RANGE-FREE LOCALIZATION AND TRACKING INWIRELESS SENSOR NETWORKS

A DISSERTATION

SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL

OF THE UNIVERSITY OF MINNESOTA

BY

ZIGUO ZHONG

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

TIAN HE, ADVISOR

SEPTEMBER, 2010

c© ZIGUO ZHONG 2010

ALL RIGHTS RESERVED

Acknowledgements

Over the last four years, I have had the privilege to work with a number of people who have

made my time at the University of Minnesota enjoyable and rewarding. I’d like to thank

all of them. Without them this dissertation would not be possible.

I am deeply grateful to my advisor, Prof. Tian He. Tian is an outstanding computer

scientist with broad knowledge, sharp intuition, and grand vision. Tian is also a great

mentor. He is very patient and gives me lots of freedom to explore the field by myself.

Under his guidance, I was able to learn the fundamental lessons of being a researcher:

finding valuable problems, investigating innovative ideas and presenting meaningful results.

His inspiration and warm personality have won my highest respect and trust.

I am extremely thankful for the time and invaluable advice from Prof. Ahmed H. Tewfik,

Prof. Ibrahim Volkan Isler and Prof. Stergios I. Roumeliotis, as well as from Prof. John A.

Stankovic, Prof. Zhi-Li Zhang and Prof. David Hung-Chang Du, who generously helped

me and strongly supported my future career.

I would like to thank all my coauthors, labmates and colleagues in Minnesota, UVA and

UIUC including Pengpeng, Ting, Yongle, Paul, Shuo, Qingquan, Fulong, Liangyin, Jason,

Yaohua, Shan, Hengchang, Jiakang, Qing, Hongyang, with whom I have shared hours of

discussion, work and laughter. It has always been enjoyable and fruitful to work with them.

Life in graduate school was not only about sensor nodes. I am glad for the happy

times spent with some of the greatest friends. Special thanks to Guojin He and Yu Wang.

Gratitude to Weijia, Weikang, Hao, Jing and Yingchun. In addition, thanks to Prof. Tew-

fik’s group on the 6th floor, Prof. Isler’s group next door, Prof. Zhang’s group and Prof.

Roumeliotis’ group both at DTC, with whom I really enjoyed discussion and parties.

Most importantly, none of this would have been possible without the unwavering support

from my family. In spite of being separated by the vast Pacific Ocean, my parents (and

parents-in-law) have always inspired me with courage, strength and love. My dearest wife,

Dana, has shared with me all the sweets and bitters of life here as a grad student, and has

never failed to believe in me. I feel exceptionally favored to have you.

Last but not the least, I gratefully acknowledge financial support from the National

Science Foundation, ACM, IEEE, USENIX, and the University of Minnesota MESS Group.

i

Abstract

Wireless sensor networks (WSN) have been considered as promising tools for many location-

dependent applications such as area surveillance, search and rescue, mobile tracking and

navigation, etc. In addition, the geographic information of sensor nodes can be critical for

improving network management, topology planning, packet routing and security. Although

localization plays an important role in all those systems, itself is a challenging problem due

to extremely limited resources available at each low-cost sensor node.

Previous research generally divides into two groups: range-based and range-free. Range-

based methods are accurate but costly for requiring per-node ranging hardware, careful sys-

tem calibration, or extensive environment profiling. Range-free approaches feature reduced

overhead at the resource constrained sensor node side, nevertheless, with less accuracy

depending on anchor density, network connectivity, event distribution, etc.

This thesis offers novel solutions to bridge the gap between low cost and high accuracy for

range-free localization. In the first part, we explore uncontrolled event-driven localization

that advances the state-of-the-art an important step towards a usable system. As the first

to apply the concept of sequence to localize nodes, our designs significantly improve system

flexibility by providing a trade-off between physical cost (anchors) and soft cost (events), a

useful layer of abstraction that adopts different sensing modalities, and a potential option

of achieving node positioning via natural ambient events.

In the second part, we focus on the challenging problem of localization with merely range-

free sensing results. Different from binary proximity, we invent the signature distance as a

metric that, for the first time, enables quantifying distance relationships among neighboring

nodes with sub-hop resolution in a range-free manner. With little overhead, this metric can

be conveniently applied for enhanced system accuracy. We further extend the discovery to

mobile target tracking. By converting the tracking problem from sequential localization to

a maximum likelihood shortest path searching in a graph, we demonstrate robust tracking

under unreliable sensing and without complex movement modeling.

By investigating into two important branches of range-free localization − event-driven

localization, and localization with local sensing − the research presented in this thesis aims

at promoting the use of low-cost range-free solutions in real world applications.

ii

Contents

Acknowledgements i

Abstract ii

List