensors or may augment them because of the followingreasons:
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CHAPTER 6 LOCALIZATIONPSfrag replacements
ut: odometry (control input)
lj : position of RFID tag j
xt: robot pose at time t
f(a)t : RFID measurement by antenna af
(1)t
f(2)t
lj
ut
ut+1xt
xt−1
xt+1
FIGURE 6.1: Bird’s eye view of 2D localization using passive RFID: Tags are attached
to walls, furniture, or assets in the environment (gray areas). Each on-board antenna has
a specific read range (dashed ellipses to the sides of the robot in red). The robot localizes
itself by evaluating odometry readings and detections of scattered transponders.
• RFID simplifies global localization, that is, estimating the position without priorinformation where the robot is initially located. This was experimentally shownin [96]. A single detection of a known RFID tag suffices to restrict the space ofpossible locations to the read range around the transponder, for instance.
• Radio waves can penetrate relocated or dynamic objects to some extent, whichis useful in dynamically changing, populated surroundings. A further, obviousadvantage over cameras in changing environments is that RFID is independent ofillumination.
• The identity of a transponder is directly supplied by the RFID reader. Computa-tionally demanding feature extraction is not required.
Yet, one has to overcome high false-negative rates and lacking distance/bearing infor-mation. To this end, we apply Monte Carlo localization (MCL) [74], which is particlefiltering in the context of localization. MCL has proven accurate and robust. It allowsboth for position tracking, which is position estimation starting from a known location,and for global localization. The kidnapped-robot problem, which is localization includ-ing global re-localization when the robot loses track of its position, can also be solvedusing MCL. However, in this thesis, we focus on position tracking and global localiza-tion. Kidnapping can be solved by common extensions of MCL such as the injection ofrandom samples or particles in likely positions [75, 154, 238].
We compare three variants of single-robot localization using RFID: On the one hand,the approach by Hähnel et al. [96] is pursued: It requires a transponder map and a sensormodel of the RFID reader (cf. Section 4.3). It is benchmarked against two variants oflocation fingerprinting on the other hand, which do not require an explicit sensor model:We describe and extend a method by Schneegans [217] which computes likelihoods ofobservations based on estimates of detection rates directly in the global frame of refer-
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6.2 RELATED WORK
ence. Second, we elaborate a variant of MCL which computes observation likelihoodsvia similarities in RFID signal space. In all cases, we aim at metric rather than topo-logical localization, that is, we estimate the Cartesian coordinates and the heading ofthe robot in continuous space. Detection areas of RFID tags offer themselves as nodesin topological localization; still, we will prefer metric positioning, because it allows forfiner position resolution, is more flexible, and integrates into common metric motionplanning front-ends.
In this thesis, we assume that transponders are mainly static. This prerequisite cer-tainly does not generally hold for tagged products in a supermarket, but is valid overshort periods and for stationary tags attached to shelves. Below we will also investigatethe robustness of localization when tags are relocated. Moreover, we presume that everytag identifier appears at most once and uniquely identifies its carrying object.
6.2 Related Work
Since its growing use in the nineties, RFID with its various standards has been exploredas a technology for localization. Especially wireless communication on mobile deviceshas fostered research into radio-based position estimation. Many researchers have in-vestigated RFID in the light of ubiquitous computing and context-awareness. Hightoweret al. [103], for instance, proposed the “Location Stack“ as a design model with layersranging from sensory input to contextual fusion of information, activities, and user inten-tions. In mobile robotics, one additionally has the opportunity to fuse RFID with othertypes of sensors or to benchmark it against reference locating systems.
Generally, RFID-related works vary along the following major dimensions, apart fromthe earlier mentioned distinction of model-based and fingerprinting solutions. Thesedimensions are closely coupled with the RFID standard as discussed in Chapter 3.
• Granularity: RFID suggests itself for proximity-based approaches, in which thelocation is associated with the cell of origin defined by the tag location. Morefine-grained approaches aim at metric localization. This is often found in robotics,where temporal filtering based on motion sensors is state of the art.
• Measured variable: As seen in previous chapters, localization can be range-free
(utilizing only binary response information or detection counts), utilize ranges (viasignal strength or time of arrival/flight), or utilize bearings (time difference ofarrival or angle of arrival). We have already seen before that the measurements canalso depend on fixed vs. variable transmission power. The variable can be modeledrelative to the sensor or to a global frame of reference (location fingerprinting).
• Estimation technique: Approaches vary between deterministic and probabilisticpose estimation. Examples of the former are angulation and lateration techniques.Among the latter extended Kalman filters, particle filters, probability grids, andnearest neighbors with probabilistic models are popular choices.
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CHAPTER 6 LOCALIZATION
For an overview of mobile robot localization we refer to Thrun et al. [237]. Closelyrelated articles describing Monte Carlo localization with laser range finders are [74, 238],sonar range sensors were used in [44]. More general comparisons of localization meth-ods and technologies were provided in [101, 180]. The mathematical background ofposition estimation problems and solutions, including fingerprinting, Bayesian, geomet-ric, and error minimization methods, was summarized by Seco et al. [222]. In [245], wecompared indoor position estimation on a mobile robot using different radio technolo-gies: detection rate measurements of passive RFID tags, signal strength indications ofBluetooth nodes, and time-of-arrival measurements of WLAN access points.
6.2.1 Model-based Localization Using RFID
In this section, we survey works in which a mobile device or robot with on-board RFIDreader localizes itself based on readings of passive RFID tags in the environment. Notethat in literature the term localization is often also used when passive transponders orobjects/persons carrying an RFID tag are tracked, by means of external sensors. Thesescenarios are closer related to mapping as treated in Section 5.2.
Proximity-based Localization
To our knowledge, in 1997 Kubitz et al. [140] were the first to publish a paper aboutpassive RFID-based localization and navigation with robots. Their robot localized glob-ally based on proximity to an identified tag. Because tag memories also contained in-formation about walls, crossings, etc., navigation behaviors could be selected. Later,Tsukiyama et al. [241] explored a simple navigation mechanism on the basis of vi-sual free space detection and RFID tags as nodes within a topological indoor map. Therobotic guide by Kulyukin et al. [141, 142] was able to assist visually impaired peoplein wayfinding in indoor environments. Similarly, Na et al. [181] designed a naviga-tion system for blind people with transponders on the floor. In the work by Mehmoodet al. [167], floor tags defined hexagonal cells over which the robot could navigate totargets. There are also commercially available systems which automatically detect andassign storage positions of palettes when a static label is identified by the RFID readeron board a forklifter (e.g., [115]).
A popular configuration, often called smart floor, is to localize on RFID tags embed-ded in the floor. In this case, HF tags are suited better because of shorter read ranges andthus smaller position uncertainty. Example works are the ones by Bohn [24, 25, 26] onhigh-density tag layouts. Munishwar et al. [179] as well as Kulyukin et al. [143, 144] re-calibrated the robot position when moving over a transponder. Raoui et al. [202] enableda robotic shopping cart to localize topologically or to re-localize metrically by passingover RFID barriers which crossed the ends of corridors in a supermarket. To refine theposition estimate when detecting several tags, Koch et al. [134] proposed the weighted
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6.2 RELATED WORK
mean of labelled positions, and Seo et al. [224] presented simulation results for apply-ing an extended Kalman filter to tag detections. Park et al. [196] measured the durationbetween the reads of two contiguous tags to infer the distance in which the tags werepassed (where the robot velocity was assumed constant). It is obvious that the accuracyof all listed approaches depends first and foremost on the density of transponders.
Detection Model-based Localization
A seminal survey into how to localize a mobile robot via RFID was presented by Hähnelet al. [96]. They first gained a probabilistic sensor model for their RFID reader, whichassociates the probability of detecting an RFID tag with the relative position of that tagto the antenna. Using this model, the positions of passive RFID tags in an office environ-ment were mapped. Monte Carlo localization was then used to estimate the position ofthe robot in the map at an accuracy of approx. 0.5 m from RFID readings and odometry.Their method represents the basis for the model-based approach of Section 6.4.
A paper closely related to our work is the one by Joho et al. [119]. They localized ashopping cart in a supermarket environment (350 tags) with on-board UHF reader. Thereader was also capable of measuring signal strength. Different sensor models were com-pared in a particle filter: a detection rate model, a signal strength model, a combinationof both, and signal strength maps learned via Gaussian processes. Using 2500 samples,they achieved errors of approx. 0.6/0.47/0.37/0.33 m, respectively.
Miller et al. [173] fused laser and passive RFID for position estimation with a particlefilter. Their robotic vacuum cleaner was equipped with two UHF antennas, similar toHähnel’s [96] and our setup. Tag positions were given, and samples were reweightedaccording to a heuristic function depending on the distance to a detected tag. Similarly,Boccadoro et al. [22] applied Kalman filtering to pure RFID detections, regarding themas noisy quantized readings of the robot pose. Their experimental results showed thatKalman filters may reveal favorable run-time when compared to particle filtering, but atleast for larger tag densities, particle filters outperformed Kalman filters by a factor oftwo with respect to localization accuracy.
Kwon et al. [148] proposed to use variable transmission power levels, based on promis-ing basic results in distance estimation between reader antenna and a passive tag. Beckeret al. [16] estimated the RFID antenna pose by a variant of gradient descent on an em-pirically learned model. Inside a tagged air plane, they achieved an accuracy of ap-prox. 0.5 m. Bulusu et al. [34] localized an active RF transceiver (418 MHz, 10 m range)by means of a connectivity rate model. Without filtering, they achieved a positioningaccuracy of 1.8 m in a 10 × 10 m environment outdoors. The robot of Bajcsy et al. [14]localized itself on a tagged floor via a tilted UHF antenna. With a read range of 0.9 m,they achieved an accuracy of 0.2 m. For estimation, they employed a histogram filter.
Subramanian et al. [228] positioned not a robot, but a person carrying a UHF reader(range 1 m) on a tagged floor. They combined tag read counts and signal strength indica-tions in a particle filter. Sensor models had been learned empirically beforehand. Later,
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CHAPTER 6 LOCALIZATION
they combined this method with Bluetooth fingerprinting and step detection for indoorpedestrian localization [229]. Also targeted at smart floors, Kämpke et al. [122] matchedlocal maps of currently read transponders to the global tag layout.
Range- and Bearing-based Localization
Due to the widespread use of mobile wireless devices, which includes laptops, cellphones and PDAs, the research community has come up with a variety of approaches.Here, we treat model-based approaches, which rely on radio propagation models andknown locations of base stations (e.g., WLAN access points). We sketch only some ofthem, since in this thesis we focus on detection rate-based solutions rather than receivedsignal strength (RSS), which is not part of EPC-standardized UHF RFID.
Among further overviews of RFID-based localization, Bouet and dos Santos selectedworks which build on angular or distance measurements and which are therefore mainlyapplicable to active RFID [29]. They assumed that the tag is mobile and read by severalreaders. Zhou and Shi reviewed signal strength-based approaches [265].
Chae and Han [37] performed two-step indoor robot localization: First, they posi-tioned coarsely via active RFID by weighted averaging of the known positions of de-tected nodes. Then, the pose estimate was refined by means of monocular vision involv-ing local image features. The reported mean error is 0.23 m. Djugash et al. [50] utilizedactive RFID tags outdoors, building upon earlier experiments of Kantor et al. [125] andKurth et al. [146]. They used time-of-flight measurements both for pure self-localizationand for simultaneous localization and mapping via Kalman and particle filters. The ac-curacy was 0.3-0.4 m measured along and perpendicular to the robot trajectory. Koutsouet al. [138] also employed a particle filter, but indoors and with RSS models. They re-ported an accuracy of 1.40-6.65 m, using active nodes attached to walls. For a similarsetup with custom-built active tags on walls, Hightower et al. [104] located tags with aresolution of a voxel of (3 m)³. They performed hill climbing in the signal strength errorspace and polynomial RSS estimation depending on distance.
Kim et al. [127, 128] measured the difference in signal field strength of target tagsusing two antennas. The estimated bearing enabled a robot to automatically dock to thetarget position.
6.2.2 Location Fingerprinting Using Visual Appearance
With regard to mobile robotics, the visual appearance of a scene is probably the mostwidely used type of fingerprint: A robot is localized using visual features extracted fromcamera images which are compared to reference views. In contrast to stereo vision orstructure from motion, the coordinates of landmarks corresponding to recognized fea-tures need not be reconstructed. All these works build on techniques from the field ofcontent-based image retrieval (CBIR). A comparison of similarity measures for CBIR
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6.2 RELATED WORK
was presented by Liu et al. [159], for instance. Examples of appearance-based local-ization among numerous articles are [232, 259], in which local integral invariants areemployed, in [259] combined with Monte Carlo localization (MCL). Kröse et al. [139]also applied MCL and derived appearance features via principal component analysis,while Linåker et al. [158] compared the appearances of scenes in omnidirectional cameraimages via polar higher-order correlation. Ulrich and Nourbakhsh compared similaritymeasures for appearance-based place recognition using color histograms [243].
Recent more general solutions without prior environment map, known as appearance-based simultaneous localization and mapping, will be treated in Section 7.2.
6.2.3 Radio Location Fingerprinting
Wireless fingerprinting approaches utilize the identification mechanisms of wireless stan-dards (WiFi, Bluetooth, GSM, etc.) which belong to active RFID. Fingerprints com-monly consist of the addresses of detected devices and information about signal strengthor link quality. Wireless location fingerprinting is particularly motivated by the fact thatgood predictions of radio propagation are difficult, if not impossible (cf. Figure 6.6 onp. 98). For a taxonomy of location fingerprinting methods, with focus rather on WLANthan on robotics, we refer to Kjærgaard [129].
An early fingerprinting approach was pursued by Bahl et al. [11]: In their in-buildingsystem RADAR, WLAN signal strength measurements were used for combined local-ization via signal propagation modeling and fingerprinting. Ladd et al. [149] extendedRADAR on a robotic platform by Markov localization. Li et al. [155] compared weightedk-nearest neighbors (WKNN) and Markov localization based on WLAN signal strengthmeasurements. Widyawan et al. [225] provided simulation results for particle filteringand probabilistic 1-nearest neighbor in the context of active RFID with signal strength.Lemelson et al. [153] performed RSS-based localization using wireless LAN. They didnot filter position estimates temporally, but the observation model was based on a distri-bution of smoothed reference fingerprints. Ferris et al. [65] localized by means of particlefiltering on mixed graph/free space representations. Signal strength models were learnedvia Gaussian processes. Sayrafian et al. [214] localized indoors by means of a rotatingantenna. They turned the power spectrum of different directions into fingerprints andtested different distance measures. Gräfenstein et al. [86] fused RSS, odometry, sonarand map knowledge in a particle filter for outdoor robot localization. They reported amean positioning error of 0.3 m with a modified low-power IEEE 802.15.4 device.
Tanaka et al. [234] and Yamano et al. [261] employed active RFID tags. They local-ized a robot by classifying signal strength feature vectors via support vector machines(SVMs). Lim and Zhang [157] performed location fingerprinting with passive UHFRFID tags. Their transponders (176) were attached to the ceiling (4.2× 8.4 m) at regu-lar distances. The position of their mobile platform was deterministically computed byintersection rules of the sets of detected transponders and reference measurements. Thereported accuracy is an error of less than 1 m in 97 % of the trials.
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Senta et al. [223] trained support vector machines with the time order of appearanceand read counts of detected passed tags. SVM training, however, is time-consuming, andso far their method was restricted to one room dimension.
Some approaches employ connectivity rates of active RF nodes, which resembles ofdetection rates of passive transponders besides that read ranges are longer. For instance,Bargh et al. presented location fingerprinting with room-level accuracy, using responserates of Bluetooth dongles [15]. Oliveira Filho et al. also relied on inquiry rates ofBluetooth nodes [189]. After calibrating inquiry rates on a regular grid of referencepositions, they localized a mobile device by computing region-based posterior probabil-ities. Denby et al. performed full-band GSM fingerprinting with room-level accuracy ina city flat [45]. They compared Gaussian processes to k-nearest neighbors and to supportvector machines.
6.3 RFID-based Localization Using Particle Filters
In RFID-based localization, the pose of the robot is to be determined from a series ofRFID measurements taken by its on-board antennas. We again follow a probabilisticsetting: We estimate the belief p(xt |m, f1:t,u1:t) of the robot pose xt at time step t,given an environment representation m with some kind of RFID reference data, a seriesof RFID observations f1:t, and a sequence of odometry readings u1:t. The term m is eithera transponder map, containing known tag positions, or a set of reference measurementsrecorded at known locations. The RFID detections f1:t are represented as in Section 5.3.1,with ft = (f
(1)t , . . . , f
(A)t ) and f
(a)t = (f
(a)t,1 , . . . , f
(a)t,L ), where f
(a)t,j ∈ N counts how often
tag j was detected by antenna a.Understanding localization as a Markov process, the density p(xt |m, f1:t,u1:t) can be
estimated recursively by Bayesian filtering as introduced in Section 2.2:
p(xt |m, f1:t,u1:t) = ηp(ft |xt,m)
∫
x′
t−1
p(xt |ut,x′t−1)p(xt−1 |m, f1:t−1,u1:t−1)dx
′t−1
(6.1)
Here, p(xt−1 |m, f1:t−1,u1:t−1) is the location prior at time step t− 1. The motion model
p(xt |ut,xt−1) gives the probability of reaching location xt if the robot performs the mo-tion command ut in position xt−1. The entire integral in (6.1) predicts the robot pose,given the former belief and the movement ut. The observation model p(ft |xt,m) rep-resents the likelihood of observing ft from xt, given m, and η finally is a normalizationfactor. The distribution p(x0) := p(x0 |m, f1:0,u1:0) captures the initial robot pose. Fortracking, p(x0) is given by a conventional starting position or by a human telling it. Theinitial distribution is then modeled either by a peaked Gaussian or a Dirac peak. For thepurpose of global localization we will depict initialization strategies which take advan-tage of sensor data to estimate p(x0) in later sections.
90
6.4 MODEL-BASED LOCALIZATION
We estimate (6.1) by a particle filter (cf. Section 2.2.2). The belief over locations isapproximated by weighted samples (x
(i)t , w
(i)t ), i = 1, . . . , Ns. x
(i)t represents a pose
hypothesis and w(i)t its importance weight. Filtering follows the usual steps of Monte
Carlo localization [74]:
1. Prediction: Given a new odometry reading ut after iteration t − 1, the robot poseat time t is predicted by propagating all particle positions according to the motionmodel p(xt |ut,xt−1) (cf. Section 4.2).
2. Correction: A new measurement ft leads to reweighting the particle weights withthe likelihood function p(f |x,m). Having used the motion model for computingthe proposal distribution, the weights are corrected according to (cf. (2.23), p. 16):
w(i)t = ηt w
(i)t−1 p(ft |x(i)
t ,m) (6.2)
The normalizer ηt ensures that∑Ns
i=1 w(i)t = 1.
3. Resampling: Resampling is performed as introduced in Section 2.2.3. To avoidparticle depletion, one resamples only if the effective sample size Neff falls belowsome threshold, e.g., Ns/2.
A major factor of robustness and versatility is that particle filters permit arbitrary noisedistributions for motion and sensor data. This makes them a good choice when usingpassive RFID. The central issue in RFID-based localization now remains how the ob-servation model in (6.1) is designed. We will address it in Sections 6.4 to 6.6, based ondifferent localization paradigms.
Perturbed Motion Model for Global Localization
Typically, the uncertainty in the robot pose is large in the first few filtering steps. More-over, the filter might get stuck in a local minimum which is optimal when only regardingthe first few observations. Hence, it is reasonable to allow the particles to better explorethe location space. A simple solution is to relax the motion model and artificially per-turb sample locations during initial iterations. This can be achieved, for instance, byadding time-decaying noise ν exp(−αt), depending on the time step t, to the rotationaland translational parameters when sampling from the motion model. There, ν is theamplitude of perturbation and α a time scaling factor.
6.4 Model-based Localization
In model-based localization the pose of the robot is determined based on a model of de-tection rates for relative displacements between RFID tag and reader antenna. The envi-ronment representation m contains the positions of RFID tags as environment features.This approach was originally pursued by Hähnel et al. [96] and taken later by several
91
CHAPTER 6 LOCALIZATION
Estimation of
tag positions
Mapping data
(RFID, reference
positions)
RFID sensor
model
Map
(tag positions)
Manual
generation
of a map
Model−based
localization
Location fingerprinting
Sensor data
during localization
(RFID, odometry)
mappin
g/c
alib
ration s
tage
localiz
ation s
tage
RFID
Snapshots
Filtered
WKNN
FIGURE 6.2: Estimation steps (rounded rectangles) and processed/generated data
(folded rectangles) in model-based localization and location fingerprinting
groups in a similar fashion [47, 119, 195], including ourselves [247]. The workflow ofmodel-based position estimation can be seen in the left part of Figure 6.2.
6.4.1 Modeling Observations
Given the Monte Carlo framework from Section 6.3, model-based localization distin-guishes itself by the type of observation model p(ft |xt,m) in (6.2). In this case, m =l1, . . . , lL is a map containing the positions li, i = 1, . . . , L, of L transponders in theenvironment. The map m is either the result of a mapping stage (see previous chapter) ormanually supplied by a human who has measured the tag locations. Moreover, a sensormodel p(q |x) as in Chapter 4 is given; it states the probability of detecting a tag q times,provided that the tag is situated in position x relative to the reader antenna. If we claimindepence of the detections of single RFID tags at all A RFID antennas on board therobot, we obtain, with similar arguments as in Section 5.3.1:
p(ft |m,xt) =A
∏
a=1
L∏
j=1
p(f(a)t,j |m,xt) =
A∏
a=1
L∏
j=1
p(f(a)t,j | lj ⊖ aa(xt) (6.3)
As before, lj ⊖ aa(xt) denotes the current position of tag j relative to RFID antenna aat time t. So, the likelihood of the current measurement is the product of the detectionprobabilities of all L tags at the A antennas of the RFID reader. Practically, however, we
92
6.4 MODEL-BASED LOCALIZATION
will ignore nondetections and replace (6.3) with:
p(ft |m,xt) =∏
(a,j):f(a)t,j 6=0
p(f(a)t,j | lj ⊖ aa(xt)) (6.4)
The argumentation follows Section 5.3.3. There we argued that most tags cannot be readmost of the time. They can safely be ignored in likelihood computations. An importantbyproduct is considerably increased efficiency: The correction step requires O(Ns · Lt)likelihood computations instead of O(Ns · L), with Lt the number of detected tags attime t.
6.4.2 Global Localization
For initializing the particle filter, there are essentially two strategies: First, samples canbe spread uniformly over the entire map. This, however, is extremely inefficient, since theentire state space needs to be covered densely. Already for medium-size environments,the size of the particle filter becomes intractable in the light of real-time requirements.Of course, once the filter has (almost) converged, the sample set can be reduced (e.g., byadaptation heuristics [99] or KLD-sampling [73]) when only further tracking the robotpose.
The much better alternative immediately generates particles in likely areas accordingto the first observations. Indeed, the high-fidelity data association of RFID offers theunique possibility to substantially reduce the space of potential robot locations upon thedetection of already a single tag. The best initialization strategy would be to directlysample from the likelihood function (6.3). Due to its being a product of nonparametricshapes, however, this is not possible. We therefore investigate two alternatives for thecase that the robot detects L0 different RFID tags j1,. . . ,jL0 in the first inquiry:
• Tag range sampling: Around each known tag location lji, we draw Ns/L0 sam-
ples uniformly from a disk of radius D, which equals the maximum RFID readrange. This is the straightforward approach as practiced earlier [96, 119], extendedto L0 concurrently observed labels in denser environments.
• Sensor model sampling: In Section 5.3.2 we proposed a sampling algorithmwhich generated tag location particles based on the known pose a of the RFIDantenna and the sensor model. Analogously, we can now sample robot position hy-potheses, provided the map of transponder positions. In order to ignore transpon-der orientations, however, we slightly modify the sampling technique:
1. The 2D sensor model p(q |x = (x, y)) is transformed into a model p(q |x)by marginalizing out the y coordinate. The distribution is represented by ahistogram over x values.
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CHAPTER 6 LOCALIZATION
2. Then, for each detected tag ji, we sample angles φ ∼ U(−π, π) and distancesd ∼ p(q | d) relative to its known location lji
. The relative coordinates aretransformed into global coordinates to constitute robot pose hypotheses.
All samples are initially assigned equal weights 1/Ns. Due to rounding, each tag actuallycontributes either ⌊Ns/L0⌋ or ⌊Ns/L0+1⌋ samples. A further intuitive alternative wouldbe to initially generate samples in the intersection of detection areas of the L0 detectedtags. This is, however, not a conservative choice due to the noisiness of RFID detections.The two proposed ways of initialization are more conservative, and already place moresamples in intersecting detection areas.
6.4.3 Experiments
In the following, we describe the results of experiments with the model-based localiza-tion method. Each experiment is associated with one or several data sets that are doc-umented in Section A. We always pursued a cross-validation approach on the recordeddata: We learned transponder maps on a stated subset of log files (typically two). Then,the robot was localized on each of the remaining logs. This step was repeated five timesto meet the random nature of particle filtering.
In the mapping stage we followed the sensor model sampling technique with 300 sam-ples per tag (in a single pass). For the sensor models we had applied quartic kernelregression based on calibration data with tags on different heights, as before.
The motion models of both robots were represented and calibrated after the approachby Eliazar and Parr [63] (see Section 4.2). The learned parameters are listed in Table 6.1.
We applied residual resampling whenever the effective sample size dropped belowhalf of the filter size, i.e., Neff < 0.5Ns. Unless otherwise noted, we set Ns = 1000.
Analogously to the experiments in Chapter 5 (cf. p. 62), we computed the mean abso-lute Cartesian localization error for each run on an entire log file, and plots contain themeans and standard deviations of this value over all repetitive runs of the particle filteron all log files. The standard deviations in these plots are marked by standard deviations
(of trial means). In the text and in tables, by default we provide mean and standard de-viation of the localization error over all time steps and log files. Additional plots containthe cumulative distributions of localization error statistics.
Position Tracking
The results of position tracking with the SCITOS G5 in the Sand 1 wing (Section A.4)are shown in Figure 6.3. There, we compare the two types of RFID sensor models as inthe previous chapter: a model with a Gaussian distribution of detection counts and onewith a Bernoulli distribution of pure detection probability. Additionally, we varied thenumber of samples and tested two different tag densities and two transmission powers.
94
6.4 MODEL-BASED LOCALIZATION
0
0.5
1
1.5
30 100 300 1000
mean a
bs. lo
caliz
ation e
rror
(m)
particles
Gaussian model
Higher density, 22.5 dBmHigher density, 30.0 dBmLower density, 22.5 dBmLower density, 30.0 dBm
0.3
0.4
0.5
0.6
0.7
1000
0
0.5
1
1.5
10 30 100 300 1000
mean a
bs. lo
caliz
ation e
rror
(m)
particles
Bernoulli model
Higher density, 22.5 dBmHigher density, 30.0 dBmLower density, 22.5 dBmLower density, 30.0 dBm
0.2
0.3
0.4
1000
FIGURE 6.3: Model-based tracking results with different sensor models, tag densities,
and transmission power levels. Means and standard deviations (of trial means) are plot-
ted against varying numbers of particles. (SR-113/SCITOS G5)
If we take a look at the curves for full transmission power and higher tag density, weobserve that the experimental accuracies over all time steps were 0.37± 0.22 m (maxi-mum 1.42 m) with the Gaussian model and 0.31± 0.20 m (max. 1.52 m) with the Ber-noulli model. The fact that the Bernoulli model performs better is surprising, becausethe Gaussian model was superior in transponder mapping (cf. Section 5.3.4). Intuitivelyone might assume that detection counts provide more information and thus higher ac-curacy than mere binary detection information. A similar observation is striking withregard to the number of samples that are required to achieve the named accuracy: Withthe Bernoulli model, 30 particles sufficed to obtain comparable errors, while the Gauss-ian model required 300 particles. This trend is also underlined by the plots for the lowertag density and the lower transmission power. The depicted large standard deviationssubsume cases in which the robot lost its position.
The graphs also show that the larger tag density had a positive effect on localizationaccuracy. While this insight is not surprising, we can also observe that decreasing theread range of the RFID reader worsened accuracy in case of the Gaussian model. Thiseffect seems counterintuitive, since the uncertainty in the relative position between robot
TABLE 6.1: Calibrated motion model parameters of the two robots
Robot µCdµCr
µDdµDr
µRdµRr
B21 0.0 0.0 1.015 0.0 0.0 0.980SCITOS G5 -0.014 0.091 1.004 -0.016 0.005 0.996
Robot σCdσCr
σDdσDr
σRdσRr
B21 0.121 0.237 0.141 0.141 0.077 0.196SCITOS G5 0.072 0.074 0.113 0.112 0.061 0.200
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CHAPTER 6 LOCALIZATION
0.2
0.3
0.4
10 30 100 300 1000me
an
ab
s.
loca
liza
tio
n e
rro
r (m
)
particles
Model with tags on same height
Higher densityLower density
0.2
0.3
0.4
10 30 100 300 1000me
an
ab
s.
loca
liza
tio
n e
rro
r (m
)
particles
Model with tags on different heights
Higher densityLower density
FIGURE 6.4: Model-based tracking results with different sensor models, tag densi-
ties, and numbers of particles (means and standard deviations (of trial means), ALR-
8780/B21, 33 dBm RF power)
and tag decreases with smaller transmission power. However, Table A.2 on p. 167 revealsthat at a smaller read range, the average number of detected transponders was smaller.Thus our experiments indicate that an increase in the number of detected tags may out-weigh the uncertainty resulting from longer read ranges, at least for a Gaussian sensormodel. With the Bernoulli model, this effect is observable for smaller particle numbers,too, but only marginally as the number increases.
A similar experiment was conducted with the B21 robot in the corridor environment(dataset CORR.HD.C2). Figure 6.4 reveals the following insights: First, a higher tagdensity does not necessarily lead to better localization results. We observed that thehigher density has an error that is increased on average by up to 4 cm (significantly, p-value 0). Second, accurate and robust tracking is already possible with few particles.It is worth noting that, with respect to the number of detected tags, the environment inFigure 6.4 is similar to the higher tag density/larger transmission power in Figure 6.3.And third, the choice of sensor model has a decisive impact on localization accuracy:In the experiments, tags were roughly at the heights of the antennas of the robot. Themodel which had been learned with smaller variations in the z coordinate of placedtransponders yielded a better accuracy, as can be seen in Figure 6.4. Thus it seems to payoff if an RFID sensor model is learned exactly for the type of transponder placement thatis pursued in the application environment.
Global Localization
We examined the convergence behavior of the two proposed initialization approaches tomodel-based global localization. To compensate for initial uncertainty, the motion modelwas relaxed by νrot = 0.8, αrot = 0.015, νtrans = 0.5, and αtrans = 0.015 (cf. p. 91).
We experimented with the large-corridor data set (SAND1.HD.30dBm, p. 167), whichhad been recorded with the SCITOS at full RF power and with the higher tag density. Ineach of five trials per log the initial robot pose was selected randomly. The results for
96
6.5 LOCATION FINGERPRINTING USING RFID SNAPSHOTS
0
0.5
1
1.5
2
2.5
1 10 100me
an
ab
s.
loca
liza
tio
n e
rro
r (m
)
time steps
Gaussian model
Sensor model samplingTag ranges
Around true pose
0
0.5
1
1.5
2
2.5
1 10 100me
an
ab
s.
loca
liza
tio
n e
rro
r (m
)
time steps
Bernoulli model
Sensor model samplingTag ranges
Around true pose
FIGURE 6.5: Results of global localization using the model-based approach: The abso-
lute localization error has been averaged over the corresponding number of time steps.
a particle filter with 1000 samples are shown in Figure 6.5, where again we compare aGaussian detection count model and a Bernoulli detection probability model (both quar-tic kernel regression). The mean absolute localization error is averaged over differentnumbers of time steps after filter initialization. Both initialization techniques, tag rangesampling (TRS) and sensor model sampling (SMS), converged to the same error afterapprox. 10-50 time steps. They differ, however, with regard to initial accuracy: Withthe Gaussian model, the Cartesian position errors of the robot after the first RFID ob-servation is 1.46± 0.69 m for SMS and 1.74± 0.66 m for TRS. That is, the robot canlocalize itself at a mean accuracy of approx. 1.5 m from scratch. The benchmark accu-racy of initializing the particle filter on a disk of radius 3 m around the unknown truepose (Gaussian model: 0.83± 0.48 m; Bernoulli model: 0.68± 0.37 m), however, wasnot achieved. In these experiments SMS performed significantly (p < 10-3) better. Thesame trend holds for the Bernoulli model at even lower initial errors of 1.31± 0.65 mfor SMS and 1.41± 0.60 m for TRS. As it seems, the extra knowledge in the shapeof distance-based detection statistics, extracted from the sensor model by the SMS ap-proach, payed off. The maximum initial errors were between 2.93 m (SMS, Bernoulli)and 3.98 m (SMS, Gaussian).
6.5 Location Fingerprinting Using Global Detection
Rates (RFID Snapshots)
6.5.1 Introduction
The presented model-based approach requires an explicit sensor model which predictsdetection rates relative to a reader antenna. As seen before, the predictive power of themodel, however, exerts significant impact on localization accuracy. A low-dimensionalmodel averages over a number of relevant parameters which actually reveal impact on
97
CHAPTER 6 LOCALIZATION
Prediction based on RFID sensor model
’-’
0 2 4 6 8 10 12 14 16
x (m)
0
2
4
6
y (
m)
Interpolated reference measurements
’-’
0 2 4 6 8 10 12 14 16
x (m)
0
2
4
6
y (
m)
0
0.02
0.04
0.06
0.08
0.1
0.12
FIGURE 6.6: Real-world example of model-based localization vs. location fingerprint-
ing: Predicted detection rates of a specific tag in different positions of the lab (averaged
over all possible orientations of the robot). LEFT: Prediction based on an RFID sensor
model. RIGHT: Interpolated estimate based on reference measurements as used in the
snapshot approach, Equation (6.8).
tag detections. Examples are orientation and height of a tag, and materials in the vicin-ity of a tag which absorb or reflect electromagnetic waves. It is impossible to considerall these factors, as argued before. The sensor model consequently fails to accuratelyapproximate the true detection behavior of RFID tags. This itself means that the obser-vation model (6.3) does not compute detection probabilities arbitrarily exactly, whichcauses inaccurate location estimates. A real-world example comparison of predictions isshown in Figure 6.6.
An alternative is location fingerprinting: The list of detected tags is regarded as afingerprint which characterizes the pose of the robot. The pose of the robot is thenestimated by comparing RFID measurements during the localization stage to either rawor interpolated reference measurements from a prior calibration stage, as indicated in theright part of Figure 6.2. In opposition to Section 6.4, however, neither a sensor modelis required nor a landmark map is estimated as an intermediate result. The environmentrepresentation m now simply consists of the pose-annotated time sequence of RFID data(fi,xi)i∈N from the calibration phase, where each xi is the pose of the antenna bywhich the corresponding inquiry fi was recorded.
In this section, we treat and extend fingerprinting with RFID snapshots, which weredeveloped by Schneegans [216, 217]. The idea is to compute smooth estimates of ex-pected detection rates directly in the global frame of reference, relative to which thereference measurements were recorded. Based on these global estimates, likelihoods ofthe current detection events of single tags are computed during the localization stage. Asa generalization, RFID inquiries are repeated over short series of C cycles. The list ofdetected tags f (a) at antenna a is then understood as a snapshot, where tag counts f
(a)j
now range from 0 (tag not detected) to C. Before, we assumed C = 1, i.e., each mea-surement was assumed to comprise a single round of detection attempts at the reader.Measuring for C cycles can be achieved either via the configuration of the RFID readeror simply by accumulating C measurements.
98
6.5 LOCATION FINGERPRINTING USING RFID SNAPSHOTS
The rest of Section 6.5 contains material from our IROS 2008 publication [244] andthe ECMR 2007 paper [217].
6.5.2 Modeling Observations
The computation of the likelihood p(ft |xt,m) in the snapshot approach comprises twosteps: First, the detection probabilities ql of all tags 1 ≤ l ≤ L are estimated for eachantenna pose a from the training snapshots. Again, L is the number of tags in the envi-ronment as known from training. Then, given these reference estimates, the likelihoodof the current RFID measurement is computed.
Each training snapshot f = (f1, . . . , fL), taken by one of the on-board antennas, allowsfor the estimation of the L detection probabilities q(f) = (q1(f1), . . . , qL(fL)) at theposition where f was taken. Since the detection probabilities cannot be observed directly,we compute the Bayes estimate ql(fl) for each tag l:
ql(fl) =
∫ 1
0
qlp(ql | fl)dql (6.5)
with p(ql | fl) =p(fl | ql)p(ql)
∫ 1
0p(fl | q′l)p(q′l)dq′l
. (6.6)
The conditional probability p(fl | ql) follows a binomial distribution:
p(fl | ql) =
(
C
fl
)
qfl
l (1 − ql)C−fl . (6.7)
The term p(ql) in (6.6) is the prior distribution of the detection probability ql. It ismodeled by a step function with a large value if ql is smaller than some θ close to zero anda constant small value in the rest of the interval (θ, 1]. This is because in the major partof the environment, a specific tag will not be detected most of the time (cf. Figure 6.6).Note that C needs to be known, and thus the snapshot-based localization mainly refersto RFID readers which offer the interactive mode (cf. Section 3.2.3).
A reliable estimate of the detection probabilities for an arbitrary antenna pose a isinterpolated from the estimates obtained from the training snapshots fπ1 , . . . , fπr
recordednear a (with π a suitable permutation of reference fingerprint indices):
q(a) = α1q(fπ1) + · · · + αrq(fπr) + βq0 (6.8)
with q = (q1, . . . , qL). The weights αj are computed by the Gaussian
αj = ξ · exp
(
−1
2(||xi − a||/σ)2
)
, (6.9)
where the xi are the reference positions where the training snapshots fi were taken. ξ isa normalization factor which ensures that
∑rj=1 αj + β = 1. The distance measure
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CHAPTER 6 LOCALIZATION
|| · || must also respect the orientations of the antennas. q0 in (6.8) is an estimate of thedetection probabilities in the absence of training scans. By the normalization β = ξ · β0,the influence of q0 decreases if many training snapshots are available close to a. q0 hasL equal entries q0 that can be obtained from the prior p(q) via:
q0 =
∫ 1
0
p(q) q dq (6.10)
Finally, the estimate q(a) is used to compute the likelihood of a robot pose. To thisend, the probabilities of the observed detection frequencies are determined by insertingthe estimated detection probabilities ql(a) of each tag into (6.7). If we assume that themeasurements of the single tags are independent, the likelihood of a snapshot f is:
p(f | a) =L
∏
l=1
p(fl | ql(a)) (6.11)
Equation (6.11) permits to weight a particle by determining the antenna pose a from thepose x of each particle, given the current observation f . If an RFID system possesses twoantennas (like ours, see Figure 1.2 on p. 6), the snapshots of the left and right antennasare taken simultaneously. If both measurements are independent – which can be assumeddue to non-overlapping antenna ranges in our case –, the resulting likelihood function is
p(f(l)t , f
(r)t |xt) = p(f
(l)t | al(x)) · p(f
(r)t | ar(x)), (6.12)
where al(xt) and ar(xt) denote the poses of the left and right antenna if the robot is
believed to be at pose xt, and f(l)t and f
(r)t are the corresponding snapshots.
6.5.3 Adaptations to Densely Tagged Environments
In densely tagged environments, the observation likelihood (6.11) is a product of a largernumber of independent likelihoods and becomes sharply peaked. The number of presenttransponders, L, in (6.11) is large (L ≫ 100 in a supermarket), and ql is close to zero formost tags l. Consequently, many particles will receive very small weights. Numericalproblems in representing the particle weights can be circumvented by computing thelog-likelihoods for particles. Weights among the set of particles, however, differ byseveral orders of magnitude. Even large particle numbers do not suffice to represent theposterior distribution well. Resampling will cause particle depletion, because very fewsamples are replicated multiple times. The worst consequence is the delocalization ofthe robot if noisy sensor data shift the samples to unlikely locations. For laser-basedlocalization, Thrun et al. [238] proposed a solution called Mixture-MCL. In each filteriteration, they sampled some particles directly according to observations. We decidedagainst this method because laser scanners provide a much higher certainty of a singlemeasurement than RFID such that additional particles can be sampled in a focused area.
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6.5 LOCATION FINGERPRINTING USING RFID SNAPSHOTS
ALGORITHM 6: Selection of the L∗ currently most discriminative transponders
Input: Current snapshot f := f(a)t ; reference snapshot q := q(aa(xt))); desired
cardinality L∗ of LOutput: Set L of most discriminative transponders
1 L := ∅; l := 02 Find permutation π1: π1(i) < π1(j) ⇒ fi ≥ fj // Sort tags in f by tag count3 foreach l: fπ1(l) > 0 and π1(l) known from training do // Prefer current detections4 if |L| < L∗ then
5 L := L ∪ π1(l)
6 Find permutation π2: π2(i) ≤ π2(j) ⇒ qi > qj // Sort reference q by tag count7 while |L| < L∗ do // Add most unexpected nondetections8 L := L ∪ π2(l)9 l := l + 1
10 return L
Smoothing of the Likelihood Function
One way of achieving a less sharply peaked likelihood function is to smooth its values.Let L be the set of tag identifiers with nonzero detection probability either in f or q(a).Ferris et al. [65], for instance, defined the smoothed likelihood function by:
p(f | a) =
(
∏
l∈L
p(fl | ql(a))
)λ
(6.13)
If the smoothing parameter λ is chosen to be λ = 1|L|
, the formula represents the geomet-ric mean over all tags in L. This way, the degree of smoothing adapts to the number ofcurrently relevant observations. Alternatively, it can be set to a constant value 0 < λ < 1.
The smoothing approach certainly decreases the tendency of very small particleweights. Yet, the likelihood of each transponder detection is treated the same way, inde-pendent of the degree of information given by its detection. For this reason, we proposedthe following approach in [244].
Partial Evaluation of the Likelihood Function
An alternative strategy is to evaluate the likelihood function only for those transponderswhich are currently most discriminative. At any position in the environment, only asmall fraction of the trained tags are likely to be detected. That is, such tags l possess anexpected detection rate ql which considerably differs from zero. They should definitelybe considered in likelihood evaluation.
A currently not detected transponder l with negligible detection probability can beignored: If we assume that the position variance of the particles is small, ql will have the
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same small value for all particles. Consequently, transponder l does not help to assesspose hypotheses. If the current snapshot f , however, contains a detected tag j which wasconsidered negligible by the estimate qj , a particle should receive a lower weight becausethe reference snapshot does not explain the particle pose well enough.
So, we evaluate the likelihood function only for a constant-size subset of L∗ ≤ Ltransponders which are most relevant with regard to the aforementioned arguments. Al-gorithm 6 depicts the procedure. Essentially, the tag indices of the currently measuredsnapshot and the estimated reference snapshot are sorted descending by detection rates.Then, only the first L∗ transponders are selected, which stand for the currently mostdiscriminative ones. The resulting set L is used to compute the conditional probability:
pL(f | a) =∏
l∈L
p(fl | ql(a)) (6.14)
6.5.4 Global Localization
The snapshot-based solution to initializing the particle filter is to generate particles withposes that are directly sampled from the training snapshots as soon as the first RFIDmeasurement f0 arrives. Formally, the ith particle (x
(i)0 , w0), with w0 = 1/Ns, is drawn
according to an approximation to the likelihood of f0:
x(i)0 ∼ p(f0 |x) ≈ η
n∑
j=1
p(f0 |xj) δ(x − xj) (6.15)
with η = (∑
j p(f0 |xj))−1 and δ the Dirac delta. The x
(i)0 assume the reference positions
of the training snapshots, i.e., antenna poses. Therefore we add the pose shift betweenantenna and robot position and perturb the resulting positions with Gaussian noise toincrease particle diversity.
6.5.5 Experiments
We examined snapshot-based localization in a series of experiments. The experimentalsetup and general cross-validation procedure was the same as in Section 6.4.3. In allexperiments, we set β0 = 0.8. Moreover, we set the prior p(ql) such that
p(ql) =
0.8 · ε−1 0 ≤ ql ≤ ε, ε = 10−3
0.2 · (1 − ε)−1 ε < ql ≤ 1(6.16)
In all snapshot experiments, the ALR-8780 reader was configured to scan once with eachantenna. Since the reader is bistatic (cf. Section 3.2.2), measurements at the cooperatingantenna pair (i.e., the same side of the robot) were joined, where tag counts were added.The number of measurement cycles, C, is therefore always a multiple of two, because the
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6.5 LOCATION FINGERPRINTING USING RFID SNAPSHOTS
TABLE 6.2: Snapshot-based position tracking results in the corridor environment for
varied numbers of measurement cycles, C, and different tag densities.
(ALR-8780/B21, L∗ = 20, Ns = 1000)
C Tag density Mean absolute Maximum absolute Mean absoluteCartesian error (m) Cartesian error (m) rotational error (rad)
2 higher 0.21± 0.13 1.46 0.112 lower 0.24± 0.14 0.94 0.114 higher 0.18± 0.10 0.75 0.114 lower 0.23± 0.19 6.10 0.12
joining subsumes inquiries of two antennas. As described in [244], we precomputed thereference estimates q(x) in a look-up table with resolution 0.1 m and 10°. Comparativeresults such as for the number of samples Ns will be presented in Section 6.7.
A decisive parameter in experiments is L∗, the number of evaluated individual tagdetection likelihoods. Basically, there are three choices: Setting L∗ = L (all transpondersknown from prior training will be evaluated), setting L∗ to a constant value smaller thanL for all time steps, or setting it L∗ = Lt such that in each time step t simply the Lt
current tag detections will be considered.
Influence of Tag Density and the Number of Detection Cycles
For a fixed number of particles (Ns = 1000), we investigated position tracking whenthe number of measurement cycles, C, and the density of surrounding RFID tags arevaried. The corridor log files (CORR datasets, Section A.1) served as experimental data.The results for L∗ = 20 are listed in Table 6.2. Position tracking was possible at amean accuracy of 0.20-0.25 m and mean rotational errors of approx. 6.5°. Mainly theCartesian error was influenced by tag density and the choice of C: The higher tag densityincreased positioning accuracy by 3.5/4.5 cm. Four measurements (C = 4) per side ofthe robot also slightly improved the results as compared to C = 2. This comes, however,at the expense that correction steps are performed only at approx. 1.25 Hz (C = 4)instead of approx. 2 Hz (C = 2). Moreover, the maximum Cartesian error indicatesthat with the lower tag density, the filter diverged sometimes. In all other experiments,position tracking was robust, without filter divergence. In further experiments in the lab(not shown here, LAB.WS.C* datasets), C = 2 was the better choice, with equivalentCartesian and rotational errors. Values of C > 4 lead to worse results. We conclude:
• Position tracking is possible at an accuracy of better than 0.25 m.
• The higher tag density actually influenced localization accuracy positively.
• Using RFID snapshots which are recorded over more measurement cycles can, butdoes not necessarily reduce localization errors; it will, however, certainly result infewer measurement updates.
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0
0.1
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1 1/L 0.5 10-1
10-2
10-3m
ean a
bs. lo
caliz
ation e
rror
(m)
smoothing parameter λ
0
0.1
0.2
0.3
0.4
1 3 5 10 20 40 80 L Ltmean a
bs. lo
caliz
ation e
rror
(m)
L*
FIGURE 6.7: Position tracking results for different smoothing parameters. LEFT: Expo-
nential smoothing of the likelihood. The result for λ = 0.001 is 1.69± 0.53 m and was
cut for the sake of clarity. RIGHT: Partial evaluation of the likelihood function. (means
and standard deviations (of trial means), ALR-8780/B21, Ns = 1000)
Influence of Likelihood Adaptations
In the corridor environment (Section A.1), we investigated the impact of the two like-lihood adaptation approaches. In both cases, we examined the mean absolute positiontracking errors for the higher tag density setting.
The results of the exponential likelihood smoothing technique (6.13) are depicted inFigure 6.7. The unsmoothed reference case is represented by λ = 1, the geometric meanby λ = 1/L. In our experiments, exponents λ = 0.5 and λ = 0.1, which correspondto the square and to the tenth root of the unsmoothed likelihood, lead to significantly(p-value < 10−10) better results. Further smoothing did not improve or even decreasedthe localization accuracy.
Also the partial evaluation of the likelihood function in Figure 6.7 (right) reducedposition tracking errors. Evaluating only L∗ = 10 yielded a fidelity of 0.21± 0.12 m ascompared to 0.29± 0.20 m for all L trained transponders (significant difference, p-value< 10−10). The result is slightly, but also significantly (p-value < 10−10) better than whenusing all Lt currently available transponders, which yielded an error of 0.22± 0.13 m.
From these findings, we conclude that both approaches – exponential smoothing andthe partial evaluation of the likelihood function – effectively reduce the peakedness ofthe likelihood function and improve position estimates in a densely tagged environment.
In further experiments we will focus on the partial evaluation only, because it weightsthe importances of individual tags. Moreover, its parameter L∗ is more intuitive and canbe adjusted to the tag density of the target environment, if desired. Otherwise, by settingL∗ = Lt the snapshot likelihood adapts itself to the current tag count.
Global Localization
We investigated the global localization error and filter convergence, as shown in Fig-ure 6.8. Snapshot sampling was benchmarked against a uniform filter initialization on
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6.6 LOCATION FINGERPRINTING USING VECTOR SIMILARITY MEASURES
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1
1 10 100me
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ab
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rro
r (m
)
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Lower tag density (lab dataset, B21)
L*=Lt, ATPL*=Lt, SNSL*=20, ATPL*=20, SNS
0.2
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n e
rro
r (m
)
time steps
Higher tag density (lab dataset, B21)
L*=Lt, ATPL*=Lt, SNSL*=20, ATPL*=20, SNS
FIGURE 6.8: Global localization results with RFID snapshots (ATP=around true pose,
SNS=snapshot sampling). LEFT: Mean abs. Cartesian localization error for the lower
tag density (∅ 160 tags). RIGHT: Results for the higher tag density (∅ 281 tags).
a disk of radius 3 m around the true, but normally unknown pose. In the experiments,we localized ten times on each of the LAB.LD.C2 (lower density, Figure 6.8 (left)) andthe LAB.WS.C2 (higher density, Figure 6.8 (right)) logs, starting from randomly drawnpositions. The reference measurements were varied and taken from two of the remaininglogs, which corresponds to approx. 1000 reference fingerprints. We used 1000 samples,and the artificial initial noise parameters for easing filter convergence were set νR = 0.4,αR = 0.015 (rotation) and νD = 0.5, αD = 0.015 (downrange).
Snapshot sampling, although slightly worse in the initial time step, achieves compara-ble performance as compared to the case where we initialized around the unknown, truepose. On average, snapshot sampling achieved an accuracy of 0.5-0.6 m from scratch.After 50-100 time steps, both initialization techniques converged to approximately thesame mean error. Again, the higher tag density promoted more accurate localization.
6.6 Location Fingerprinting Using Vector Similarity
Measures
In this section, we present a universally applicable approach to location fingerprintingusing RFID detection rates. It is suited for any kind of EPC-compliant RFID reader andbuilds upon a long tradition of fingerprinting using similarity measures with wirelesstechnologies such as WLAN (IEEE 802.11), Bluetooth, GSM, and others. Here, weapply the same ideas to RFID-based localization while incorporating temporal filteringfor the sake of accuracy and robustness.
The remainder of Section 6.6 is an extended version of our ISR 2010 publication [249].
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6.6.1 Weighted k-Nearest Neighbors (WKNN) Fingerprinting
In the simplest form of fingerprinting, the current pose is assumed to be the one whoserecorded signals during the calibration stage best match the current sensor data. Match-
ing is measured in terms of some kind of similarity measure, which is a function yieldinga scalar similarity value when comparing two vectors of sensor data. An example is thecosine similarity. Equivalently, a dissimilarity measure such as the Euclidean distancecan be employed, where small distances in signal space promise closeness with respectto location. Formally, let (xi, fi), i = 1, . . . , n, be n reference positions xi, wherethe fi ∈ R
d are the corresponding recorded d-dimensional measurements, as before. Inwireless fingerprinting, they would contain the received signal strengths (RSS) of d basestations. In our mobile robot scenario, d = L is the number of available RFID tags,and each fi corresponds to a vector of detection rates as counted by one of the on-boardantennas in position xi. For convenience, we build upon a single antenna by now.
A simple estimate of the current position x, given a new measurement g, is
x = argmax(xi,fi)
sim(fi,g) or x = argmin(xi,fi)
d(fi,g), (6.17)
where sim is a similarity measure and d is a dissimilarity measure, respectively. This is aspecial case of k-nearest neighbors (k-NN), where the position is the average of those kpositions whose reference measurements match best: Let π : 1, . . . , n → 1, . . . , nbe a permutation such that π(i) ≤ π(j) ⇒ sim(fi,g) ≥ sim(fj,g). Then, the k-NNposition estimate is x = 1
k
∑ki=1 xπ(i), where special attention has to be paid to averaging
orientations. For k > 1, this estimate is apparently more robust than the simple 1-NNestimate from (6.17). Additionally, the reference positions can be weighted according tothe similarities of the corresponding measurements:
x =1
∑ki=1 sim(fπ(i),g)
k∑
i=1
xπ(i) sim(fπ(i),g) (6.18)
This is the weighted k-nearest neighbors (WKNN) pose estimate. The similarity mea-sure sim must be nonnegative and should be symmetric (sim(f ,g) = sim(g, f) ∀ f ,g).Analogously, a dissimilarity measure d should also be nonnegative and symmetric, withd(f , f) ≤ d(f ,g) ∀ f 6= g, and the larger the value of d, the more dissimilar are its vectorarguments, in contrast to similarity measures. In Section 6.6.2 we will describe candidatemeasures of similarity and dissimilarity.
Fingerprint Retrieval by Inverted Indexing
Finding those k fingerprints which are most similar to a measurement vector g naïvelywould require to browse all reference measurements. It is possible, however, to immedi-ately prune all references fi, i = 1, . . . , n, for which sim(g, fi) = 0: These measurements
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6.6 LOCATION FINGERPRINTING USING VECTOR SIMILARITY MEASURES
TABLE 6.3: Vector similarity and dissimilarity measures for comparing tag lists f and g
Similarity measure Abbr. Formula: simAbbr (f ,g) = . . . Range
Cosine similarity COSPL
l=1 flgl√PL
l=1(fl)2·√
PLl=1(gl)
2[0, 1]
Histogram intersection HIST∑L
l=1 min(fl, gl) [0,∞)
Bhattacharyya coefficient BHA∑L
l=1
√flgl [0,∞)
Overlap score OSC log(1 + simNCT (f ,g) simCOS (f ,g)) [0,∞)
Dot (or scalar) product DOT∑L
l=1 flgl [0,∞)Number of common tags NCT |l | flgl > 0, l = 1, . . . , L| [0,∞)
Dissimilarity measure
Minkowski distance Lp (∑
l |fl − gl|p)1p [0,∞)
Hellinger distance HD
√
∑Ll=1(
√fl −√
gl)2 [0,∞)
χ2 statistics CHI∑L
l=1(fl − µl)2/µl, µl = fl+gl
2[0,∞)
Bray-Curtis dissimilarity BC (∑L
l=1 |fl − gl|)/(∑L
l=1(fl + gl)) [0, 1]
Jeffrey divergence JD∑L
l=1(fl log (fl/µl) + gl log (gl/µl)) [0,∞)
certainly have disjoint sets of detected tags. Pruning can be implemented via an inverted
index κ. The index κ maps transponder identifiers to measurement indices in which thecorresponding tag was detected during the calibration stage:
κ : 1, . . . , L → 21,...,n : l 7→ i | fi,l > 0, i = 1, . . . , n (6.19)
Consequently, similar fingerprints only need to be searched within the index set
K(g) =A⋃
a=1
⋃
l: g(a)l
>0
κ(l) (6.20)
of all reference fingerprints having at least one tag in common with g. This way, werestrict the search to a small local subset of calibration measurements. The search com-plexity depends on the number of detected tag identifiers in g for the lookup and on thedensity of fingerprints taken during the calibration stage. In particular, the time complex-ity does not depend on the size of the environment, which is a major factor of scalability.
6.6.2 Vector Similarity Measures for Long-Range Passive RFID
The choice of similarity measure can have major impact on the localization result. Inthe technical literature, a variety of similarity measures have been employed for differentapplications. The most suitable measure is normally data- and hence task-dependent.Similarity measures for long-range passive RFID should take into consideration:
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1. False-negative detections occur frequently and must not be overrated. RFID tagsmay not be detected even if detected by a prior inquiry in the same position.
2. The number of common tag IDs in two compared measurements may be more im-portant than how often each of the tags was counted: Detection rates are typicallynoisy. If there are several RFID tags spread over the environment, the overlap oftag identifiers helps to refine the position of the RFID antenna. This insight followsfrom the experiments with the Gaussian and the Bernoulli sensor model (p. 95).
3. Data association is known. Hence measurement vectors can be compared in acomponent-wise fashion. Cross-bin similarity measures (such as earth mover’sdistance or cross-correlation) are not required.
In Table 6.3 we list candidate similarity and dissimilarity measures. The measuresthat we brought together exhaustively cover the most common functions used for loca-tion fingerprinting and image retrieval (e.g., [46, 159]). For details about the singlemeasures we refer to Appendix B. It suffices to recognize that all functions satisfy theabovementioned requirements. We need not bound sim (f ,g): The k-nearest neighborssearch is scale-independent, and particle weights will be normalized due to (6.2). More-over, d does not have to be a metric. Aspect 1 (frequent false negatives) is reflected byan additive rating of different tags, rather than multiplication.
In our approach, dissimilarity measures must be transformed into similarity functions:If d ∈ [0,∞) is a distance value, then a similarity value s(d) is given by1:
s(d) =1
d + ε∈ (0, ε−1], ε > 0 (6.21)
Examplary evolutions for different functions are illustrated in Figure 6.9. The curvesare averaged over several samples on small intervals along the 3D distance (6.26). As canbe seen, the mean similarities of pairs of RFID measurements are correlated with the dis-placement between their recording positions. This justifies fingerprinting for localizationin this section and also for trajectory estimation in the next chapter.
6.6.3 Filtered WKNN Fingerprinting
The WKNN approach provides position estimates with every new RFID inquiry, butdoes not exploit the temporal coherence of robot poses. We therefore interleave WKNNwith particle filtering by tailoring an observation model function in the style of (6.2).
1This is not the only method of how to transform distance to similarity, even for the case treated herethat d is quasi-unbounded. Another transformation is s(d) = exp (−τ · d) for some positive real τ .We found, however, that the resulting behavior is quite sensitive to the values of τ , because the func-tion converges to zero quickly, and committed ourselves to (6.21). We should underline that also theconstant ε does have impact on both the resulting values of s and the final localization accuracy. The-oretically, the variable should thus be subject to optimization. However, ε = 1 is an intuitive, welljustifiable choice, since s(0) = 1.
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FIGURE 6.9: LEFT: Smoothed example values of a selection of similarity measures.
They are plotted against 3D distances between recording positions of the compared fin-
gerprints. The 3D distance measure is the square root of (6.26) on p. 109 (with σd = 0.5,
σr = 0.3). RIGHT: Raw samples of the cosine similarity of fingerprint pairs, plotted
against the 3D distance between recording positions.
The filtered version is supposed to be more robust and more accurate, but still simple toimplement.
Let g = (g(1), . . . ,g(A)) be the current measurement during the localization stage,
with tag counts for all A antennas. We compute similarities sim(g(a), f(a)i ) individually
for all antennas a, 1 ≤ a ≤ A. Then, the individual similarities at all antennas areweighted:
sim(g, fi) :=A
∑
a=1
sim(g(a), f(a)i ) · n(g(a), f
(a)i )
∑Aa=1 n(g(a), f
(a)i )
(6.22)
where n(g(a), f(a)i ) := max(|g(a)|, |f (a)
i |) (6.23)
be the maximum number of detected tags in the vectors g(a) and f(a)i . Using sim, we de-
termine the k most similar reference fingerprints fπ(1), . . . , fπ(k). If there are only k′ < kfingerprints of non-zero similarity, one proceeds with only k′ fingerprints. Then, wecompute the likelihood p(g |x,m) of observing g, given a robot pose hypothesis x andM reference fingerprints in m:
p(g |x,m) =M
∑
j=1
p(g |x,Fj) p(Fj |x) (6.24)
=M
∑
j=1
νssim(g, fj) νd exp
(
−1
2d2(xj,x)
)
(6.25)
Equation (6.24) follows from the law of total probability. In (6.25), we model p(g |x,Fj)(with Fj = (fj,xj)) by the similarity of g and fj , normalized with a suitable νs. More-over, p(Fj |x) is represented by a density depending on the distance between x and the
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y (
m)
x (m)
Sampling from non-disjoint references
Reference fingerprintsParticles
24
26
28
30
32
4 6 8 10 12
y (
m)
x (m)
Uniform sampling among k most sim. ref.
Reference fingerprintsParticles
24
26
28
30
32
4 6 8 10 12
y (
m)
x (m)
Sampling from similarity distribution
Reference fingerprintsParticles
24
26
28
30
32
4 6 8 10 12
FIGURE 6.10: Comparison of the three initialization techniques in an example situa-
tion (1000 particles, true robot position in the image centers, Gaussian noise N (0, 0.42)added to x and y): In this example, the uniform sampling approach (left) spread samples
uniformly over a large area. Sampling from the k = 16 most similar reference finger-
prints (middle) is slightly more focussed. Sampling from the similarity distribution (right)
concentrates on few predominantly similar reference positions.
jth reference fingerprint fj , again normalized with a suitable νd. d2(·) is a squared dis-tance assessing both translational and rotational displacement:
d2(xi,xj) =(xi − xj)
2
σ2d
+(yi − yj)
2
σ2d
+(θi ⊖ θj)
2
σ2r
(6.26)
The ⊖ denotes the difference of angles, restricted to the interval [−π, π]. σd and σr
are bandwidth parameters for the translational and the rotational distance components,respectively, as in (6.9). The final approximation
p(g |x,m) ≈ νk
∑
j=1
sim(g, fπ(j)) exp
(
−1
2d2(xπ(j),x)
)
(6.27)
assumes that the k most similar measurements capture most of the likelihood in (6.25).We further set ν = νsνd. The likelihood (6.27) can finally be used in a particle filterfor position tracking by plugging it into (6.2). Note that ν never needs to be computedexplicitly, because sample weights are normalized after applying the observation model.
6.6.4 Global Localization
For the initialization of the particle filter during global localization, we can take advan-tage of recorded reference fingerprints again. We will experimentally investigate theeffectiveness of the following methods, where g be the first RFID measurement used tosteer the initialization process and (fi,xi)1≤i≤n be the reference fingerprints:
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6.6 LOCATION FINGERPRINTING USING VECTOR SIMILARITY MEASURES
• Uniform sampling from nondisjoint references (NDR): Particle positions aresampled uniformly from all reference fingerprints which have at least one tag incommon. That is, one can directly request hypotheses from the inverted index (cf.Section 6.6.1) and sample from them. Formally, we sample (with replacement) Ns
indices i ∼ U(K(g)) and generate samples (xi, w), w = 1/Ns.
• Uniform sampling from k most similar references (MSR): The second alter-native is motivated by the idea that the k most similar reference fingerprints areclose to the true initial pose with high probability. Thus, one can uniformly sam-ple from their recording positions. Formally, we sample (with replacement) Ns
indices i ∼ U(π(1), . . . , π(k)) and generate samples (xi, w), w = 1/Ns.
• Sampling from the similarity distribution (SD): The third option is to samplefrom reference fingerprints according to their similarities with the first observa-tion g. Formally, we sample (with replacement) Ns indices i ∼ sim(g, fi) andgenerate samples (xi, w), w = 1/Ns.
In all three cases, the diversity of the sampled positions is increased by adding Gauss-ian noise. We have made the slightly simplifying assumption that the recording positionsof calibration fingerprints are distributed approximately uniformly. Otherwise, we wouldhave to take the density of recording positions into account.
6.6.5 Experiments
Weighted k-Nearest Neighbors Without Filtering
We first investigated the localization accuracy of the weighted k-nearest neighbors ap-proach as described in Section 6.6.1. That is, we computed the pose of the robot accord-ing to (6.18); we did not apply particle filtering yet. This approach is relevant for mobiledevices without odometry or resource limitations. The computer museum/corridor dataset (Section A.2) served as experimental data, in which the SCITOS G5 had been steeredthrough an environment with two different numbers of tags on five different paths each.Its RFID reader transmitted at full power (1 W). Each of the similarity and dissimilaritymeasures from above was examined by varying the number of neighbors (k), the numberof reference fingerprints (n), and by testing on the two tag densities. In each configura-tion, we used two log files as reference data, from which n reference fingerprints wereselected randomly. Then, we localized the robot on each of the remaining three log filesand averaged over all absolute 2D Cartesian localization errors.
The results are visualized in Figure 6.11. Each bar in a chart represents mean andstandard deviation of means of all 60 localization runs of a fixed configuration. Thetop row of the charts shows the results of the lower tag density, the bottom row of thehigher tag density. The distinction of 500 and 2000 reference fingerprints corresponded
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COSHISTC*H
OSCBHA
L2
L1HDCHI
JDBC
DOT
NCT
FIGURE 6.11: Weighted k-nearest neighbors fingerprinting without filtering
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6.6 LOCATION FINGERPRINTING USING VECTOR SIMILARITY MEASURES
to an average distance of 0.42 m and 0.15 m, respectively, between neighboring referencefingerprints which do not differ by more than 45°.
We can observe that the best results (0.49± 0.44 m, standard deviation of trial means0.03 m) were obtained for the largest densities of reference measurements and transpon-ders, which is not surprising. By contrast, errors of approx. 0.9 m occur for the combi-nation of smaller tag and smaller fingerprint density in the best case (0.94 m with BHA,k = 4). Generally, the choice k = 4 yielded the best performances of each similaritymeasure in all four plots. One might have expected that the larger k, the better shouldbe the resulting pose estimates. This is obviously not the case, since k = 16 was signifi-cantly worse. So, as a first conclusion, we see that (6.18) is only an approximation to thetrue likelihood of the robot pose.
If we compare the different similarity measures, we observe that the similarity mea-sures COS, HIST, C*H, OSC, BHA as well as the Bray-Curtis dissimilarity (BC) per-formed best. The Bhattacharyya similarity (BHA) yielded the smallest mean errors forall parameter choices. The often used L2 norm and L1-norm were surprisingly inac-curate. We emphasize that a different transformation of dissimilarities into similarities(cf. (6.21)) would show different results, but would also have to be justified.
Filtered Weighted k-Nearest Neighbors
In the second series of experiments, we did apply particle filtering as described in Sec-tion 6.6.3. We consulted the same experimental setup as in the previous experimentwithout filtering. The motion model of the SCITOS had been learned from laser logfiles, using the method by Eliazar and Parr (cf. Section 4.2.2). We tracked positions with1000 samples and chose residual resampling as resampling technique.
The results are shown in Figure 6.12. The four subfigures illustrate the effect of thetwo different transponder densities and two different numbers of reference fingerprints(M = 500, 2000), while the parameter k was varied. Each outcome is based on 300 runsof a particle filter with 1000 samples. The parameters σd = 0.5 and σr = 0.3 were fixed.The robustness towards small changes of σd and σr was documented in our paper [249].
The first insight is that the particle filter considerably increased localization accuracy.The best mean localization errors without filtering had been approx. 0.5 m. In opposi-tion, the filtered WKNN approach reduced tracking errors to approx. 0.2 m. One reasonfor this is that the filter incorporates prior position knowledge, while unfiltered WKNNcomputes a new position hypothesis from scratch at each point in time. Another reasonis that the filter links successive poses via odometry, which is accurate over short terms.
As further illustrated by Figure 6.12, all similarity measures yielded roughly the sameaccuracy for the higher tag density and M = 2000 reference fingerprints. For k = 4, 16,the mean errors were approx. 0.2 m or better. COS (0.18 m± 0.12 m for k = 4), HIST
(0.19 m± 0.13 m for k = 4), and BHA (0.18 m± 0.12 m for k = 4) revealed the highestaccuracy in many of the experiment settings. In case of the higher tag density, even thebenchmark measures, DOT and NCT, yielded good accuracy.
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FIGURE 6.12: Position tracking by filtered weighted k-nearest neighbors fingerprinting
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6.6 LOCATION FINGERPRINTING USING VECTOR SIMILARITY MEASURES
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FIGURE 6.13: Position tracking example of filtered WKNN in the computer museum (cf.
Section A.2). The section of the true and the estimated path on the left are marked grey in
the localization error plots on the right. (mean Cartesian error: 0.24 m; mean rotational
error: 5.03°)
If the transponder density or the number of reference fingerprints was decreased, track-ing errors and variances increased, which corresponds to intuition. On average, the track-ing accuracy of the measures of dissimilarity (L1, L2, HD, CHI, and JD), except BC, de-graded faster than the accuracy of the measures of similarity (COS, HIST, BHA, OSC,and C*H), which is documented by larger means and variances. In our experiments, es-pecially the L1 and the L2 norm were sensitive to tag density and number of referencemeasurements.
An example path as estimated by filtered WKNN is illustrated in Figure 6.13.
Effectiveness of the Inverted Index
Table 6.4 lists how many fingerprint comparisons were saved by pre-selecting nondis-joint reference measurements using the inverted index. In a large environment such asthe Sand 1 wing only a fraction of comparisons is required, and the index considerablyreduces the number of similarity computations. Even in a relatively small environmentsuch as the lab (50 m² free space), three quarters of all reference fingerprints were pruned.
TABLE 6.4: Efficiency of reference pre-selection using an inverted index
Environment Largest distance between Mean reduction oftwo reference positions (m) fingerprint comparisons
Sand 1 wing 89.7 97.3 %Museum/corridor 39.9 83.5 %Robotics laboratory 11.4 74.1 %
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FIGURE 6.14: Mean errors and standard deviations during global localization, using
the filtered WKNN method. (SR-113/SCITOS, dataset SAND1.HD.30dBm)
Global Localization
The mean localization errors of the three proposed initialization methods are depicted inFigure 6.14. As a benchmark, they are compared with the uniform filter initialization ona disk of radius 3 m around the true, but normally unknown pose. In the experiments,we localized on each of the SAND1.HD.30dBm logs five times, starting from randomlydrawn positions. 150 experiments contribute to each curve in Figure 6.14. We used1000 samples, set k = 4, and the artificial initial noise parameters for promoting filterconvergence were set to νR = 0.4, αR = 0.015 (rotation) and νD = 0.5, αD = 0.015(downrange).
The outcomes show that all three proposed sampling techniques achieved comparableglobal localization accuracy as the synthetic benchmark. Sampling from nondisjointreferences (NDR) yielded the best initial accuracies. After few time steps, all methodsconverged to similar mean errors. The initial deviations were not statistically significant.
6.7 Experimental Comparison
While in previous sections we cast light on specific characteristics of the single local-ization methods, the following experiments dedicate to a comparison to one another. Asbefore, the subsequently presented experiments were repeated several times on a num-ber of log files in different environments. We underline that we paid attention to testingall methods on the same data and providing them with the same initial conditions. Un-less otherwise noted, the filtered WKNN approach was tested with histogram similarity(HIST) as similarity measure, where we set k = 8.
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FIGURE 6.15: Tracking accuracy on the lab dataset (ALR-8780/B21). LEFT: Mean
errors and standard deviations (of trial means). RIGHT: Accuracy vs. cumulative fre-
quency, based on more than 9,000,000 time steps.
6.7.1 Tracking Accuracy
We compared the position tracking accuracies of the three localization techniques ontwo different datasets. The results for the corridor dataset are presented in Section 6.7.2.Figure 6.15 depicts the Cartesian position errors on the lab dataset (LAB.WS.C2), inwhich about 300 tags could be observed. Repeatedly, two logs of approx. 1000 RFIDmeasurements served as a reference, and the robot was tracked on the remaining log files.The particles were initially set to the known starting position of the robot.
The model-based approach was tested with two different sensor models, as on p. 96.Again, the model revealed influence on the tracking error: For the model learned withtags at different heights (3DD), the mean error was 0.36 m, as opposed to 0.39 m forthe model with tags at the RFID antenna height (2DD). RFID snapshots performed best,with tracking errors of 0.23 m using all known tags (L∗ = L), 0.24 m when evaluatingL∗ = 20 tags, and 0.24 m using only the currently detected tags (L∗ = Lt). The filteredWKNN approach achieved an accuracy of 0.27 m.
6.7.2 Influence of Tag Density
Another position tracking experiment was conducted with the B21 robot in the corridor.This time we examined two different tag densities: For the lower tag density, approx-imately three RFID labels could be detected in each inquiry, while the higher densitypermitted to observe almost eight tags per inquiry on average. (The latter statistic iscomparable to the previous experiment on the laboratory dataset.) The outcomes areshown in Figure 6.16. Each bar represents 1800 experiment runs.
The best results (0.24 m for the lower tag density and 0.21 m for the higher density)were obtained by the snapshot approach when reducing the number of likelihood eval-uations to L∗ = 20. The trap of a too peaked likelihood is again reflected in the large
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FIGURE 6.16: Tracking accuracy on the corridor dataset (means and standard devia-
tions of trial means, ALR-8780/B21)
variances in case of the higher transponder density. Note that Lt is 7.7 on average (cf.Section A.1).
In these experiments, only the snapshot technique was able to take advantage of thehigher tag density. The model-based approach even yielded the counterintuitive resultthat precision became worse when the tag density was increased. Moreover, a compar-atively large number of particles guaranteed the robustness of all techniques; the largervariances had been caused by few delocalizations.
6.7.3 Global Localization
The convergence behaviors of all presented localization methods are compared in Fig-ure 6.17. The underlying experiments were conducted with the ALR-8780 reader on theB21 and 1000 particles on the lab dataset (LAB.WS.C2) at full RF transmission power.To avoid a bias caused by perhaps unequally sophisticated filter initialization techniques,we proceeded as before: The particles were generated uniformly within a radius of 3 maround the true initial pose, which is not known normally. Ten different starting positionswere drawn randomly from each of the logs, where two logs were excluded for map-ping (model-based approach, 300 samples for mapping, initialization by sensor modelsampling) or for reference snapshots/fingerprints. To compensate for initial pose uncer-tainty, the motion model was relaxed by νrot = 0.4, αrot = 0.015, νtrans = 0.5, andαtrans = 0.015 (cf. p. 91).
As visualized, the robot self-localized globally at an accuracy between 0.5 and 1.0 m.The smallest initial errors (0.55-0.68 m) were achieved with the snapshot approach oper-ating on restricted subsets of tags (L∗ = Lt, L∗ = 20). Filtered WKNN and the snapshottechnique evaluating all L trained tags assume medium positions (0.70-0.94 m). Themodel-based approach yielded the largest initial errors (0.94-1.09 m).
Comparing Figure 6.5 (p. 97) and Figure 6.14 (p. 116), we get the supplementary resultfor the SCITOS robot: On the Sand 1 wing dataset (SAND1.HD.30dBm) the WKNNfingerprint initialization techniques achieved global localization at a mean accuracy of
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FIGURE 6.17: Comparison of convergence during global localization in the lab environ-
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FIGURE 6.18: Comparison of position tracking results in the corridor environment un-
der two sorts of real-world noise (1000 particles): LEFT: Simulated sensor silence as
occurring in crowded environments. RIGHT: Simulated tag relocations as occurring in
environments with moving tagged objects.
0.63± 0.36 m (2000 reference fingerprints, histogram intersection, k = 4). In oppo-sition, the model-based approach revealed significantly larger errors of 0.68± 0.37 m(p-value < 0.05). In both cases, the comparison rested upon the synthetic benchmark ofa filter initialization around the unknown true pose.
6.7.4 Robustness in Crowded and Dynamic Environments
In all previous experiments we assumed tags to be stationary and the environment to besparsely populated with humans. We wanted to investigate the robustness of the localiza-tion techniques under noisier conditions. That is why in a first experiment we performeda comparison under simulated sensor silence: Sensor silence means that single tags re-spond less often or not at all. This behavior can be expected in crowded places such as
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supermarkets, where humans may shield surrounding tags in shelves. We simulated thisphenomenon by randomly and repeatedly muting the actually recorded response rates oftags in our dataset logs. The degree ζ ∈ [0, 1] of sensor silence denotes the situation thata ratio of ζ of all tag detections in an inquiry were switched silent.
The results of the experiments can be found in Figure 6.18 (left). The snapshot ap-proach operating only on the remaining detected tags (L∗ = Lt) performed best forall levels of sensor silence, with errors of always < 0.3 m. Filtered WKNN was con-stantly more inaccurate, but quite robust to sensor silence, with errors of always < 0.4 m.The snapshot approaches with constant number of tag evaluations (L∗ = 20) or usingall known tags (L∗ = L) appear to be more sensitive to nonresponding RFID labels.This result could have been expected, because their likelihood functions explicitly pun-ish nondetections. Model-based localization has larger errors than the other methods forζ ≤ 0.4, but surprisingly its level of accuracy remains virtually constant for all ζ. Notethat the employed sensor model (cf. Figure 4.9 on p. 49) already accounts for a largedegree of not detected transponders.
In a second experiment, we randomly interchanged a fraction of µ tag identifiers ina pairwise fashion. The aim was to simulate relocated tagged objects. Usually, if anindoor environment is modified, particularly the accuracy of fingerprinting approaches issupposed to degrade greatly [222].
The outcomes are illustrated in Figure 6.18 (right). The ranking of the methods issimilar with two exceptions: In total, localization was sensitive to interchanged tagsthroughout the spectrum of applied methods. The filtered WKNN approach seems to beparticularly susceptible to relocated transponders.
6.7.5 Comparison of Run Times
Run times are compared in Figure 6.19. They represent the mean durations of incor-porating a single observation according to the presented observation models. A particlefilter with Ns = 1000 samples was run repeatedly on the corridor dataset (CORR.HD.C2,see Section A.1). The measurements were performed on a Pentium 4 CPU at 3 GHz with1 GB RAM. All methods were able to process the arriving sensor data in real time. Thefiltered WKNN fingerprinting technique outperformed the other methods by a factor 2to 5. The times of the snapshot approach mainly depend on how many independent taglikelihoods (L∗) need to be evaluated. By comparison, WKNN without filtering, notvisualized in the figure, took approx. 1.5 ms (max. 7 ms) on average.
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FIGURE 6.19: Run time com-
parison of the methods: mean
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with 1000 particles
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6.8 Conclusion
Summary
In this chapter, we have treated self-localization based on the detection of inexpensiveRFID tags by an RFID reader on board the mobile robot. Due to the noisiness of pas-sive RFID and lacking range/bearing information, we chose Monte Carlo localizationas a robust, nonparametric, probabilistic positioning framework. By tailoring specificobservation models to the particle filter, we have compared three different localizationtechniques: The first one [96] is based on a transponder map and a sensor model whichcomputes observation likelihoods for 2D relative transponder locations in an antenna-centric frame of reference. The second one [217] also computes tag-dependent likeli-hoods, but directly in the global frame of reference, based on snapshots taken during aprior calibration stage. The third method is, just as the second approach, an instance oflocation fingerprinting; it compares the current RFID scan and reference fingerprints bymeans of a similarity measure from which it derives inquiry-dependent likelihoods.
The methods were experimentally investigated and compared to each other. The bestmean position tracking results were approx. 0.2 m (filtered WKNN on CMC dataset,RFID snapshots on CORR dataset). In all experiments, fingerprinting approaches per-formed better than the model-based approach with regard to tracking accuracy and con-vergence during global localization. On the examined datasets which had been recordedwith the B21 robot, the RFID snapshot technique yielded the best results. We finally alsoinvestigated the robustness of the three techniques to two types of real-world noise: sen-sor silence and relocated tags. To our knowledge, this was the first study of robustnessof passive transponder-based position estimation in dynamic environments.
Discussion and Outlook
When comparing the model-based with the fingerprinting approaches, we identify thefollowing advantages and limitations: The model-based approach has the advantage thatthe required map can also be generated or corrected manually. This means that a refer-ence positioning system such as laser-based MCL is not required.
The fingerprinting approaches are appealing because they do not require an explicitsensor model. Location-specific detection characteristics are implicitly learned during
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the calibration stage. This made them superior with regard to (1) convergence duringglobal localization and (2) accuracy of position tracking. Quite the contrary, in themodel-based approach, relevant model parameters are ignored or averaged over, and theaddition of relevant model parameters would be difficult. When extending the model-based approach, one could investigate further parameters such as tag orientations or thenumber of detected tags. Theoretically, it is also feasible to incorporate environmentalinfluence factors (as shown by Wölfle et al. [260], for instance), but the resulting modelsare still simplified and require additional spatial knowledge of the environment. An is-sue which still holds is that location fingerprinting is only possible in or close to mappedareas: Without sensor model, it is not straightforward to predict reference measurementsfurther away from calibrated fingerprints.
An interesting aspect is that localization errors of the model-based approach weresmaller than typical mapping errors in Chapter 5. The conclusion is that the learned mapscontain implicitly learned environment characteristics and unmodeled interrelationships,although tag position estimates deviate from true locations. Moreover, the robot pose isfiltered over several, albeit uncertain tag positions.
Clearly, RFID is not suited for collision avoidance, and hence cannot substitute range-measuring devices. The question whether RFID can replace laser scanners or cameraswith respect to localization accuracy is more difficult to answer, although the precisionof laser-based Monte Carlo localization has clearly not been achieved. The positiontracking results with mean errors of below 0.25 m, however, promise that traditional pathplanning and following approaches can be adopted, perhaps with minor modifications.The verification of this perspective is beyond the scope of this work.
As part of future work, it will be useful to permit the revision of tag maps and referencemeasurements, since tag arrangements may change over time – and will certainly if onlythe given tag infrastructure of future supermarkets should be exploited.
As demonstrated, all RFID-based localization techniques operate in real time on state-of-the-art PC hardware. Since RFID requires no feature extraction, it suggests itself forcomputationally less capable devices. Then, it may be beneficial to apply additional tech-niques such as KLD-sampling [73] or real-time particle filters [147]. The case study byHightower and Borriello [102] gives an intuition of the real-time applicability of particlefiltering on different types of processors.
In this chapter we still assumed that the robot possesses another locating system whichprovides reference positions during the mapping stage. In the next chapter we investi-gate strategies to eliminate the reference locating system, which paves the way for trueautonomy in unknown environments and only using RFID for place recognition.
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Chapter 7
Trajectory Estimation
In this chapter we enable a robot to track its position in an environment without priormap. After an introduction in Section 7.1 and a review of related work in Section 7.2 weprovide two approaches to trajectory estimation: The first method in Section 7.3 utilizesa particle filter to estimate the path traveled. Then, in Section 7.4, we propose anothertechnique based on sparse nonlinear optimization of the pose graph. Both approachesare evaluated experimentally. Finally, we conclude this chapter in Section 7.5.
7.1 Introduction
The mapping stage, which is also a prerequisite of self-localization, so far required ref-erence positioning. The manual annotation of positions by a human, however, is cum-bersome; additional locating systems like laser-based positioning, on the other hand,cost extra money. In this chapter we eliminate the reference positioning system in notyet seen, RFID-tagged environments. The underlying issue is known as simultaneous
localization and mapping (SLAM). It denotes the coupled problem of generating an en-vironment map while keeping track of the robot’s position in the newly determined map.SLAM has been studied intensively over the past two decades and is often regardedsolved at “a theoretical and conceptual level” [60]. As we will see in Section 7.2, practi-cal realizations of SLAM in the context of passive RFID are rare.
For our purposes, we reduce the underlying problem to trajectory estimation, that is,determining the history of poses that the robot assumed during exploration. Formally,the full SLAM problem is to estimate the posterior
p(x0:T ,m | z1:T ,u1:T ,x0) (7.1)
of robot path x0:T = x0, . . . ,xT and map m, both being not directly observable, giventhe histories of observations z1:T and motion controls u1:T . The pose x0, typically thezero vector, fixes the origin of the newly created map. The joint SLAM state (7.1) canbe factored into
p(m |x0:T , z1:T ) p(x0:T | z1:T ,u1:T ,x0), (7.2)
because features in the map m are conditionally independent, given the exact path x0:T
of the robot that renders observations independent [60, 239]. This factorization is known
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as Rao-Blackwellization. The density on the left hand of (7.2) is mapping with known
poses and exactly what we did in Chapter 5 (where observations zi corresponded to RFIDmeasurements fi). The density on the right hand side estimates the trajectory of the robot.So, the Rao-Blackwellization step mathematically justifies the treatment of SLAM as atrajectory estimation problem.
Most SLAM solutions can be assigned to one out of three major classes: extended
Kalman filters (EKFs), Rao-Blackwellized particle filters (RBPFs), and graph optimiza-
tion techniques. The latter two paradigms are the methods of our choice and will bedescribed in Sections 7.3 and 7.4. In the following, we therefore briefly review onlyEKFs. For more general SLAM overviews, we refer the reader to [12, 60, 239].
Extended Kalman filters [121] assume that both motion and observations can be lin-earized and have additive Gaussian noise distributions. EKFs solve the online SLAM
problem, i.e., the density p(xt,m | z1:t,u1:t,x0) is estimated at each time step t. Thecore estimation steps then involve only matrix operations [60, 237, 256]. EKF SLAMprovably converges due to the correlation of landmark and vehicle poses if the aboveassumptions hold. However, filter updates naïvely require to invert the joint covariancematrix upon arrival of every sensor reading, which takes O(L2.4) time [237]. In a su-permarket we expect many thousands of landmarks if each RFID tag is considered anenvironment feature. Hence scalability is an issue, since sensor data should be processedin constant time to guarantee on-line applicability. Further negative aspects are the lin-earity and Gaussian noise assumptions, which are not (exactly) met in our application.That is why we decided against EKFs.
Apart from the employed estimation technique, scientific works on SLAM differ inhow loop closure is decided. Loop closure (LC) denotes the situation that the robotrevisits some earlier observed place or area of the environment. The detection of suchcases is elementary since it permits to correct accumulated odometric errors and to deriveconsistent1 maps. The three SLAM paradigms themselves actually differ also in howloop closure affects the improvement of the estimated path: EKFs propagate back theuncertainty revealed by a closed loop over correlated landmark position estimates. Loopclosure with RBPFs is only implicit; inconsistent particle trajectories which representinaccurately tracked cycles are ruled out over time. In graph-based SLAM, loop closureis treated explicitly by adding edges to the SLAM graph.
The core contribution of this chapter lies in robust ways of enabling loop closure inSLAM using RFID (Figure 7.1). In the case of passive long-range RFID, the challengelies in overcoming missing position information and large uncertainty. Our objectiveis loop closure at an accuracy which is far better than RFID read range. We focus onfingerprinting-based observation models, since their localization results were most en-couraging.
In this chapter we extend a fingerprint Ft at time t to the tuple Ft = (ft,xt, dΣt , rΣ
t ).
1In SLAM, the consistency of the resulting map is an often used synonym of its accuracy, includingtopological correctness and exemption from artifacts.
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7.2 RELATED WORK
Start
xtx
(1)t′
x(2)t′
xt xt′
FIGURE 7.1: Loop closure: LEFT: Two realizations of noisy particle trajectories (solid
and dotted lines). If two RFID measurements ft and ft′ , t′ > t, are very similar, pose x
(1)t′
of the first particle is more likely than pose x(2)t′ of the second particle, since it is closer
to the earlier position xt. RIGHT: In graph-based trajectory estimation, nodes xt and
xt′ with highly similar observations are linked by an edge of length and rotation zero.
The uncertainty of the constraint, i.e., the error induced by claiming that position and
orientation are identical, is accounted for by covariance matrices. Note that the figure
is supposed to sketch the true (although not yet known) trajectory of the robot; the link
between xt and xt′ is added no matter how far these nodes are from each other according
to odometry.
Compared to our earlier definition of a fingerprint, we have added the accumulated abso-lute odometric translation and rotation dΣ
t and rΣt , respectively, measured from the initial
time step up to t. Recall that the measurement ft = (f(1)t , . . . , f
(A)t ) consists of A vectors
of detection counts. f(a)t,l counts how often antenna a has detected tag l. xt = (xt, yt, θt)
is the odometric recording position and heading of the robot.
7.2 Related Work
7.2.1 SLAM, Trajectory Estimation, and Loop Closure in General
SLAM and loop closure with cameras or laser range finders is a well-studied topic. Be-cause there are numerous publications, our subsequent survey lists only exemplary con-tributions. By means of 2D and 3D laser range finders, loops in graph-based SLAM areclosed by matching the latest scan with single scans [163] or a series of scans which havebeen assembled to a prior map estimate [94, 186]. Several scan matching techniqueshave been proposed over the last years. Examples of model-free registration schemesare iterative closest point (ICP) [19] and its variants [211], iterative dual correspon-
dence (IDC) [163], or the normal distributions transform (NDT) [20]. Chen et al. [39]applied random sample consensus (RANSAC) to finding transformations between over-lapping 3D point clouds. Other approaches explicitly make use of line features [95, 227]
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or corresponding planes [197].FastSLAM as an instance of RBPFs was introduced by Montemerlo et al. [175]. Land-
marks were represented by EKFs; extensions to grid maps were proposed later [89, 97].There, laser scan matching is often used for improving odometry and the filter proposalin short terms. In hybrid metric-topological approaches such as Atlas [28], local mapsare matched with each other on a higher level to close large loops. Clemente et al. [42]mapped larger-scale outdoor scenes with a monocular camera. The geometric compati-bility of correlating features in local maps indicated closed loops in their approach.
The area of appearance-based SLAM (e.g., [7, 43, 136, 137, 183, 212]) is technicallysimilar to fingerprinting-based trajectory estimation: Similarities to the visual signaturesof previously visited places signal closed loops. Feature positions in world coordinatesneed not be reconstructed. Rybski et al. [213], for instance, investigated graph-based vi-sual SLAM in a setup with limited sensing capabilities. It is similar to our approach, butthe uncertainty of constraints was estimated from the number of competitive measure-ments which voted for a closed loop. König et al. [136] and Kessler et al. [126] pursuedindoor appearance-based SLAM using a RBPF. They matched local paths as carried byeach particle and modeled omnidirectional visual similarity depending on spatial dis-tances between snapshots. Their works are related to our particle filter-based approachin Section 7.3 in that we also compute likelihoods based on distance-dependent similar-ities, although in our case by nonparametric modeling. The idea of the adaptive sensormodel, which is updated on the fly, is similar to our automatic model derivation which isdescribed in Section 7.4.4.
Recent appearance-based works transform visual features into feature vocabularies(“bags of words”), which allow for robust loop-closure detection [8, 43, 107].
In opposition to purely appearance-based SLAM, Sim and Little [226] presented atechnique that simultaneously estimates the global coordinates of visual landmarks. Asa consequence, they were able to generate occupancy grids from the 2D projection of theresulting map. The map allowed for obstacle avoidance and exploration, which is noteasily feasible in appearance-based SLAM.
An entirely different trajectory reconstruction strategy which relies only on the fusionof forward and backward odometry was presented by ten Hagen et al. [235].
7.2.2 RFID-based SLAM, Trajectory Estimation, and Loop Closure
Laser-based FastSLAM was also employed by Hähnel et al. [96] in their earlier citedapproach to estimate the trajectory of their robot for mapping RFID tags in an office en-vironment. With our approaches in this chapter we investigate if it is possible to renderthe laser redundant. Kleiner et al. [130] pursued graph-based SLAM with sparsely spreadpassive transponders. Their approach relies on the direct proximity to a short-range tag(and thus high certainty in the relative position between the robot and the tag). It can bepursued by multi-robot teams in a distributed fashion. Although quite different in setup,Kleiner’s method is still closest to our graph-based solution below. Tanaka’s work [233]
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7.3 TRAJECTORY ESTIMATION USING PARTICLE FILTERS
was similar, but he used active RFID and optimized the SLAM graph by stochastic gra-dient descent. An overview of cooperative localization methods using active radio nodeswas given by Patwari et al. [199]. These methods are similar to graph-based SLAM asintroduced in Section 2.3. Kantor et al. [125] and Djugash et al. [50] utilized an ex-tended Kalman filter for localization, mapping, and SLAM with active RFID tags. Theirmethods exploit measured signal strength between the transponders. Ferris et al. [64]employed Gaussian process latent variable models for SLAM based on WiFi. A personwith a handheld device was localized indoors without prior map and without odome-try, but only by means of constraints on indoor pedestrian motion and a prior calibratedmodel of WiFi signals with respect to location distance.
Bolliger [27] superseded exhaustive training before localization with the help of userinteractions: In their system, users could add new GSM, Bluetooth, and WiFi fingerprintsto a central database whenever a location was not yet known. Trajectory estimation alsoaims at overcoming prior calibration, but does not require user interactions.
We treat trajectory estimation as an instance of passive SLAM, that is, the estimationprocess only observes. The opposite case in which the SLAM module also proactivelycontrols the robot is known as active SLAM or exploration. RFID-based explorationwas done by Ziparo et al. [267]. They simulated a robot with on-board UHF RFIDreader. Range was estimated from signal strength and fed to an EKF for simultaneouslocalization and mapping. The achieved Cartesian error was 0.4-0.7 m.
7.3 Trajectory Estimation Using Particle Filters
7.3.1 General Approach of Rao-Blackwellized Particle Filters
Rao-Blackwellized particle filters [55] are one class of SLAM approaches which explic-itly utilize the factorization (7.2) of the joint SLAM state: A particle filter is used toestimate the path of the robot, p(x0:T | z1:T ,u1:T ,x0). Associated with each sample isa map which contains landmark positions as observed along the trajectory of the sam-ple. This way, the sample set approximates the belief over the robot’s position and themap. The Rao-Blackwellization allows to deduce the landmark positions analyticallyand avoids filtering in the larger joint state space. The particle maps, i.e., the densityp(m |x0:T , z1:T ), are represented by grid maps [97] or by independent EKFs for eachlandmark [175]. Compared to purely EKF-based SLAM, the independence of landmarkestimates, given the path of the robot, prevents the nonlinear complexity of update steps.
We perform estimation analogously to particle filter-based localization as on p. 90:
1. Prediction: Identical to p. 90
2. Correction: Samples are reweighted upon arrival of the latest sensor reading, giventhe histories of particle poses and observations:
w(i)t = ηtw
(i)t−1p(zt |x(i)
0:t, z1:t−1) (7.3)
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3. Resampling: Identical to p. 90
4. Map update: The map of each particle is updated by means of a mapping operation,based on the known pose of the robot.
Over time, particles with inaccurate trajectories and therefore inconsistent maps willreceive lower weights due to step 2 and vanish by resampling. Data association withother sensors than RFID is handled implicitly in that current sensor readings may matchdifferent observed features as estimated by different particles.
For the purpose of trajectory estimation, we omit mapping. Instead, we store thetrajectories of all samples, collect the raw sensor data of each time step, and directlyoperate on x0:t and z1:t. This way, computation time with respect to map updates issaved. On the other hand, the time complexity for correcting the particle weights instep 2 becomes time-dependent in the worst case, as shown later.
As the result, our method returns the most likely trajectory of the robot. In general, thesubsequently detailed RFID observation model could also be used to augment particlefilter-based SLAM approaches using laser range finders or cameras.
The remainder of Section 7.3 is mainly based on our IROS 2009 publication [248].
7.3.2 Observation Modeling and Loop Closure
Closed-Loop Detection
Loop closure is only implicit in RBPF-based SLAM. In our approach, we close loopsmore explicitly in that we pre-select earlier measurements which may indicate cycles.To this end, we again exploit the fact that the degree of similarity of two RFID mea-surements taken at two positions indicates how close the two positions are. Based ontraining data, we learn a nonparametric model of the likelihoods of different degrees ofsimilarities, conditioned on the distance between two measurement positions. Note thatthis model assesses two positions of the robot relative to each other; in contrast to thesensor models of previous chapters, it does not relate the transponder location to therobot’s position. Nevertheless, the similarity of two measurements strongly depends onthe distance and relative orientation between the tags and the reader antennas of the twocompared measurements, of course. Operating directly on similarity prevents us fromstruggling with not yet known transponder locations.
The likelihood function assesses two observations, given two positions along the tra-jectory of a particle, with regard to their relative displacement. The idea is sketched inFigure 7.1 (left). Let sim be a similarity measure with range of values R ⊆ R. Let fur-ther B : R → N be a discrete partition of R into indiced intervals. Then we can defineZ as the random variable for the discretized similarity of two RFID measurements. Fur-thermore, let d be the random variable which denotes the Euclidean distance ||xi − xj||between the positions where two fingerprints were taken. Now, p(Z = B(sim(fi, fj)) | d)stands for the likelihood of observing a discretized similarity B(sim(fi, fj)) in two fin-gerprints fi and fj recorded at a given distance d.
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7.3 TRAJECTORY ESTIMATION USING PARTICLE FILTERS
FIGURE 7.2: Learned likelihood
functions p(Z = b | d) depending
on the distance d and for differ-
ent numbers (1-7) of equal tags in
two compared RFID fingerprints.
1e-20
1e-15
1e-10
1e-05
1
0 1 2 3 4 5 6 7 8 9 10
likelih
ood
distance (m)
1234567
Learning the Loop-Closure Model
In order to quantify p(Z = b | d), we learn it nonparametrically from prior recordedcalibration data, similar to our model learning approach in Chapter 4: Training dataFi = (fi,xi)1≤i≤n are collected first, which are simply a set of n RFID fingerprints.At this stage RFID tags are assumed to be placed similarly as in the target environment inwhich trajectory estimation is to be performed. For instance, the tags should be attachedto walls at different heights if the target environment will later also comprise transpondersat varying heights, e.g., on products in shelves.
The likelihood p(Z = b | d) can be rewritten if we apply Bayes’s formula:
p(Z = b | d) = p(d |Z = b)p(Z = b)
p(d)(7.4)
The density p(Z = b) follows from the training data by simple counting how often an in-terval index b = B(sim(fi, fj)) in any pair fi and fj of training measurements is observed.The terms p(d) and p(d |Z = b) require density estimation, i.e., the estimation of proba-bility densities, based on the discrete set of sample distances. We suggest kernel density
estimation, which is a kernel-based nonparametric means of estimating the (arbitrarilyshaped) density function of a random variable (e.g., [221]). Mathematically, it equalskernel regression (Section 2.1) without target values. For a one-dimensional Gaussiankernel, as in our implementation, the optimal kernel bandwidth h can be determined viathe normal reference rule h = 1.06σn−1/5, where n is the number of samples and σ isthe standard deviation among them. While p(d) is estimated from all pairs of trainingfingerprints, the estimation of p(d |Z = b) for a fixed b only involves pairs of trainingfingerprints of assigned interval index b.
An example of learned likelihood functions is depicted in Figure 7.2. There, we mea-sured similarity by the number EQU(fi, fj) =
∑Aa=1
∑
l:f(a)i,l
=f(a)j,l
=11 of equally detected
tags in two RFID measurements fi and fj . Prior experiments had shown that the numberof equal tag IDs in two measurements, summed up over all antennas, yielded one of the
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CHAPTER 7 TRAJECTORY ESTIMATION
highest values of (absolute) Pearson correlation and also mutual information, as com-pared to other similarity measures. Moreover, EQU can be computed very efficiently.
The resulting simple shape of our learned likelihood functions in Figure 7.2 promisesthat one could also fit the log-likelihoods by adequate functions (e.g., Gaussians). Thefunction parameters could be estimated from a small set of calibration data or even bechosen heuristically without calibration, and the calibration stage could be left out.
7.3.3 Trajectory Estimation in the Recall Phase
In the recall phase, we compute p(Z = B(sim(ft, fj)) | ||xt − xj||) for pairs of finger-prints, Ft and Fj . In the particle reweighting step at time t, we first compare ft to allfj, 0 < j < t, by computing btj := B(sim(ft, fj)), accelerated by an inverted fingerprintindex. We claim that btj ≥ bmin for some threshold parameter bmin, because only in caseof sufficient similarity, enough evidence of revisiting the same place is provided. So, ifbtj ≥ bmin, measurement j is a candidate to be used for reweighting.
Since it may happen that in some areas of the environment there are many similaritycandidates whereas in others there are only few, the number of candidates is boundedin order to enforce homogeneity in assigned likelihoods. This is achieved by first com-puting a set of candidates S(ft, f1:t−1) as described before and then choosing the bestsmax measurements of highest similarity to ft, where smax is a user-defined parameter.Algorithm 7 summarizes these steps.
Finally, all particles are reweighted in step 2 on p. 127 according to the chosen similarmeasurements and based on the trajectories x
(i)0:t that the particles embody. Here, we
assume that the likelihoods of all similarities are independent:
p(ft |x(i)0:t, f0:t−1) =
∏
(b,j)∈
S(ft,f1:t−1)
p(
Z = B(sim(fi, fj))∣
∣
∣ ||x(i)j − x
(i)t ||
)
(7.5)
The model could easily be extended to orientations, rather than distances only. Yet,although we do not weight a particle based on its current orientation, its orientation isimplicitly assessed: Two particles with identical values of x and y but with differentorientations will end up in distinct positions if the robot travels some distance. Then,they will be rewarded different likelihoods upon the next closed-loop detection. On theother hand, if a pair of fingerprints along the robot’s path has actually been taken in sameplace, but with different orientations of the robot, the RFID measurements will be likelyto differ entirely at each antenna if read ranges do not overlap. This will prevent thefingerprint pair from being selected as a similarity candidate and hence prevent a particlerepresenting the same position from erroneously being assigned a small weight.
For Ns particles and L landmarks (transponders) in total, the worst case costs of a sin-gle filtering step in our approach are O(Ns ·smax+t·L). It takes Ns ·smax reweightings ofNs samples. Since the observation at time step t is compared to all t− 1 previous sensor
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7.3 TRAJECTORY ESTIMATION USING PARTICLE FILTERS
ALGORITHM 7: Computation of loop-closure correspondences in particle filter-
based trajectory estimation.
Input: Current and recent RFID measurements ft, f1:t; desired number of candidatessmax; discrete similarity threshold bmin
Output: The set S(ft, f1:t−1) of similarity candidates1 S ← ∅
2 for j ← 0 to t − 1 do
3 btj ← B(sim(ft, fj)) // discretized similarity of ft, fj4 if btj ≥ bmin then
5 S ← S ∪ (btj , j) // similarity candidate
6 if |S| > smax then
7 sort S descending w.r.t. to first tuple component8 trim S to first (i.e., most similar) smax elements
9 return S
readings, the complexity is linear in t. For unlimited online-applicability, however, fil-tering steps should be feasible in constant time. This holds even though our experimentshave shown [248] that the robot could operate for approximately one day before it couldnot process observations in time any longer.
Practically, the number of tag detections per inquiry, L, is bounded by some constantLmax for technical reasons. Moreover, an inverted fingerprint index permits to excludeseveral of the previous t− 1 measurements from similarity computations. That is why inthe average case, the number of fingerprint comparisons to be computed depends on thedensity of previously recorded fingerprints – and thus on RFID read range, the velocityof the robot, and the number of loops. Most importantly, the expected run time does notdirectly depend on t itself, although the number of loops will depend on time.
Since we store the trajectories of all Ns particles and, independently, the sequence(f1, . . . , fT ) of observations, the space complexity is O(T ·Ns+T ·Lmax). By comparison,FastSLAM has reweighting costs of O(Ns · Lmax) and space complexity O(Ns · L).
7.3.4 Experiments
Experiments were conducted on twelve log files of the lecture hall dataset (A104.33dBm).They had been recorded with the B21 and its on-board ALR-8780 RFID reader at full RFpower level. The paths traveled possess cycles and end in the same position where therobot started. This way, we could test the RFID-based closed-loop detection and assessthe quality of the estimated path by comparing the deviation between the first and thefinal pose. The environment had been prepared with more than 400 tags on walls andfurniture, roughly at the height of the upper RFID antennas. For details, we would liketo refer to Section A.3. In all subsequent experiments, we ran the particle five times for
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FIGURE 7.3: Particle
filter-based trajectory
estimation: influence
of parameters
0 0.2 0.4 0.6 0.8
1 1.2 1.4 1.6 1.8
2 2.2
0.5 1 1.5 2 2.5 3
mean C
art
esia
n e
rror
(m)
similarity threshold bmin
smax=1smax=2smax=4smax=8
each investigated configuration. We always used a very low resampling threshold of 5 %of the effective sample size in order to avoid particle impoverishment.
The error between the true and the estimated trajectory was computed as follows:Ground truth was provided via laser-based Monte Carlo localization. We aligned theestimate with ground truth by minimizing the sum of errors of all robot poses, using theICP matching formula with known pairwise correspondence of all pose indices alongthe robot’s path. We denote the resulting error value by residual Cartesian error. Thismeasure is not conservative, but it is useful to measure the consistency of the generatedtrajectory: The coordinate frame of the reference positions is different from the initialframe of the particles, and a particle’s trajectory can be quite consistent even if it isinitially distorted. The mean residual Cartesian error and the maximum deviation of thetracked final position of odometry alone were 2.12 m and 9.56 m, respectively.
Influence of Loop-Closure Parameters
First, we fixed the number of particles (Ns = 1000) and experimented with differentloop-closure parameters. The mean residual Cartesian errors, averaged over all runs andlogs, are shown in Figure 7.3. As similarity measure, we used the weighted average ofthe number of common tags (NCT) over all antennas (cf. (6.22) on p. 109). Dependingon the chosen similarity threshold bmin and the number of comparisons per time step,smax, the mean Cartesian error of the best parameter set was 0.46 m (which is the opti-mum, with bmin = 2 and smax ∈ 4, 8). As can be seen, there is an optimal thresholdwhich trades off the number of pose pairs with sufficient similarity and the required de-gree of similarity between them. Moreover, bounding smax turned out useful, indicatedby the large errors of smax = 8. This can be explained with similar arguments as inSection 6.5.3 about snapshot-based self-localization: A less peaked likelihood preventsoverconfident particle weights, relaxes the strictness of the independence assumption in(7.5), and avoids particle depletion.
An example of an estimated trajectory is drawn in Figure 7.4 (right). Ground truth iscompared with recorded odometry, which suffers from large accumulated errors.
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7.3 TRAJECTORY ESTIMATION USING PARTICLE FILTERS
-16
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
-12 -10 -8 -6 -4 -2 0 2 4 6 8
y (
m)
x (m)
ground truthodometry
-4
-2
0
2
4
6
-12 -10 -8 -6 -4 -2 0 2 4 6 8y (
m)
x (m)
ground truthestimated traj.
FIGURE 7.4: Estimation example: LEFT: True trajectory of the robot and recorded
odometry. Especially rotational errors distort the uncorrected path. RIGHT: Estimated
trajectory (mean residual Cartesian error of 0.40 m), using a filter with 1000 samples.
Influence of the Number of Particles
Estimation errors for varied numbers of particles are listed in Table 7.1. The mean resid-ual error and the final deviation are averaged over all filter runs. The maximum Cartesianerror is the maximum error of the most-deviating node in the experiment with the worstresult. Along-track error (ATE) and cross-track error (XTE) are the Cartesian errors indirection (ATE) and perpendicular (XTE) to the robot’s path, as often reported in SLAMpapers.
As can be seen, trajectory estimation significantly reduced errors as compared toodometry without correction. For 1000 and 3000 particles, the outcomes are compa-rably accurate. Increasing the filter size beyond 3000 samples did not yield further im-provements. Fewer particles resulted in considerably larger deviations in the final pose,which should have ideally been zero. In opposition to grid-based FastSLAM, for in-stance, where around 30 samples suffice to create consistent maps for an environment ofour size, RFID-based SLAM requires significantly more samples while providing lowertrajectory accuracy.
In general, it is impossible to predict the number of samples which is required toperform SLAM or trajectory estimation in surroundings of unknown size. This difficultyprompted us to investigate the graph optimization paradigm of the next section.
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CHAPTER 7 TRAJECTORY ESTIMATION
TABLE 7.1: Accuracy of particle filter-based trajectory estimation by the number of
particles and fixed parameters smax = 4, bmin = 2. Errors are given in meters.
Residual Cartesian error ATE XTE Final deviationNs mean ± std.dev. maximum (mean ± std.dev.)
30 0.82 ± 0.62 3.46 0.49 0.45 1.15 ± 0.84100 0.58 ± 0.46 2.68 0.36 0.35 0.89 ± 0.61300 0.54 ± 0.45 2.84 0.33 0.32 0.63 ± 0.631000 0.47 ± 0.40 2.24 0.29 0.29 0.49 ± 0.333000 0.45 ± 0.39 3.66 0.29 0.29 0.35 ± 0.18
Odometry 2.12 ± 1.44 7.95 1.17 1.18 3.91 ± 4.91
7.4 Trajectory Estimation Using Pose Graph
Optimization
7.4.1 General Graph-based SLAM Approach
In graph-based SLAM, the environment is represented by a graph whose vertices are pastrobot and landmark positions which are to be estimated. Edges between the nodes aregiven by geometric constraints plus uncertainty estimates. Methods for optimizing theSLAM graph have already been presented in Section 2.3. Recall that its edges consistof rigid-body transformations between two nodes i and j with expected values δij =(∆xij, ∆yij, ∆θij) (2D translation plus rotation) and associated covariance matrices Σij .
It is more efficient to recover only the trajectory of the robot, x0:T , i.e., to optimizeonly the pose graph, because of the reduced number of constraints. The pose graphcomprises only odometric edges and estimated displacements between nodes which havebeen visited at more distant time steps. Such nodes are linked by common observationsand embody loop closure.
7.4.2 Observation Modeling and Loop Closure
Closed-Loop Detection
Having detected a closed loop in graph-based SLAM, an edge is added to the graph,which is parameterized by the estimated transformation between the two correspondingpositions and the uncertainty associated with this transformation. Closed-loop detection
on a coarse level using a single RFID transponder is straightforward. The parameteri-
zation of loop-closure edges turns out slightly more difficult: A precise transformationbetween start and end node of a loop is required although distance and bearing to ob-served transponders are unknown. Besides, we aim at robust, fine-grained loop closurewhich utilizes the information from several simultaneous tag detections.
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7.4 TRAJECTORY ESTIMATION USING POSE GRAPH OPTIMIZATION
We present two solutions to this issue: One solution is to consult the laser range finder,because metric transformations between the recording positions of two scans can befound at high accuracy. This approach will be described in Section 7.4.5.
It has been our goal, however, to investigate the SLAM capabilities of RFID alone.Therefore, in the first instance our second solution relies on that we can detect suffi-ciently accurately if the robot revisits some position. To this end, we again employsimilarity measures, as proposed in our ICAR 2009 paper [246] and pursued by BinYang in his master’s thesis [262]. Loop closure is claimed if the similarity of two RFIDmeasurements at times t and t′ exceeds some threshold. Then, we will infer that theirrecording positions are identical. That is, we will add a constraint δt,t′ = (0, . . . , 0),with all components zero, to the graph. Since it is unlikely that two poses with similarRFID inquiries are actually perfectly the same, even loop-closure edges feature smallerrors. These errors, however, are typically much smaller than accumulated odometricdeviations. They are compensated for by the associated covariance of the loop-closurelink. As an estimate of the corresponding uncertainty, Σt,t′ , one can choose a diagonalmatrix with small values on its main diagonal, expressing that the transformation is onlyinduced if places are very similar. Our suggestion is to calibrate the loop-closure modelin a training phase beforehand, as described in the next section.
Model Calibration
In order to obtain a model of uncertainty for the employed similarity measure of RFIDfingerprints, we begin as in Section 7.3.2. We collect a number of RFID fingerprints ina training phase and annotate them with their true positions. For each pair of measure-ments, we compute the degree of similarity using some suitable measure and determinethe true displacement of their recording positions. These samples are grouped by smallintervals of similarity values, for which means and covariances of displacements arecomputed. These covariances represent the uncertainty of our loop-closure model: Theyquantify the error distribution of identifying two positions as identical which are close toeach other, but actually not equal. Figure 7.5 exemplifies the standard deviations alongone specific dimension obtained for different values of the cosine similarity.
7.4.3 Trajectory Estimation in the Recall Phase
Summarizing general graph-based SLAM and RFID-based loop closure, we proceedduring the recall phase as follows:
1. The robot explores the environment and collects odometry and RFID data.
2. After data collection, we construct a graph spanned by edges according to odom-etry. Edge covariances are derived from the robot’s motion model2. The nodes of
2One can transform the learned parameters of an Eliazar/Parr-alike motion model to parameters of arigid-body motion model by repeated sampling from the former and recomputing the parameters with
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CHAPTER 7 TRAJECTORY ESTIMATION
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9sta
ndard
devia
tion
COS
σx,y (m)σθ (rad)
FIGURE 7.5: Calibrated standard deviations of distances and angles between the ref-
erence positions of two fingerprint sequences (COS measure, ϑD = 3.0 m, histogram
resolution 0.1). For instance, two sequences of large similarity 0.9 can be expected to be
recorded in very similar poses (distance 0.14 m, angular difference 0.15 rad).
the graph are poses in which RFID inquiries were taken.
3. If desired, fingerprints are smoothed over consecutive time steps: ft is replaced bythe mean of all directly preceding measurements in a distance of ϑD.
4. Similarities of pairs (fi, fj) of RFID measurements are computed. The difference inabsolute accumulated forward translation between their recording positions mustexceed the threshold ϑLCD, which we set to 20 m.
5. If sim(fi, fj) ≥ ϑS for some user-specified similarity threshold ϑS , loop closureis inferred. An edge δt,t′ = (0, . . . , 0) is added to the graph. The associated errorestimate Σij is determined from the prior calibrated model.
7.4.4 Automatic Interleaved Model Learning
The graph-based approach has two aspects which we can improve: First, it requires acalibration stage to train a loop-closure model beforehand. Second, the learned modelconforms to the calibration environment, but there is no guarantee that the target envi-ronment is similar with respect to tag arrangement or the employed type of transponders.The model also might have to be re-trained whenever the RFID setup changes.
As a solution, we have developed a modification which learns the loop-closure modelon the fly while the robot is exploring the target environment. The key idea is that odom-etry is sufficiently accurate over short distances, even if only for very few meters, suchthat we can train a classifier based on RFID similarities and odometry in a supervisedfashion. This classifier is then used to decide loop closure between robot positions whichare distant in time. The organization of the single steps is illustrated in Figure 7.6. Ini-tially, RFID measurements are preprocessed by combining sequenced fingerprints over
respect to the latter.
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7.4 TRAJECTORY ESTIMATION USING POSE GRAPH OPTIMIZATION
FIGURE 7.6: Overview of graph-based SLAM with interleaved RFID model learning
short distances. Then, we derive an observation model which learns to classify closedloops. Since the classifier is trained on the target data, it adapts to the current RFIDsetup and the traversed environment. In a second pass over the recorded data, the derivedmodel detects closed loops, followed by graph optimization (Section 2.3). Any frame-work that relies on rigid-body transformations with uncertainty estimates can be chosen,e.g., [91, 193, 231]. We presented the approach at ICRA 2010 [250].
Combination of Fingerprints
Since recorded RFID data are noisy3, we combine successive fingerprints which are suf-ficiently close to each other. This is similar to Lee et al. [152], who proposed shortkernel-smoothed series of measurements for more robust self-localization. We interpo-late detection rates in a combined fingerprint Gt = (gt,xt, d
Σt , rΣ
t ). It differs from Ft
only by the replaced real-valued measurement vector with g(a)t :=
∑tj=0 wjg
(a)j of aver-
aged detection frequencies with∑
j wj = 1 and
wj ∝
exp(
−12d2(Ft,Fj)
)
, (dΣt − dΣ
j ≤ ϑd) ∧ (rΣt − rΣ
j ≤ ϑr)0 else
(7.6)
and d2(Ft,Fj) =(dΣ
t − dΣj )2
ϑ2d
+(rΣ
t − rΣj )2
ϑ2r
. (7.7)
3In that even in the very same position, inquiries may come to quite different results [32, 33]
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CHAPTER 7 TRAJECTORY ESTIMATION
Observation Modeling
The modeling phase comprises three substages: First, features are extracted which de-scribe the similarity of pairs of combined fingerprints. Then, the resulting feature vectorsare scaled, cleaned from outliers, and used for classifier training.
Feature Extraction from Pairs of Proximate Fingerprints: We claim that for anno-tating training samples, odometric errors are negligible over short distances, and comparepairs of fingerprints which were recorded not too far away from each other. In the workat hand, we assume that at distances of less than 10 m odometry is sufficiently accurate.This threshold should be adapted to the employed robot and ground surface, but we thinkthat 10 m is a decent value for most indoor platforms. For each such pair (Gi,Gj) of fin-gerprints, we compute a 2A-dimensional feature vector m(gi,gj). Its columns describethe similarity of the combined RFID measurements gi and gj . Similarities are computedfor each of the A antennas independently, and the features are concatenated:
m(gi,gj) = (m1(g(1)i ,g
(1)j ), . . . ,mA(g
(A)i ,g
(A)j )) (7.8)
Each subvector ma(gi,gj), a = 1, . . . , A, is a combination of a similarity sim at one’s
choice and the logarithm of the number of tag IDs which appear in g(a)i or g
(a)j :
ma(gi,gj) = ( sim(g(a)i ,g
(a)j ), log(|g(a)
i ∪ g(a)j | + 1) ) (7.9)
If g(a)i = g
(a)j = ∅, we set sim(g
(a)i ,g
(a)j ) = 0. The reason for also storing the number of
unified tag IDs is that the similarity value may be large if only few tags were detected andcommon in two RFID measurements. The enclosing logarithm is supposed to preventthat larger values of tag numbers dominate the corresponding component.
For the computation of covariances, we further remember the relative distances ∆dand angles ∆θ between the recording positions of the involved fingerprints. Finally, weassign one of two class labels y ∈ LC
+, LC− to each training vector:
y =
LC+ |∆d| < 0.5 ∧ |∆θ| ≤ 30
LC− else
(7.10)
Class LC+ contains feature vectors from which loop closure can be inferred: The record-
ing positions of the source fingerprints are located in distances and angles of below 0.5 mand 30°, respectively. These small bounds describe the situation that the robot has visitedthe same place again. In opposition, LC
− contains feature vectors of compared finger-prints with distant recording positions, from which loop closure should not be inferred.
Scaling of Feature Vectors and Outlier Removal: The computed features have di-mensions whose ranges differ. During classification, some dimensions might thus dom-inate others. That is why we map each dimension to the range [−1; 1], as common inmany classification tasks.
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7.4 TRAJECTORY ESTIMATION USING POSE GRAPH OPTIMIZATION
After scaling, feature vectors in LC+ are removed if one of its entries equals -1. This
means either that an antenna has not detected any tag in any of the two fingerprints, orthat the tag lists of two fingerprints are disjoint. Classification is more reliable if suchobviously undesirable training samples are filtered out.
Classifier Training and Computation of Covariances: Given the generated trainingdata, a classifier can be trained whose task it is to recognize a previously visited place.Our approach does not depend on a specific type of classifier. In our implementation,we employ k-nearest neighbors (k-NN). Training is fast, as it only requires to store newtraining samples (lazy learning). Since classification can be implemented efficiently, theclassifier could also be used for on-line trajectory estimation.
In k-NN classification, a query vector q is classified by retrieving those k training sam-ples m(i1), . . . ,m(ik) which yield the smallest distance ||q − m(ij)|| among the trainingdata. k is either pre-specified or determined via cross-validation on the training data. Lety(·) access the class labels of the retrieved training vectors. The predicted class y(q) isthe one of the majority of the retrieved training vectors:
y(q) = argmaxc
p(y(q) = c) (7.11)
with p(y(q) = c) =1
k
∣
∣ij | y(m(ij)) = c, j = 1, . . . , k∣
∣ (7.12)
The probability p(y(q) = c) also rates the confidence of the classification result.We finally have to compute covariance estimates which describe the uncertainty of a
loop-closure constraint in the pose graph. That is why we group training features fromthe loop-closure class, LC
+, by their class probabilities, obtained by feeding them to thek-NN classifier. For each group, we store in a table the means (which are theoreticallyand practically close to zero) and covariances of the stored relative positions and relativeorientations between the compared fingerprints which produced the feature vectors. Thisstep is the same as in the calibration in Section 7.4.2, except that the grouping is nowbased on classification probabilities rather than similarity values.
Trajectory Estimation
The derived loop-closure model from the first pass over the sensor data can now be usedto detect if fingerprints taken at distant time steps indicate that the robot has assumeda pose similar to an earlier one. In this stage, we proceed as in steps 1 and 2 in Sec-tion 7.4.3. Then, loop-closure constraints are added to the pose graph, as described inthe subsequent steps.
Feature Extraction from Pairs of Distant Fingerprints: In order to test for closedloops, feature vectors are computed for pairs (Gi,Gj) of fingerprints with a large differ-ence in absolute distance traveled, that is, |dΣ
i − dΣj | ≥ ϑLCD. For pairs which satisfy this
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criterion, feature vectors are computed and scaled in the same fashion as above. We setϑLCD = 20.0 m.
Classification and Derivation of Constraint Candidates: The feature vectors fromthe previous step are classified: If y(m(gi,gj)) = LC
+, the robot may have been in sim-ilar positions in time steps i and j. Let pij = p(y(m(gi,gj)) = LC
+) denote the corre-sponding classification probability. We will add the tuple (i, j, pij) to a set of preliminaryconstraint candidates if and only if pij exceeds some threshold ϑp. The user-supplied pa-rameter ϑp is one of the few ones in our approach. As our experimental results show, thechoice of ϑp is not too crucial. ϑp = 0.8 should be a good value in most scenarios.
Screening of Constraint Candidates: False loop closures endanger the consistencyof maps and trajectories obtained by SLAM algorithms. Many SLAM solutions thusemploy checks for the joint compatibility of observations (e.g., [42]). In some respectsanalogously, we thin out the set of constraint candidates to yield better robustness tooutliers:
1. Local selection: For each constraint candidate (i, j, pij) we remove further candi-dates (l,m, plm) in a window of ϑw meters before and after i along the robot’s pathif their classification probabilities are smaller, i.e., plm < pij .
2. Ambiguity check: If there are pairs of constraint candidates (i, j, pij) and (i,m, pim)which share one node i, we will reject both constraints if j and m refer to two nodeswhich are close in time, but which differ significantly in accumulated odometricdistance. (Formally, for d := |dΣ
j − dΣm|, if d < ϑLCD and d > ϑAMB, where we set
ϑAMB = 2 m.) Then, visually, the two constraints have detected closed loops fortwo too distinct target positions.
After screening, edges will be added to the pose graph for all remaining constraintcandidates. The rigid-body transformation between pairs of nodes is parameterized byan expected value of 0 for both translation along x and y, and rotation. The covarianceestimate of each constraint, depending on the probability provided by the classifier, islooked up in the table of model covariances.
7.4.5 Fusion with Laser Range Data
The combination of laser scan matching plus graph optimization for ensuring global con-sistency is a classical SLAM approach [87, 94, 186]. Here, we cast light on this type oftask from another perspective: We propose to first precompute a trajectory using RFID,by which globally consistent loop-closure points can be found easily and efficiently. Byapplying the techniques from Section 7.4.4, accurate loop-closure candidates are identi-fied robustly.
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In a second step, laser scan matching can be applied in several ways: The trajectory canbe refined by few pairwise registrations. It is also possible to generate an occupancy gridmap by sparse incremental scan matching, based on the estimated trajectory representingconsistent prior knowledge. We will follow the first option.
There are some advantages over purely laser-based SLAM: First, loop-closure searchis focused using RFID fingerprints. This way data association efforts are avoided whichoften appear in symmetric environments and for large cycles. Second, the subsequentlaser processing requires efficient, sparse scan matching only.
Scan Matching
We assume that RFID and 2D laser data, probably at a much higher scan frequencythan RFID, are recorded simultaneously. By registering pairs of scans, the relative dis-placement between two positions for which RFID data are available can be computed.We here pursue ICP-based matching [19]: Let R = r1, . . . , rnr
be a set of nr scanpoints ri = (xr,i, yr,i) of a single scan, the reference scan, and S = s1, . . . , sns
bea set of scan points of another scan to be matched. ICP iteratively determines corre-spondences between S and R and adds a transformation to S such that it fits best to R.These two alternating steps are repeated until convergence (or divergence). For comput-ing the 2D rotation R ∈ R
2×2 and translation t ∈ R2 which best superimposes S on
R, there is a closed-form least-squares solution given a fixed set of corresponding pointsC ⊆ S × R [19, 163]. If S and R are recorded in laser-centric coordinates, (R, t) yieldsthe relative poses between their recording positions and allows us to accurately estimatethe desired pose transformations between RFID-based loop-closure candidate positions.According to ICP, C associates each point si ∈ S a closest point r′ from R in each it-eration. The definition of closeness and the derivation of corresponding points from thereference R typically varies. In our implementation, correspondence is decided based onthe minimal Euclidean distance to line segments between neighboring points (rj, rj+1).The quality of the match can be measured by the determinant of the covariance of corre-spondences. The overlap can additionally be assessed by a score
score(C) :=∑
(s,r)∈C
exp(−α||s − r||22) (7.13)
for a suitable α (α = (0.1)−1 = 10 in our case). Due to only partial overlaps of twoscans, the correspondence search often suffers from misleading associations. We there-fore apply RANSAC [67], which is a method for robust model fitting by sampling fromnoisy data sets: Instead of finding C for the entire scan S, we sample NRANSAC timestwo points in S and determine their correspondences C′ ⊂ C. Two point pairs are suffi-cient to determine a 2D transformation and assess the resulting overlap between S andR. Finally, the transformation of the best-matching C′ is selected as the outcome of thecurrent ICP iteration. For a given expected fraction o of outliers among the data, d = 2
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Episodes of the robot’s path
which belong to different loops
Sampled pair of RFID measurements
ix
iy
FIGURE 7.7: LEFT: Additional stages (with blue/dark background) for combining
RFID-based loop-closure detection and laser-based constraints. RIGHT: Addition of
laser-based geometric constraints between sampled pairs of nodes on a grid (dotted
connections). These pairs are distant in time, but potentially close in location space as
indicated by the first graph optimization step.
sampled points, and a desired confidence c for an error-free sample, one chooses [67]:
NRANSAC = ⌈(log(1 − c)/ log(1 − (1 − o)d)⌉ (7.14)
The RANSAC-based approach by Fontanelli et al. [70] is similar, but they selected cor-responding points in the reference scan based on the distance between the sampled pointsin the new scan.
Laser Fusion Steps
Scan matching can easily be integrated in three different manners, two of which areshown in Figure 7.7:
1. Laser-supported odometry: Matching consecutive scans permits to correct short-term odometric inaccuracies.
2. Screening of RFID-based loop-closure candidates, Figure 7.7 (left): After thescreening step in Section 7.4.4, matching the scans of two poses with indicatedclosed loops yields the desired metric transformation between them. If the score
and the determinant of the covariance matrix of the matching satisfy some thresh-olds, the RFID-based loop-closure decision will be accepted: The previous zerotransformation will be replaced by the scan transformation, and the covariance
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TF, ϑD=1.0
FIGURE 7.8: Accuracy of graph-based trajectory estimation with similarity thresholds,
cut at 1.4 m for the sake of clarity. LEFT: Results of the sparse-matrix solution. RIGHT:
Outcomes using TORO.
of the laser scan matching will be adopted. Otherwise, the loop closure will berejected.
3. Addition of constraints: Optimized once, the graph can be assumed to be globallyconsistent. As shown in Figure 7.7, we can introduce an improvement step andsystematically sample additional constraints: Nodes of the optimized graph areassigned to coarse grid cells. Then, for each occupied cell (ix, iy), we sample pairsof nodes (a, b) of which node a belongs to (ix, iy) and node b belongs to any cell(i′x, i
′y) with |ix − i′x| ≤ 2 and |iy − i′y| ≤ 2. If the accumulated odometric distance
between both nodes exceeds the loop-closure threshold ϑLCD, their laser scanswill be matched. In case of a good matching, a constraint between a and b with thelaser-based rigid-body transformation and covariance matrix will be added to theSLAM graph. Optimizing the graph for a second time yields the final estimatedtrajectory.
7.4.6 Experiments
Graph-based Trajectory Estimation with Prior Calibration
On the same log files as in Section 7.3.4 (A104.33dBm dataset), we first examined thegraph-based approach with loop-closure model trained beforehand. Measurements werecompared in three manners: (1.) by direct comparison of pairs of fingerprints using thecosine similarity (COS); (2.) by comparison of unweighted means of measurements, av-eraged over all preceding fingerprints in a distance of ϑD =1.0 m, using the cosine sim-ilarity (COS); and (3.) by comparison using the term frequency measure (TF), averagedover all preceding fingerprints in a distance of ϑD =1.0 m. Loop closure was inferred ifthe computed similarity exceeded a pre-specified threshold of ϑS at each antenna pair ofthe B21. The minimum absolute accumulated odometric translation between two loop-
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TF, ϑD=1.0
FIGURE 7.9: Characteristics of loop-closure constraints between measurement nodes
exceeding the given similarity thresholds ϑS , distinguished by the utilized similarity
measure and the smoothing distance ϑD. LEFT: Numbers of loop-closure constraints.
RIGHT: Mean Cartesian error of loop-closure constraints.
closure positions was set ϑLCD = 20 m.The obtained mean residual Cartesian errors are shown in Figure 7.8. The left hand
side depicts the results of the sparse-matrix solution to graph optimization (cf. Sec-tion 2.3.2), while the outcomes on the right hand were obtained using TORO [91], astochastic gradient descent (SGD) optimizer (cf. Section 2.3.3)4. Obviously, the esti-mates of SGD were not as accurate. Nevertheless, the best value of 0.55 m (COS withaveraging over ϑD = 1, ϑS = 0.7) is comparable to particle filter-based estimationwith ≥ 300 samples. Computation times, however, were below one second for each ex-periment run, whereas the sparse-matrix approach took some seconds (see below). Asoriginally motivated by Olson et al. [193], one could use SGD to bootstrap the moreaccurate matrix approach.
Among the results of the sparse-matrix approach (Figure 7.8 (left)), cosine similarityachieved the best result at a mean error of 0.26 m (when combining measurements overa 1 m distance, ϑS = 0.5). This value outperforms the results of the presented particlefiltering technique on the investigated dataset. The term frequency measure achieved notas accurate, but quite threshold-insensitive results.
To better explain the distributions of estimation errors, Figure 7.9 visualizes charac-teristic numbers about inferred loop-closure constraints of the three similarity measures:the number of inferred links (left) and the Cartesian error of the links (right). The latteris measured by the distances between the true linked positions, which are assumed to beidentical in our approach. The higher the similarity threshold ϑS above which loop clo-sure is accepted, the more accurate are added constraints, but the fewer links are actually
4Rather than using the learned edge covariances, we replaced the covariance matrices by 3×3 identitymatrices: The reason was to overcome difficulties and resulting artifacts of the stochastic gradientdescent approach in handling heterogeneous uncertainties, as also observed by Takeuchi et al. [231].The learned covariances actually led to worse accuracy.
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-5
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y (
m)
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ODOGT
EST
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4 8 12
0
200
400
600
800
time steps
ESTInferred constraints
Constraints after screening
x (m)y (m)
time steps
FIGURE 7.10: LEFT: A sample trajectory (labeled “EST”) obtained at full power level
and with a classification threshold of ϑp = 0.6. “GT” (ground truth) is the actual path
of the robot. “ODO” denotes odometry. In this case, a mean residual Cartesian error
of 0.396 m was achieved, based on 294 selected loop-closure constraints that remained
after the screening stage. 20,917 training samples contributed to the observation model.
RIGHT: The estimated trajectory over time with inferred constraints before and after
screening.
added. The best threshold (ϑS = 0.4) was a good compromise between the number andthe individual precision of inferred edges. In total, our findings indicate that large num-bers of constraints guarantee insensitivity towards the inaccuracy of created links. This isplausible, since RFID detections are not able to recognize places and orientations at veryhigh accuracy, but if positions are coarsely redetected more frequently, the trajectory canbe corrected steadily.
Graph-based Trajectory Estimation with Interleaved Modeling
The graph-based trajectory estimation approach with automatic observation modelingwas again tested on the same twelve log files as in Section 7.3.4 (A104.33dBm dataset).In all experiments, we used the cosine similarity for comparing RFID measurements. Wefurther set k = 16 and ϑw = 1 m (the local screening window), ϑd = 1.0 and ϑr = 30
(cf. (7.7)). This time, we applied only the sparse-matrix solution [231] to optimizing thepose graph.
At full power level, between 11,170 and 45,701 feature vectors were derived for clas-sifier training. This shows that, although we trust odometry only in the short term (10 mdistance in our case), path lengths of 107-294 m result in a lot of training data beingavailable to learn the observation model on the fly.
An exemplary reconstructed path with typical estimation errors is illustrated in Fig-ure 7.10. The general mean accuracy of our approach can be seen from Figure 7.11and Table 7.2, depending on the loop-closure classification threshold ϑp. For all valuesof ϑp, the residual Cartesian trajectory error was approx. 0.4 m when only RFID andodometry were used. Based on our earlier conclusions, the constancy is owed to the
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esid
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art
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or
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without laserlaser-based constraint parameterization
additional laser constraints
FIGURE 7.11: Accuracy of graph-based trajectory estimation with interleaved modeling
TABLE 7.2: Results of graph-based SLAM with interleaved modeling
Probability Residual Cart. error Number of Cart. error of Rot. error ofthresh. (ϑp) mean ± std. dev. (m) constraints constraints (m) constraints (rad)
0.5 0.36 ± 0.24 446 ± 355 0.24 0.110.6 0.39 ± 0.28 441 ± 356 0.23 0.110.7 0.36 ± 0.24 433 ± 357 0.22 0.100.8 0.40 ± 0.30 431 ± 356 0.21 0.100.9 0.41 ± 0.33 421 ± 358 0.20 0.101.0 0.40 ± 0.34 413 ± 359 0.19 0.10
Odometry 2.12 ± 1.44
constantly large number of recognized places5. Hence, the choice of the user-suppliedparameter ϑp is not critical. The mean Cartesian error of induced loop-closure edges wasapprox. 0.2 m, while their rotational error was below 6.5° on average.
Characteristics of loop-closure classification performance are shown in Table 7.3. Aclass assignment is considered correct if the true displacement between two fingerprintrecording positions was inside the specified decision bounds (|∆d| < 0.5 m, |∆θ| ≤ 30,cf. (7.10))6. The table underlines that the two screening steps both effectively reducethe false-negative rate (to 0.02 %). Errors of this kind are critical in SLAM applications,particularly graph-based SLAM, since erroneous loop closures may affect the overallconsistency of the final estimate. The true-positive rate is also decreased by screening,
5By contrast to the ICRA version [250] of our approach, we have improved the loop-closure classificationin that the number of inferred constraints is larger and, at the same time, their accuracy is better. Themain differences are the modified screening step in Section 7.4.4 and a different evaluation dataset.
6The true-positive rate is the ratio of correct assignments to the loop-closure class LC+ by the number of
all possible correct loop closures. The false-positive rate is the number of false assignments to LC+,
divided by the number of true loop-closure rejections. The false-discovery rate divides false positivesby the sum of false and true positives.
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TABLE 7.3: Statistics of loop-closure detection (ϑp = 0.5)
Before screening After selection of After ambiguitylocally best constraint check
True-positive rate 32.94 % 18.94 % 16.30 %False-positive rate 0.21 % 0.07 % 0.02 %
False-discovery rate 27.78 % 16.86 % 13.20 %
TABLE 7.4: Results of graph-based SLAM with interleaved modeling of different power
levels (ϑp = 0.7). Cartesian errors are given in meters, rotational errors in radians.
Power Residual Cart. error Number of LC Cart. error of Rot. error oflevel mean ± std. dev. (m) constraints LC constraints LC constr.
33 dBm 0.36 ± 0.24 433 ± 357 0.22 0.1029 dBm 0.32 ± 0.17 758 ± 358 0.21 0.1125 dBm 0.30 ± 0.24 1940 ± 1206 0.30 0.0921 dBm 0.28 ± 0.19 537 ± 369 0.14 0.09
but this type of errors is less crucial as long as sufficiently many poses are still recog-nized. That this is the case can be extracted from the third column of Table 7.2.
Example estimation results for reduced transmission power levels of the RFID readerare demonstrated in Table 7.4. The underlying experimental data are described in Sec-tion A.3. Lower power levels decreased estimation errors: At a level of approx. 0.1 W(21 dBm), the robot’s path was reconstructed at an accuracy of 0.28 m, which is a reduc-tion by 24 %.
Example durations of loop-closure classification for a trajectory with 1200 poses areshown in Figure 7.12. The red curve, which represents classification without invertedfingerprint index, grows steadily. It follows the black curve, which stands for the numberof previous observations in loop-closure reach. Variations are caused by variable featureextraction times – which depend on the number of tags in pairs of measurements – anddurations of the k-nearest neighbors search. The blue curve, which stands for durationswhen using an inverted index, grows also, but the search space of potential loop-closureobservations has decreased considerably.
Results of Laser Fusion
Figure 7.11 also contains the outcomes of fusing RFID, odometry, and laser data. Inthe experiments, the residual Cartesian error was reduced from approx. 0.40 m to ap-prox. 0.23 m if constraint candidates were checked based on scan matching.7
7Constraints were rejected if the determinant of the match covariance matrix exceeded 10-12 or if thematch score was smaller than 30 % of the maximum of scan points of the two matched scans. ICP
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FIGURE 7.12: Example durations of deciding loop closure with and without inverted
fingerprint index (cosine similarity, k = 16, no fusion with laser). The monotonically
increasing black curve is proportional to the number of earlier fingerprints which exceed
the odometric loop-closure distance threshold ϑLCD.
A further reduction to 0.15-0.20 m error was achieved by sampling additional laser-based constraints after the first pose graph optimization. 170 constraints were sampledon average when assigning nodes to a grid of cell size 2 m. We sampled three timesbetween neighboring cells with Manhattan distance 2. All accepted scan matchings wereadded to the pose graph, after which it was optimized a second time.
So far we assumed the perspective that scan matching can improve RFID-based tra-jectory estimation. Let us now take up the contrary position that RFID can assist laser-based SLAM. Using a single RFID tag detection as prior information for loop closure isstraightforward. In the following, however, we show that our fine-grained loop-closuretechnique, based on the similarity features of several tag detections, can substantially re-duce the required number of scan matchings when closing cycles. First, we remark thatmatching two RFID measurements took less than 1/100 ms (COS measure, 11.4 tagsper measurement on average) on a 3 GHz PC during our experiments. By contrast, laserscan matching as described took several milliseconds (75 ms on average for 180 beams)8.Now, we counted the mean number of RFID inquiries along the path of the robot whichshare at least one transponder ID. This number is an indicator of how many candidateend points there are for closing loops at a coarse level. The outcome is listed in Ta-ble 7.5. At full RF transmission power, 150± 56 RFID measurements would indicate are-entered area. If only a fraction of them had to be tested, the robot would have to spend
convergence was assumed below changes of 1 mm and 1° or after 10 iterations. We set NRANSAC =20, which corresponds to c = 90% confidence at a rate of o = 2/3 outliers. The scans were applied areduction filter [95] of 0.05 m and a distance filter for range values exceeding 20 m.
8A performance comparison of scan matching approaches can be found in [191]. Matching can bespeeded up by prior extraction of higher-level features such as lines or corners. Olson, for instance,presented sophisticated ways of loop-closure hypothesis generation and data preprocessing [190]. Yet,on a slightly slower PC than ours line extraction itself as well as the fastest algorithm in the formerpublication were two orders of magnitude slower than RFID fingerprint matching.
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TABLE 7.5: Mean number of pairs of RFID inquiries along the path of the robot which
share at least one transponder ID
33 dBm (2 W) 29 dBm 25 dBm 21 dBm
150 ± 56 124 ± 57 56 ± 9 23 ± 14
TABLE 7.6: Timing characteristics of estimation steps
Stage Mean duration (s)
Exploration (time traveled per trajectory) 526.01±138.22Loop-closure model learning 2.99± 0.71RFID-based loop-closure detection 21.32± 13.59Loop-closure detection with RFID+laser 25.82± 18.70Adding further laser-based constraints 123.77± 74.27Graph optimization 6.02± 6.64
a considerable amount of time on closed-loop detection. Our results show that, by reduc-ing the RF power to 21 dBm temporarily, that issue may be solved, especially becausecandidate positions are close to each other due to the reduced read range. This scenarioresembles the easier case that single, proximately detectable HF tags are employed forloop closure [130, 267].
Example generated occupancy grid maps are shown in Figure 7.13. They were com-puted by entering the laser scans at the estimated trajectory positions into the respectivegrid (e.g., [237, p. 286]). The purely RFID-based trajectory estimate is globally con-sistent, but rotational inaccuracies have introduced errors, which reveal themselves byblurred boundaries. By applying scan matching to successive poses (laser odometry)and rejection/parameterization of RFID-based loop-closure constraints, the visual gridquality improved substantially. Random sampling additional laser-based edges furtherincreased the map accuracy slightly, but not considerably. We should add that the gridmaps were generated mainly for human visual inspection of the trajectory estimate. Ourprimary purpose was to incorporate the laser for improving the underlying path recon-struction. Nevertheless, the achieved accuracy suggests that the occupancy grid couldalso be used for laser-based navigation.
The run times of estimation steps are listed in Table 7.6. They were obtained with adual-core 3 GHz PC (1 GB RAM). As can be seen, the entire data processing of RFIDand odometry alone was almost 20 times faster than the exploration stage. Thus, on-line loop-closure detection in our approach is possible, although our implementationcurrently delivers estimates off-line. The fusion with laser range data is applicable on-line, though scan matching is still the bottleneck in our software. Optimizing the entiregraph via the sparse-matrix approach [163, 231] took six seconds on average. On thesame data, TORO was 50 times faster, although not as accurate. Future work should use
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FIGURE 7.13: Example laser occupancy grids, generated by the fusion with laser data:
TOP LEFT: Grid based on a trajectory only estimated with RFID and odometry. TOP
RIGHT: Fusion with laser-based odometry and laser-based parameterization of RFID-
detected loop closures. BOTTOM LEFT: Further added 170 sampled laser constraints.
BOTTOM RIGHT: Ground truth (via GMapping, Vasco [174], and manual finishing)
it to pre-estimate the trajectory, followed by accurate sparse-matrix optimization.
7.5 Conclusion
Summary
In this chapter, we have presented two novel trajectory estimation techniques which en-able a robot to track its position in a not yet seen, RFID-tagged environment. In the parti-cle filtering approach, prior nonparametrically calibrated likelihood functions permittedto correct particle weights in loop-closure situations. The second approach pursued non-linear sparse optimization of the pose graph, in which fingerprint similarities permittedto infer zero-length loop-closure constraints. Uncertainty models for the latter technique
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7.5 CONCLUSION
were derived either from prior calibration or were directly learned on the target data. Theinterleaved modeling requires no prior observation model and makes no assumptions forthe RFID setup. In particular, it is adaptive to the power level, the way the RFID antennasare mounted on the robot, and environmental characteristics, which have major impacton long-range RFID measurements.
In all developed approaches only the arbitrary, given infrastructure of RFID tags in theenvironment is utilized. We also showed how to efficiently fuse UHF RFID with laserrange data for the sake of improved trajectory accuracy. In opposition to classical laser-based SLAM, scan matching is applied only sparsely, because fine-grained RFID-basedloop closure provides prior information.
The accuracy of the purely RFID-based approaches ranges from approx. 0.3 m (graph-based approach with prior calibration) to approx. 0.45 m (particle filter). We also experi-mented with different power levels and gave evidence of the accuracy and the robustnessof the inherent loop-closure classification mechanisms.
Discussion and Outlook
The derived trajectory allows for mapping the positions of RFID transponders in anotherpass over the sensor data, using RFID mapping approaches [47, 96]. Alternatively, RFIDmeasurements plus the corrected poses could serve as a reference for self-localizationwith RFID fingerprints [217, 244].
The presented approaches are well suited for environments with higher tag densities,that is, scenarios in which given tag infrastructures allow for several tag detections perinquiry. Surroundings with corridor-alike arrangement are beneficial, because we rely onthe revisiting of places with similar orientations of the robot. Although this appears tobe a limitation at first glance, aisles are typical in the target applications involving RFIDsuch as supermarkets. An example of a challenging path is shown in Figure 7.14: Onlyfew positions are revisited within close distance, and the orientation of the robot in suchareas differs considerably. Fusing RFID with laser data improves such situations.
When comparing the pursued SLAM paradigms with each other, the applied particlefilter has the advantage that it is an online method. Rao-Blackwellized particle filtershave been a popular basis for SLAM using a variety of other sensors. It is also possibleto augment such approaches with our method when data association is crucial. Yet, par-ticle filters, which are to learn maps based on particle histories, suffer from the problemthat the required number of particles depends on the (a priori unknown) size of the en-vironment: Samples exponentially forget the past [60] due to the degeneracy introducedby resampling. Resampling itself is inevitable due to the substantially growing varianceover time, as often asserted in literature [13, 166]. Moreover, we applied a vanilla parti-cle filter which estimates the marginal density p(xt |u1:t, z1:t) rather than the distributionover the full trajectory, p(x0:t |u1:t, z1:t). The estimation of the latter is subject to smooth-
ing approaches [17, 57, 81]. They, however, typically feature a complexity quadratic inthe filter size and linear in the number of time steps. Still, smoothing would operate on
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CHAPTER 7 TRAJECTORY ESTIMATION
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GT EST
FIGURE 7.14: Example of a challenging trajectory: an unstructured path with few loop-
closure points featuring comparable robot orientations. The solid black curve (GT) rep-
resents ground truth, the dashed blue curve (EST) the estimated path, and the grey vec-
tors depict deviations of corresponding nodes. The origin is the starting position. Using
RFID alone (left), the trajectory reveals larger, but bounded errors. Errors are reduced
by computing laser-based transformations between loop-closure points (middle). Addi-
tional laser-based constraints finally increase accuracy considerably (right).
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7.5 CONCLUSION
the same transition and observation models as the ones proposed above.The graph-based methods overcome such issues. By adding and removing constraints,
knowledge about the displacement between nodes can be treated flexibly. This even holdsfor past loop-closure decisions, which are perhaps identified as false later on. Althoughwe computed trajectories offline, our experiments showed that loop-closure detection isefficient enough to integrate them with online graph optimization. The accuracy was bet-ter, too, but accuracy does not only depend on the estimator, but also on outlier rejectionefforts.
The mean trajectory errors of pure RFID-based estimation were larger than for self-localization in Section 6.7, where we achieved mean absolute localization errors of ap-prox. 0.25 m at full transmission power. The difference is that the density of provided ref-erence fingerprints was larger. This improves positioning accuracy considerably. Clearly,the accuracy of laser SLAM is not (yet) achieved, where trajectories deviate by few cen-timeters. By comparison, the reported errors in the earlier cited appearance-based workby Kessler et al. [126] were 0.21 m and 0.53 m on paths of 20 m and 2400 m.
There are several methods which could be integrated in the future to further improvethe robustness of loop closure. Examples are locally adaptive models of measurementsimilarity [126], the association of several nodes in a series [107, 136], or the identifica-tion of inconsistent constraints [192].
Another potential extension is to utilize the same mechanisms as prior information formap matching, that is, for merging maps acquired by several robots during multi-robot
SLAM. Due to the achieved accuracy of place recognition, the search for potential mapmatches can be sped up.
Future extensions should also take nonstatic, relocated tags into account, in order topermit truly persistent RFID-based mapping in dynamic environments. Moreover, theconcurrent estimation of transponder positions may be desirable.
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CHAPTER 7 TRAJECTORY ESTIMATION
154
Chapter 8
Conclusion
8.1 Summary
Long-range RFID represents a valuable addition to the sensory capabilities of a mobilerobot. It permits to solve key navigation problems which a robot faces if it has to actautonomously. In this thesis, we have made progress in the fields of three central per-ception tasks: mapping, localization, and trajectory estimation using passive RFID. Thedeveloped solutions cost-efficiently utilize the given RFID infrastructure of near-futureretail and logistics scenarios.
In Chapter 2 we briefly introduced basic techniques which helped to solve estimationproblems in later chapters. Technical and physical properties of passive long-range RFIDwere investigated in Chapter 3. Among other introductory results, we treated the slowRFID sensor update rates of 1-2 Hz and the low self-similarity of consecutive measure-ments, which indicated high variability in observations. The findings underlined thatrobust, probabilistic approaches would be required to cope with uncertainty. We thencontributed to the following chain of topics which build on each other.
Modeling In Chapter 4 we presented a solution to semi-automatically learn a model oftag detection rates with a mobile robot, which was achieved by means of nonparametricregression on recorded training data. The goal was to capture the true read rates, sinceparametric modeling shields decisive, often difficult to incorporate parameters. Our ap-proach builds upon a pre-specified list of tag locations and a set of RFID recordings withannotated positions. Both the recording of the data and the subsequent computation ofa model, including cross-validation, for 2D relative displacements took a few minutesonly. As a consequence, one can quickly re-train the sensor model in case that the RFIDsetup partially changes. In Chapter 4 we also discussed motion models to characterizemovements of the robot and quantify inherent noise.
Mapping Based on a learned RFID sensor model and knowledge of its position, therobot was enabled to estimate the static positions of transponders in Chapter 5. Thisvariant of robotic mapping permits to continuously inventory RFID-tagged objects bya mobile platform. Building upon related research, we employed particle filtering and
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CHAPTER 8 CONCLUSION
devised a number of improvements: A delayed initialization technique was developedin which particles were generated by sampling from the sensor model. This approachyielded a reduction of the filter size by approx. 95 %. At the same time, mapped tagpositions were more accurate. The second acceleration was obtained by introducing aniterative mapping scheme: Processing the recorded observations more than once permit-ted to reduce the filter size in each of the passes over the data. We compared differentresampling and perturbation techniques, depending on which the increase of efficiencywas 35-60 % while achieving at least the same mapping accuracy.
To additionally take advantage of geometrically accurate sensors, we presented a fu-sion technique which incorporates volumetric maps as prior belief. At full transmissionpower, which corresponds to maximum uncertainty of a single tag detection, the taglocalization error was reduced by 10-33 % in combination with a laser occupancy grid.
In the scope of our experiments, we also examined the impact of the type of sensormodel, which lead to the surprising result that the simpler detection probability modelcan sometimes be more accurate than a better resolved, but noisier model of RFID readcounts. Negative information, finally, was shown to slightly improve mapping accuracy,but to disproportionately increase computational demands.
Localization The estimation of its pose is a key ability of a robot; it paves the way forpath planning and location-dependent missions. A dense distribution of RFID tags suchas in future supermarkets suggests itself for various forms of place recognition-relatedapplications such as self-localization. In Chapter 6 we studied three different positioningtechniques in combination with Monte Carlo localization. Two of them relied on locationfingerprinting such that no explicit sensor model was needed. They were benchmarkedagainst model-based positioning as often described in literature. The highest accuracywas achieved by the fingerprinting approaches: We were able to robustly track a robot atmean deviations of below 0.3 m. The snapshot approach was most accurate. The mostefficient algorithm was based on fingerprinting with similarity measures. Model-basedlocalization was sensitive to type and calibration of the sensor model. On the other hand,it appeared quite robust to dynamic environment effects such as sensor silence. In thescope of similarity-based fingerprinting, we studied a wide range of similarity measures.They revealed significant differences in terms of accuracy when particle filtering was notapplied. In opposition, with filtering they were virtually equivalent.
RFID is of special importance for global localization, as places can be recognized un-ambiguously, though with uncertainty. In the scope of all compared techniques, variousways of generating initial belief over the robot’s position were developed for the purposeof global localization. Under the same initial conditions, the fingerprinting approacheswere shown to be initially more accurate and to converge more quickly. The best meaninitial errors, achieved by the snapshot approach, were close to 0.6 m.
156
8.2 DISCUSSION
Trajectory Estimation As a subtask of simultaneous localization and mapping, weproposed and realized novel ways of trajectory estimation using passive UHF RFID.They enable a robot to track its position in a previously unknown, tagged environment.In the particle filtering approach, prior nonparametrically calibrated likelihood functionsreweight particles in loop-closure situations. The second approach pursues nonlinearsparse optimization of the pose graph, in which RFID fingerprint similarities permit toinfer loop-closure constraints. Uncertainty models for the latter technique can be derivedheuristically or by prior calibration. Alternatively, the interleaved modeling variant re-quires no calibration, but learns the model in a prior pass over the target data. It makes noassumptions on the RFID setup. In particular, it is adaptive to the power level, the waythe RFID antennas are mounted on the robot, and environmental characteristics, whichhave major impact on long-range RFID measurements.
We also showed how to efficiently fuse UHF RFID with laser range data for the sakeof improved trajectory accuracy. Using only RFID and odometry, mean errors of 0.3 mand better were achieved by means of graph optimization approaches. Depending on thedegree of laser data used, the error was further reduced to 0.15-0.25 m.
All proposed techniques were investigated by means of extensive experiments withtwo different kinds of real robots and RFID hardware as well as in different experimen-tal environments. Where possible, selective aspects were benchmarked against closelyrelated approaches.
8.2 Discussion
In this thesis, we have tackled a number of before unaddressed problems and proposedimprovements to existing approaches. This section is dedicated to general advances, butalso limitations that have not been discussed at the ends of specific chapters.
The presented enhancements of mapping RFID tag locations were shown to be effi-cient tools for robotic inventory. They have two main limitations: First, the achievedaccuracy is limited and would not yet permit to detect moderate disordering of taggedobjects of less than approx. 1 m. Still, the errors were small as compared to typicalRFID range. We demonstrated techniques to improve accuracy and efficiency within theinherent uncertainty of tag detections. These techniques are generally applicable and canbe integrated in related particle filter-based RFID mapping approaches. Second, someof the techniques required that a sequence of measurements was available. Althoughthis prevents immediate tag position estimation during the first observations of a tag, weshowed better efficiency. For inventory, this aspect is more important, because transpon-der locations can then be determined quickly, one after another. Quite the contrary, itis unimaginable that the robot simultaneously maintains huge sample sets for each ofthe several ten thousands of goods in densely tagged environments. Related researchoften focuses on the accuracy of a single filter, without considering scalability in target
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CHAPTER 8 CONCLUSION
application scenarios.In recent years, a plethora of RFID-based localization methods have been published.
A major issue is that the various approaches are difficult to compare. For active RFIDstandards such as IEEE 802.11 (WLAN), some software packages are freely available(e.g., [2]) and serve as a baseline. This is not yet the case for passive RFID, in particularon mobile platforms. There are even no benchmark datasets, in opposition to frequentlyused SLAM data repositories (e.g., [3, 113]), and we have not found a satisfactory UHFRFID simulator which could provide a common basis for localization experiments withRFID-equipped mobile robots. We solved this problem by benchmarking against theoften used approach by Hähnel et al. [96], although sensor modeling was slightly differ-ent. In addition, we aimed at a large number of experiments in different environments inorder to promote representativeness and repeatability of results.
An often ignored issue in RFID localization is the acquisition of reference positions forlearning transponder maps. On mobile robots, complementary sensors can be employedif human efforts are to be avoided. They allow for autonomous exploration or at leastaccurate ground truth during manual operation. Still, extra sensors are required. To ourknowledge, we have addressed for the first time the learning of positions using UHFRFID in unknown environments such as RFID-tagged supermarkets. The developedtrajectory estimation solutions render extra positioning systems redundant. This is aconsiderable step to truly autonomous platforms which employ mainly RFID.
In this work, we have utilized the strengths of RFID fingerprinting, which increasedpositioning accuracy and simplified RFID modeling. An accepted drawback of radiofingerprinting is that the training stage is time-consuming when performed by a hu-man [222]. Actually, fingerprinting on mobile robots overcomes this criticism: Theautonomous operation of the robot, perhaps still supported by orthogonal locating sys-tems, permits the robot to efficiently explore and map its environment. Admittedly, thefingerprinting paradigm reaches its limits in applications such as mapping. There, thepositions of RFID tags need to be estimated explicitly, which requires a sensor-relativeRFID sensor model. By serializing compound tasks, however, one can utilize the ad-vantages of fingerprinting and postpone model-based operations to subsequent stages.An example is mapping in unknown environments: Trajectories can be estimated with afingerprint approach, followed by model-based mapping, given the reconstructed path ofthe robot.
Although this thesis has focused on mobile robotics, the developed methods couldgenerally be applied to any mobile platform which is able to carry UHF RFID sensorequipment. Examples are interactive shopping carts [10, 83] and forklifters [4, 120].Similarity-based location fingerprinting was particularly efficient and generally appli-cable such that it suggests itself for the transfer even to resource-constrained mobiledevices.
Finally, beyond the clear benefits of long-range passive RFID, the technology hasprovided two central sources of uncertainty until now: slow sensor update rates, whichmake it difficult to date observations precisely, and a large detection range inside which
158
8.3 OUTLOOK
standardized readers only provide noisy detection counts of a tag. Industrial efforts,however, make us expect considerably improved reader performance.
8.3 Outlook
There are a number of promising directions of impact which deserve future research ef-forts. The most obvious and demanding extension is to cope with dynamic environments,in which transponders may move and in which radio noise is caused by crowds of peo-ple. Especially relocated tags dilute the benefits of RFID against the background of dataassociation in combination with place recognition.
Throughout this thesis, we set a high value on the general applicability of the presentedlocalization and mapping techniques. That is why we only used the standardized 96-bit electronic product code. Many state-of-the-art RFID tags, however, offer additionaluser memory which can be filled with arbitrary data a large number of write cycles. Itcould be used for various tasks in robotics, such as synchronization among multi-robotteams [268], storing further information about the environment (e.g., [140]), mimickingpheromones [165], or for communicating short messages from and to users containingadvice or commands.
In this thesis, the fusion of RFID and laser lead to improvements in perception. Thecombination with cameras appears promising, too, above all with regard to texture-basedrecognition of goods in robotic inventory or for complementary loop closure in SLAMapplications.
RFID-based trajectory estimation offers several points of contact: For instance, dif-ferent loop-closure classifiers as well as enhancements from the closely related field ofappearance-based SLAM could be probed. Moreover, an active SLAM solution, includ-ing exploration which is adaptive to RFID tag density, is an open issue. With respect tolife-long robot operation in dynamically changing environments, RFID and laser revealorthogonal characteristics and could be used to realize robust field systems indoors.
Interesting developments can finally be expected from forthcoming RFID hardware.Sensor update rates as well as the sensitivity of RFID readers and tags – and thus thereliability of detection – can be expected to increase continuously. New generations ofRFID readers report additional sensor data such as signal strength or angle of arrival.Such technological advances promise even better accuracy in the tasks studied in thisthesis. Additionally, passive transponders are being developed which will feature ad-ditional sensing capabilities such as for temperature and acceleration. In the long term,robots will not only reside in transponder-equipped environments autonomously, but alsointeract with manifolds of tiny, self-identifying systems. Altogether, the various formsand trends of radio-frequency identification will raise exciting new research topics forthe navigation of mobile robots.
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CHAPTER 8 CONCLUSION
160
Appendix A
Experimental Setup, Environments,
and Data Sets
In the following, we present descriptions of the experimental setup and the indoor envi-ronments in which we conducted the experiments of this thesis. All rooms belong to theSand building of the Wilhelm Schickard Institute at the University of Tübingen. In thesubsequent sections, the environments are illustrated by the corresponding occupancygrid maps and by some representative photographs. The grid maps represent the 2D con-tours of the rooms at the height of the laser scanners, which is approx. 0.38 m. Whitecolor symbolizes free space and black refers to unalterably occupied cells (mostly walls,shelves, doors, and heatings). Regions whose occupancy is unknown (e.g., beyond wallsor where doors may open) are marked blue. The grid maps were created offline fromlogged laser data by means of the laser grid SLAM software GMapping [89] and subse-quent scan matching using the CARMEN [174] tool Vasco. Eventually, the maps weremanually cleaned from artifacts.
In each environment, several log files with sensor data were recorded. We alwaysstored:
• laser data
• odometry
• ground truth positions
• RFID data, which comprise for each antenna the detected tag identifiers and thedetection counts of each tag
All data were stamped with the current time of the on-board computer of the respectiverobot. In case of RFID measurements, which have nonnegligible durations of severaltenths of a second (typically 0.5-0.8 s), each timestamp refers to the time point in themiddle between beginning and ending of a measurement.
Ground truth positions were estimated by Monte Carlo localization (localize modulesupplied with CARMEN [174]) with laser and odometric data, where the occupancygrid maps served as references for localization. Manual inspection of laser localizationshowed that the mean absolute Cartesian errors were 7.85 cm ± 7.47 cm. Rotationalerrors were 1.21°± 1.43°.
The RFID antennas on board the robots were mounted as sketched in Figure A.1. The
161
APPENDIX A EXPERIMENTAL SETUP, ENVIRONMENTS, AND DATA SETS
0.105 m
0.2
30
m 45.0°
45.0°
x
y
0.2
30
m
0.8
00
m
0.9
95
m
0.6
55
m
54.0°
54.0°
0.220 m
0.1
50
m0
.15
0 m
x
y
FIGURE A.1: Mounting of RFID antennas on the robots: Top and lateral views of the
B21 (left) and the SCITOS G5 (right)
type of passive UHF RFID transponders that we used was Alien Technology Squiggle(ALN-9540). They conform to the EPC Class 1 Generation 2 standard (cf. Chapter 3).
Overviews of all datasets are given in Tables Table A.1, A.2, and A.3 on page p. 165and thereafter. A dataset consists of a number of log files which were recorded with thesame setup of the robot’s hardware and the arrangement of the surroundings. Each sethas a brief name by which it is identified in the corresponding experiment sections of thisthesis. A log file represents the recordings of sensor data as listed above while the robottraveled completed path. All log files in a dataset were recorded with the same setup. Wevaried the paths taken by the robot, but aimed at comparable durations and lengths.
For each dataset, we first list the number of log files in the second column of the datasettables. The number of RFID measurements denotes the number of inquiry results per logfile as obtained from the RFID reader. The number of observed, distinct tags is the car-dinality of distinct tag identifiers that were reported in all RFID inquiries of a log. Thisnumber is suggestive how many transponders had been spread over the experimental en-vironment, even if not all were detected. Length of the trajectory and duration of the logfile are stated in two further columns. The column tag detections per measurements rep-resents the number of transponders which were detected in each single inquiry, summedover all antennas of the robot. For each of the detected RFID labels, the tag count per
tag detection then describes how often a specific tag was detected if it was detected in aninquiry. Only the SR-113 reader, which is operated asynchronously (cf. p. 26), featurestag counts considerably larger than one. The counts for the Alien reader and C = 2 weresometimes reported slightly larger than one. In all our experiments, we set them to one.Finally, the distance between measurement pairs describes the closest distance betweenthe recording positions of two inquiries. This value is supposed to depict the measure-ment density, but note that it is an optimistic value: Usually, two consecutive inquiriesare closest to each other, but the next measurement perpendicular to the path of the robotmay be much further away.
For each dataset we have listed the number of log files which belong to the dataset.Several values are analyzed, where each cell of the table has the following structure:
162
A.1 ROBOTICS LABORATORY AND CORRIDOR
FIGURE A.2: The first experimental environment, which consisted of the robotics labo-
ratory (marked light grey) and the adjacent corridor (light green). Transponders were
located in areas which are marked orange. The viewpoints and directions of the photos
are sketched by the associated small grey arrows.
The first row denotes minimum and maximum, separated by a hyphen. The second rowcontains the mean value (indicated by ∅), and the sum in the third row is marked by a Σ.
A.1 Robotics Laboratory and Corridor
The first experimental environment consists of two adjacent rooms, as shown in Fig-ure A.2: a laboratory with approx. 50 m² traversable space, and a corridor of approx. 75 m²free space. The dataset identifiers of the former in Table A.1 begin with LAB, the onesof the latter with CORR. We installed 39 permanent transponders in the corridor and 23in the laboratory.
In the corridor, the permanent tags were glued on a piece of carton and then attached
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APPENDIX A EXPERIMENTAL SETUP, ENVIRONMENTS, AND DATA SETS
to the concrete wall, roughly at the height of the upper antennas (0.8 m). The meanpairwise distance between neighboring tags was approx. 1.5 m. This setting describesthe CORR.LD datasets. In further experiments, referenced as the CORR.HD datasets,we placed additional tags on carton boards (the same ones as in Figure A.6) between thepermanent transponders. This almost tripled the tag density straight along the corridor.
In the lower-density experiments in the laboratory (LAB.LD.* datasets), tags were at-tached to walls and wooden desks at distances of approx. 1 m on average and roughly atthe height of the upper RFID antennas. In the higher-density experiments (LAB.WS.*datasets), we attached them to walls at a density of four per meter and at about thesame height as before. The center of the laboratory further contained a metal shelf(2 m×1.2 m) with almost 400 empty, individually RFID-tagged product packages atdifferent heights in order to imitate a supermarket environment (see Figure A.2). Thedatasets LAB.LD.MA/MS/MF were only used for mapping and only distinguish fromeach other by the average speeds of the robot, which were 0.16, 0.09, and 0.36 m/s, re-spectively. The LAB.WS.MV dataset was also for mapping, but was recorded with theshelf in the middle of the lab. The suffix .Cn symbolizes the configured cycle countC = n of the RFID reader if C was varied (cf. Section 6.5). In all other experimentswith the ALR-8780 reader, the configuration was C = 2.
Although we recorded separate datasets in the laboratory as well as the corridor, theyare coupled: From either of them it was possible to detect also nearby transpondersin the respective other room. This is the reason why the documented experiments inTable A.1 reveal more recorded transponders than originally installed in only one of therooms. This caused inhomogeneity in tag density, which was intended, because in targetenvironments such as supermarkets RFID-based navigation algorithms will also have todeal with inhomogeneous distributions of RFID labels.
Note that in opposition to all other grid maps, the map of lab and corridor (as depictedin Figure A.2) was created from a scaled, scanned architectural floor plan which wasmanually cleaned and updated.
A.2 Corridor and Computer Museum
The second environment is the one depicted in Figure A.3. It comprises the corridorfrom Section A.1 and an adjacent hall. The total traversable space is approx. 160 m².The corridor is the same as in Section A.1. This time, we recorded log files with theSCITOS robot transmitting at full RF power (1 W, 30 dBm).
We attached the RFID tags to walls, at different heights between the floor and theheight of the RFID antennas (0.8 m). The installation was intendedly not overly system-atic, besides that we tried to spread tags roughly in a balanced distribution. We testedtwo different transponder densities. The first density corresponded coarsely to distancesof 1.0-2.0 m between each pair of neighboring tags. In total, 173 tags were observable.This dataset is called CMC.HD.30dBm. The second, higher density (315 labels) of the
164
A.2 CORRIDOR AND COMPUTER MUSEUM
TABLE A.1: Overview of the lab and corridor experiment data recorded with the
B21/ALR-8780
Data set Num
.lo
gfi
les
Num
.R
FID
mea
sure
men
ts
Num
.ob
serv
ed(d
ist.
)ta
gs
Tra
ject
ory
leng
th(m
)
Dur
atio
nof
trav
el(s
)
Tag
det.
per
mea
sure
men
t
Tag
coun
tpe
rta
gde
tect
ion
Dis
t.m
eas.
pair
s(m
)
LAB.LD.C2 10 307-891 145-190 69-195 238-692 0-25 0-6∅: 474.3 ∅: 160.9 ∅: 106.4 ∅: 367.6 ∅: 5.5 ∅: 1.2 ∅: 0.12Σ: 4743 Σ: 1064 Σ: 3676
LAB.WS.C2 10 443-938 269-306 89-188 340-725 0-28 0-6∅: 554.6 ∅: 281.0 ∅: 116.4 ∅: 425.4 ∅: 7.9 ∅: 1.1 ∅: 0.09Σ: 5546 Σ: 1164 Σ: 4254
LAB.WS.C4 10 213-482 282-314 90-205 311-713 0-41 0-9∅: 265.9 ∅: 291.5 ∅: 111.3 ∅: 387.6 ∅: 15.3 ∅: 1.2 ∅: 0.16Σ: 2659 Σ: 1113 Σ: 3876
LAB.WS.C6 10 180-389 287-334 97-193 359-762 0-52 0-9∅: 227.3 ∅: 300.8 ∅: 121.8 ∅: 449.7 ∅: 21.2 ∅: 1.3 ∅: 0.16Σ: 2273 Σ: 1218 Σ: 4497
LAB.WS.C8 10 129-253 281-318 97-188 343-681 0-76 0-11∅: 159.1 ∅: 294.7 ∅: 118.7 ∅: 420.2 ∅: 26.9 ∅: 1.4 ∅: 0.20Σ: 1591 Σ: 1187 Σ: 4202
LAB.LD.MA 5 670-980 159-189 63-85 394-598 0-30 0-5∅: 756.6 ∅: 172.4 ∅: 71.1 ∅: 453.3 ∅: 6.4 ∅: 1.2 ∅: 0.06Σ: 3783 Σ: 355 Σ: 2266
LAB.LD.MS 5 508-821 155-166 36-59 426-745 0-24 0-7∅: 626.8 ∅: 158.8 ∅: 45.6 ∅: 532.6 ∅: 5.5 ∅: 1.2 ∅: 0.05Σ: 3134 Σ: 228 Σ: 2663
LAB.LD.MF 5 584-732 166-182 119-151 323-408 0-30 0-4∅: 673.0 ∅: 173.6 ∅: 134.4 ∅: 370.6 ∅: 6.5 ∅: 1.1 ∅: 0.08Σ: 3365 Σ: 672 Σ: 1853
LAB.WS.MV 10 394-653 246-287 47-79 261-413 0-33 0-6∅: 520.7 ∅: 267.4 ∅: 62.9 ∅: 338.2 ∅: 7.4 ∅: 1.1 ∅: 0.08Σ: 5207 Σ: 629 Σ: 3382
CORR.LD.C2 10 699-1775 138-168 92-228 319-775 0-16 0-5∅: 955.8 ∅: 147.5 ∅: 122.9 ∅: 420.2 ∅: 3.0 ∅: 1.1 ∅: 0.08Σ: 9558 Σ: 1229 Σ: 4202
CORR.LD.C4 10 364-1010 116-172 84-208 286-719 0-32 0-8∅: 554.0 ∅: 132.4 ∅: 119.8 ∅: 413.5 ∅: 4.8 ∅: 1.5 ∅: 0.14Σ: 5540 Σ: 1198 Σ: 4135
CORR.HD.C2 10 782-1683 202-243 121-246 408-841 0-23 0-8∅: 984.7 ∅: 217.1 ∅: 147.0 ∅: 500.8 ∅: 7.7 ∅: 1.1 ∅: 0.09Σ: 9847 Σ: 1470 Σ: 5008
CORR.HD.C4 10 358-933 161-184 86-214 298-724 0-27 0-7∅: 481.8 ∅: 172.6 ∅: 116.5 ∅: 394.6 ∅: 12.1 ∅: 1.5 ∅: 0.16Σ: 4818 Σ: 1165 Σ: 3946
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APPENDIX A EXPERIMENTAL SETUP, ENVIRONMENTS, AND DATA SETS
FIGURE A.3: Computer museum and adjacent corridor
CMC.LD.30dBm dataset corresponds to pairwise distances of 0.5-1.0 m.The paths had lengths of 183-273 m. The mean velocity of the robot was approx. 0.4 m/s,
the maximum speed was 0.6 m/s. Further details about the single recorded log files ofthe CMC.* datasets can be found in Table A.2.
A.3 Lecture Halls and Adjacent Rooms
Another dataset was recorded with the B21 robot and its on-board ALR-8780 reader inthe environment depicted in Figure A.4. This environment consists of a small lecture hall,an adjacent entrance hall, a kitchen, and a connecting corridor. It was chosen as a testbedfor trajectory estimation because it features a medium-size loop. With respect to the readrange of the RFID reader, it is large enough such that the vast majority of measurementsare disjoint when being compared in a pairwise manner. This property guarantees that theexperimental results promise to be valid also for larger cyclic environments. A minorityof the logs were recorded in a single-loop environment two floors above the one fromFigure A.4; it is is very similar in size and shape, as shown in Figure A.5, and it featureda comparable density and arrangement of transponders.
We distributed about 400 tags in this environment. Its free space is approx. 195 m².The recorded trajectories contain loops, and tags were spread in corridor-alike shapes
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A.4 SAND 1 WING
TABLE A.2: Overview of all experiment data recorded with the SCITOS/SR-113
Data set Num
ber
oflo
gfi
les
Num
ber
ofR
FID
mea
sure
men
ts
Num
ber
ofob
serv
ed(d
isti
nct)
tags
Tra
ject
ory
leng
th(m
)
Dur
atio
nof
trav
el(s
)
Tag
dete
ctio
nspe
rm
easu
rem
ent
Tag
coun
tpe
rta
gde
tect
ion
Dis
tanc
ebe
twee
nm
eas.
pair
s(m
)
SAND1.LD.30dBm 5 858-1089 80-83 238-262 447-570 0-4 0-26∅: 960.2 ∅: 81.8 ∅: 248.3 ∅: 502.2 ∅: 1.4 ∅: 10.8 ∅: 0.22Σ: 4801 Σ: 1241 Σ: 2511
SAND1.LD.23dBm 5 889-1145 69-77 244-276 469-605 0-3 0-26∅: 1020.6 ∅: 72.8 ∅: 258.4 ∅: 540.1 ∅: 1.1 ∅: 15.7 ∅: 0.23Σ: 5103 Σ: 1292 Σ: 2700
SAND1.HD.30dBm 5 1078-1525 297-303 259-279 548-780 0-11 0-26∅: 1265.0 ∅: 300.8 ∅: 264.7 ∅: 645.2 ∅: 3.2 ∅: 6.8 ∅: 0.16Σ: 6325 Σ: 1323 Σ: 3226
SAND1.HD.23dBm 5 836-1191 250-274 233-287 427-610 0-8 0-30∅: 999.4 ∅: 260.4 ∅: 256.2 ∅: 511.5 ∅: 2.0 ∅: 11.3 ∅: 0.19Σ: 4997 Σ: 1281 Σ: 2557
CMC.HD.30dBm 5 1011-1108 303-315 212-218 522-568 0-27 0-24∅: 1057.0 ∅: 308.0 ∅: 215.9 ∅: 544.1 ∅: 8.4 ∅: 3.3 ∅: 0.12Σ: 5285 Σ: 1079 Σ: 2720
CMC.LD.30dBm 5 1001-1021 129-173 182-273 673-730 0-16 0-26∅: 1010.6 ∅: 147.0 ∅: 245.1 ∅: 710.7 ∅: 4.4 ∅: 5.4 ∅: 0.11Σ: 5053 Σ: 1225 Σ: 3553
(see Figure A.4), similarly to the arrangement of shelves in storehouses and supermar-kets. The traveled paths contain several loops, some of them significant overlaps.
A detailed description of the log files can be found in Table A.1 in the section about theA104 datasets. The identifiers of the datasets depict the transmission power level. Forinstance, the A104.21dBm logs were recorded with a configured RF power of 21 dBm.
A.4 Sand 1 Wing
The Sand 1 wing, visualized in Figure A.6, was chosen as a large-scale environmentfor benchmarking localization and mapping with the SCITOS robot. It is acyclic andconsists of one major corridor, more than 90 m in length, and a couple of shorter arms.
We deployed two different tag densities in these surroundings: In the lower-densitysetting, referenced as the SAND1.LD.* datasets, 90 transponders were mounted along
167
APPENDIX A EXPERIMENTAL SETUP, ENVIRONMENTS, AND DATA SETS
FIGURE A.4: Lecture hall A104 and adjacent rooms
the corridors, and their locations were determined manually. The transponders werefixed on paper sheets, which in turn were attached to doors, walls, and radiators. Theirplacement height varied between 0.52 m and 1.15 m. For the distribution of labels see inFigure 5.14 on p. 81.
For the second series of experiments, more than 200 additional tags on card boardswere placed between the transponders of the former experiment series. The boards weresimply put on the floor in an upright position such that the attached tags were fixed atheights between 0.01 m and 0.62 m. This time, we measured the positions of only 24 ofthem. The concerned datasets begin with the identifier prefix SAND1.HD.
For each density, log files with two different, constant RF power levels (30 dBm and22.5 dBm) were recorded. The corresponding dataset identifiers reflect the (rounded)transmission power value.
168
A.4 SAND 1 WING
FIGURE A.5: Lecture hall A301 and computer museum
TABLE A.3: Overview of all experiment data for loop closure recorded with the
B21/ALR-8780
Data set Num
ber
oflo
gfi
les
Num
ber
ofR
FID
mea
sure
men
ts
Num
ber
ofob
serv
ed(d
isti
nct)
tags
Tra
ject
ory
leng
th(m
)
Dur
atio
nof
trav
el(s
)
Tag
dete
ctio
nspe
rm
easu
rem
ent
Tag
coun
tpe
rta
gde
tect
ion
Dis
tanc
ebe
twee
nm
eas.
pair
s(m
)
A104.33dBm 12 495-1486 119-427 107-294 373-933 0-37 0-5∅: 868.7 ∅: 315.3 ∅: 174.8 ∅: 570.7 ∅: 11.6 ∅: 1.1 ∅: 0.09Σ: 10425 Σ: 2098 Σ: 6848
A104.29dBm 5 621-1603 116-404 99-188 329-928 0-29 0-5∅: 1037.8 ∅: 270.4 ∅: 150.9 ∅: 585.9 ∅: 9.5 ∅: 1.1 ∅: 0.08Σ: 5189 Σ: 754 Σ: 2929
A104.25dBm 4 1227-1517 113-339 163-249 586-831 0-22 0-5∅: 1380.0 ∅: 247.0 ∅: 190.6 ∅: 693.5 ∅: 5.1 ∅: 1.1 ∅: 0.06Σ: 5520 Σ: 762 Σ: 2774
A104.21dBm 6 640-1664 99-333 72-186 298-798 0-20 0-5∅: 1036.8 ∅: 198.5 ∅: 134.6 ∅: 486.2 ∅: 4.0 ∅: 1.2 ∅: 0.08Σ: 6221 Σ: 807 Σ: 2917
169
APPENDIX A EXPERIMENTAL SETUP, ENVIRONMENTS, AND DATA SETS
FIGURE A.6: Sand 1 wing, second floor, University of Tübingen
170
Appendix B
Measures of Similarity and
Dissimilarity
Throughout this thesis, vector similarity and dissimilarity measures are examined to com-pare RFID measurements. The goal is to relate closeness in signal space to distances inthe location space of the robot. Compact overviews of all measures are given in Table 6.3on p. 107 in the context of self-localization.
In the following, we assume that f = (f1, . . . , fL) and g = (g1, . . . , gL) are L-dimensional measurement vectors each of which is taken at one RFID antenna. fl, gl ∈ R
(fl, gl ≥ 0), l = 1, . . . , L, represent the detection rates of some tag l.
B.1 Measures of Similarity
Histogram intersection (abbreviated by HIST) is a widespread measure of similarity.
simHIST(f ,g) =L
∑
l=1
min(fl, gl)
It was originally developed to compare color histograms [230] for image retrieval. Giventwo RFID measurement vectors, it sums up the tag counts that two measurements havein common in each component. This makes the measure partly robust to extremal valuesin single components.
Another classical similarity measure is the cosine similarity (COS):
simCOS(f ,g) =
∑Ll=1 flgl
√
∑Ll=1 (fl)
2 ·√
∑Ll=1 (gl)
2
Visually, it represents the cosine of the angle spanned by two vectors. As a variant, wealso examine C*H, a function which simply multiplies the values of COS and HIST, withthe idea to yield a more distinctive measure combining COS and HIST.
171
APPENDIX B MEASURES OF SIMILARITY AND DISSIMILARITY
The Bhattacharyya coefficient (BHA)
simBHA(f ,g) =L
∑
l=1
√
flgl
is similar to the vector dot product, but possesses an additional inner square root. Thismakes the coefficient less sensitive to larger tag detection counts in single components.
A measure known from document retrieval is term frequency (TF). In opposition to theother similarity coefficients, it distinguishes importances of detected tags: Transponderswhich are dominant in a certain part of the environment may be identified in order toadapt to local variations in the number of observable tags. First, among the closest, mostrecent nt measurements the detection frequency of tag l at antenna a is counted:
c(a)t,l =
nt−1∑
i=0
f(a)t−i,l (B.1)
The weight of tag l is then defined by
w(a)t,l =
c(a)t,l
∑Lj=1 c
(a)t,l
(B.2)
In analogy to document retrieval, this weight equals the term frequency of tag l among thetag detections in all recent fingerprints. It is important to note that these weights are alsoused for the measurement sequence to be compared with. This weighting achieves theadaptation to location-specific tag density. At the same time, the property of symmetry isviolated. Now, the score of the measurement with antenna a for one recent fingerprint f (a)
t−i
is determined by
s(a)t−i =
L∑
l=1
f(a)t−i,l w
(a)t−i,l, i = 0, . . . , nt − 1 (B.3)
We multiply the scores of all A antennas to obtain the score of the entire fingerprint:
st−i =A
∏
a=1
s(a)t−i (B.4)
For a sequence of the previous nt measurements, the average score st is st = 1nt
∑nt
i=0 st−i.The final step is to compute a similarity value simTF ∈ [0.0; 1.0] from the scores of twomeasurement sequences:
simTF(ft, ft′) =min (st, st′)
max (st, st′)(B.5)
172
B.2 MEASURES OF DISSIMILARITY
Additionally, we proposed a novel measure
simOSC(f ,g) = log (1 + simNCT (f ,g) simCOS(f ,g))
which we called overlap score (OSC) [249]. The idea was to use the cosine similarity,COS, and weight it with the number of tags in common, NCT. The enclosing logarithmintroduces nonlinearity, with the idea that another tag in common only marginally in-creases the likeliness that both RFID measurements stem from the same position.
B.2 Measures of Dissimilarity
Vector dissimilarity measures assess in what way two vectors differ. If a dissimilar-ity measure also is a metric, i.e., the triangle inequality holds additionally, it is calleddistance measure. A widespread class of distances are the Minkowski distances (or Lp-
norm).
dp(f ,g) =
(
∑
l
|fl − gl|p) 1
p
Euclidean distance (p = 2), L2, and Manhattan/city block distance (p = 1), L1, aretwo special cases which are frequently used in the fingerprinting literature. However,when it comes to comparing RFID measurements, one can find undesirable mathematicalproperties. As one example, let us consider three measurements f , g, and h, where thecounts of the jth tag are fj = 0, gj = 1, hj = 2, and for simplicity let all other tag countsequal some value c. Then dp(f ,g) = dp(g,h). This is counterintuitive, because given ameasurement gj = 1, the tag count hj = 2 is a stronger indication that h was recordedin the same area as g than that f was recorded in the same place, because tag j was notdetected in f .
An alternative against this background is the Hellinger distance (HD, the square rootof the squared chord measure [159]):
dHD(f ,g) =
√
√
√
√
L∑
l=1
(
√
fl −√
gl
)2
It differs from the Euclidean distance by a nonlinearity in the vector components, whichsolves the above paradox. Another option is to scale deviations with the inverse of themean of two measurements. This is captured by the χ2 statistics (CHI):
dCHI(f ,g) =L
∑
l=1
(fl − µl)2/µl, µl =
fl + gl
2
(We set the lth summand zero if fl = gl = 0.) In probabilistic terms, dCHI represents thelikeliness of f being drawn from a distribution g.
173
APPENDIX B MEASURES OF SIMILARITY AND DISSIMILARITY
The Bray-Curtis dissimilarity (BC) [31], as also described in [168], is a normalizedversion of the Manhattan distance:
dBC(f ,g) =
∑Ll=1 |fl − gl|
∑Ll=1(fl + gl)
It has been used widely in botany and ecology for measuring biodiversity.The fifth dissimilarity measure, also known from information theory, is the Jeffrey
divergence (JD):
dJD(f ,g) =L
∑
l=1
(
fl logfl
µl
+ gl loggl
µl
)
, µl =fl + gl
2
It represents the symmetric, numerically stable variant of the Kullback-Leibler diver-gence and has reportedly been employed in image retrieval [46].
B.3 Benchmark Measures
In order to investigate the difference in performance between the traditional similaritymeasures above and other rather simple functions, the following two benchmark func-tions are useful: The first measure is the vector dot product (or scalar product), DOT:
simDOT (f ,g) = f · g =L
∑
l=1
flgl
The more detected tags in common (fi, gi > 0) and the greater the tag counts in bothcomponents fi and gi under investigation, the higher the similarity. Moreover, the dotproduct is appealing because of its simplicity of computation. That is why it replaced thesquared Euclidean distance in [35] using the following equality for normalized vectors:
||f − g||22 = 2 − 2fTg
A weakness, on the other hand, is that measurement pairs yielding the same product flgl
in a component will receive the same similarity value. For instance, simDOT((1), (4)) =simDOT((2), (2)) = 4. Note that the Bhattacharyya coefficient reveals the same issue,but it is less sensitive to larger tag detection counts in single components due to the innersquare root. Moreover, it may be undesirable that simDOT((0), (c)) = 0, independent ofc (a property that holds for all presented measures of similarity, too).
Another non-classical benchmark is the number of common tags (NCT) in two mea-surements:
simNCT (f ,g) = | l | flgl > 0, l = 1, . . . , L |In opposition to the other measures, the number of detections of a specific RFID tagis quantified in a boolean fashion only. Although potentially valuable information isignored, that mechanism makes the measure robust to outliers in the detection values.
174
Appendix C
Exemplary 3D Sensor Model
In Chapter 4 we were concerned with RFID sensor modeling. In the scope of this thesis,learned representations ultimately serve for 2D self-localization. Beyond this purpose,3D models of RFID detection behavior are useful: The localization of tagged objectsin 3D and autonomous inventory are examples. Figure C.1 visualizes the means of anexemplary three-dimensional model for the SR-113 reader at full transmission power(1 W). It was computed from 608,074 training samples, which stem from 2975 RFIDmeasurements with 2 antennas, where 64 tag positions were known. The recording ofthe RFID data lasted approx. 25 minutes. Regression was performed via k-NN (k = 35,cross-validated) and took 30.54 s on a 3 GHz PC. The stored model has a resolution of
z=0.0 m
0 1
2 3
4x (m) -2
-1
0
1
2
y (m)
0
2
4
6
8
10
z=0.3 m
z=0.6 m
z=0.9 m
z=1.2 m
FIGURE C.1: Slices of a learned three-dimensional sensor model using k-nearest neigh-
bors regression (SR-113 reader, 1 W power)
175
APPENDIX C EXEMPLARY 3D SENSOR MODEL
0.05 m along each dimension such that it requires 14 MB RAM and 414 KB disk space(compressed). The entire cross-validation, iterating over k = 5, 10, 15, . . . , 150, had aduration of approx. 23 minutes.
176
List of Figures
1.1 Target scenarios of the thesis . . . . . . . . . . . . . . . . . . . . . . . 21.2 Experimental platforms . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1 Example of the presented regression techniques . . . . . . . . . . . . . 82.2 Examples of kernel functions (Gaussian, uniform, quartic, triangular) . 102.3 Dynamic Bayes net representing the first-order Markov process . . . . . 132.4 Illustration of graph optimization . . . . . . . . . . . . . . . . . . . . . 18
3.1 RFID systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2 Interactive vs. autonomous inquiries . . . . . . . . . . . . . . . . . . . 263.3 Alien Squiggle, Impinj Propeller, and Omni-ID Mini tags . . . . . . . . 273.4 Read range experiments: ALR-8780 and three types of tags . . . . . . . 283.5 Read range experiments: SR-113 and two types of tags . . . . . . . . . 293.6 Cumulative numbers of different detected tags . . . . . . . . . . . . . . 303.7 Frequency of detected numbers of transponders in a static setup . . . . 313.8 Similarity matrices for RFID inquiries in a static setting . . . . . . . . . 32
4.1 Coordinate frames for robots, RFID antennas, and tags . . . . . . . . . 364.2 Modeling 2D movements of the robot . . . . . . . . . . . . . . . . . . 374.3 Learned motion model for the B21 robot . . . . . . . . . . . . . . . . . 394.4 Overview of the stages for learning a sensor-centric RFID model . . . . 444.5 Manually recorded and learned k-NN models . . . . . . . . . . . . . . 464.6 Comparison of 2D detection probability models using kernels . . . . . . 474.7 Cross-validation: Errors and prediction times using kernels . . . . . . . 484.8 Binning: cross-validation statistics and 2D model . . . . . . . . . . . . 494.9 Comparison of regression results using 2D and 3D data . . . . . . . . . 494.10 A 2D model featuring mean and variance of detection counts . . . . . . 51
5.1 Visualization of particle filter initialization approaches . . . . . . . . . 595.2 Mapping: varying sample sizes, initializ. methods (SR-113/SCITOS) . . 635.3 Mapping results for varying particle numbers (ALR-8780/B21) . . . . . 645.4 Mapping accuracy vs. precision (SR-113/SCITOS) . . . . . . . . . . . 655.5 Run times of particle reweighting steps . . . . . . . . . . . . . . . . . . 655.6 Example particle filter evolution . . . . . . . . . . . . . . . . . . . . . 675.7 Mapping error per tag depending on the number of detections . . . . . . 68
177
LIST OF FIGURES
5.8 Mapping errors after adding artificial rotational noise . . . . . . . . . . 695.9 Mapping accuracy of iterative estimation (SR-113/SCITOS) . . . . . . 725.10 Overview of fusion stages . . . . . . . . . . . . . . . . . . . . . . . . . 735.11 Illustration of the structural initialization approach . . . . . . . . . . . . 755.12 Example of a generated transponder map in the laboratory . . . . . . . 775.13 Mapping precision and results for tags on contours . . . . . . . . . . . 785.14 Example mapping results . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.1 Bird’s eye view of 2D localization using passive RFID . . . . . . . . . 846.2 Model-based localization vs. location fingerprinting . . . . . . . . . . . 916.3 Model-based tracking results (SR-113/SCITOS) . . . . . . . . . . . . . 956.4 Model-based tracking results (ALR-8780/B21) . . . . . . . . . . . . . 966.5 Results of global model-based localization . . . . . . . . . . . . . . . . 976.6 Real-world example of model-based localization vs. fingerprinting . . . 986.7 Likelihood smoothing results . . . . . . . . . . . . . . . . . . . . . . . 1046.8 Global localization results with RFID snapshots . . . . . . . . . . . . . 1056.9 Similarity values depending on 3D distances of recording positions . . . 1086.10 Comparison of initialization techniques in an example situation . . . . . 1106.11 Weighted k-nearest neighbors fingerprinting without filtering . . . . . . 1126.12 Position tracking with filtered WKNN fingerprinting . . . . . . . . . . 1146.13 Position tracking example . . . . . . . . . . . . . . . . . . . . . . . . . 1156.14 Comparison of global localization strategies with filtered WKNN . . . . 1166.15 Tracking accuracy on the lab dataset (ALR-8780/B21) . . . . . . . . . 1176.16 Tracking accuracy on the corridor dataset (ALR-8780/B21) . . . . . . . 1186.17 Comparison: global localization in the lab environment . . . . . . . . . 1186.18 Comparison: robustness to sensor silence and relocated tags . . . . . . 1196.19 Run time comparison of the methods . . . . . . . . . . . . . . . . . . . 120
7.1 Loop closure: particle filtering vs. graph optimization . . . . . . . . . . 1257.2 Learned likelihood functions for trajectory estimation . . . . . . . . . . 1297.3 Influence of parameters of the particle filter approach . . . . . . . . . . 1327.4 Example trajectory estimated by the particle filter approach . . . . . . . 1337.5 Learned covariances for graph-based loop closure . . . . . . . . . . . . 1367.6 Graph-based SLAM with interleaved RFID modeling . . . . . . . . . . 1377.7 Combining RFID-based loop-closure and laser-based constraints . . . . 1427.8 Accuracy of graph-based estimation with similarity thresholds . . . . . 1437.9 Numbers/errors of loop-closure constraints with similarity thresholds . . 1447.10 Sample trajectory (graph-based approach, interleaved modeling) . . . . 1457.11 Accuracy of graph-based estimation with interleaved modeling . . . . . 1467.12 Durations of loop closure with and without inverted fingerprint index . . 1487.13 Example occupancy grids after fusion with laser data . . . . . . . . . . 1507.14 Example of a challenging trajectory without and with laser fusion . . . 152
178
A.1 Mounting of RFID antennas on the robots . . . . . . . . . . . . . . . . 162A.2 Robotics laboratory and adjacent corridor . . . . . . . . . . . . . . . . 163A.3 Computer museum and adjacent corridor . . . . . . . . . . . . . . . . . 166A.4 Lecture hall A104 and adjacent rooms . . . . . . . . . . . . . . . . . . 168A.5 Lecture hall A301 and computer museum . . . . . . . . . . . . . . . . 169A.6 Sand 1 wing, second floor, University of Tübingen . . . . . . . . . . . 170
C.1 Learned 3D detection rate model . . . . . . . . . . . . . . . . . . . . . 175
List of Tables
0.1 Symbols for constants, variables, sets, distributions, and operators . . . xv0.2 Abbreviations used throughout the thesis . . . . . . . . . . . . . . . . . xvi
3.1 RFID frequency bands and typical read ranges . . . . . . . . . . . . . . 233.2 Durations of inquiries of the ALR-8780 reader . . . . . . . . . . . . . . 33
4.1 Classification of RFID modeling approaches . . . . . . . . . . . . . . . 414.2 Preprocessing statistics and durations of cross-validations . . . . . . . . 50
5.1 Effective sample sizes for different types of sensor models . . . . . . . 665.2 Comparison of mapping results with and without nondetections . . . . . 685.3 Mapping accuracy and run-times for iterative estimation . . . . . . . . 735.4 Results of uniform and structural initialization . . . . . . . . . . . . . . 77
6.1 Calibrated motion model parameters of the two robots . . . . . . . . . . 946.2 Snapshot-based tracking for varied tag density and cycle count . . . . . 1036.3 Similarity and dissimilarity measures for RFID measurements . . . . . 1076.4 Efficiency of reference pre-selection using an inverted index . . . . . . 115
7.1 Influence of the number of particles on the particle filter approach . . . 1347.2 Results of graph-based SLAM with interleaved modeling . . . . . . . . 1467.3 Statistics of loop-closure detection (ϑp = 0.5) . . . . . . . . . . . . . . 1477.4 Graph-based SLAM with modeling of different power levels . . . . . . 1477.5 Loop closure candidates based on at least one shared transponder . . . . 1497.6 Timing characteristics of estimation steps . . . . . . . . . . . . . . . . 149
A.1 Lab and corridor experiment data recorded with the B21/ALR-8780 . . 165A.2 Experiment data recorded with the SCITOS/SR-113 . . . . . . . . . . . 167A.3 Experiment data for loop closure recorded with the B21/ALR-8780 . . . 169
179
LIST OF FIGURES
180
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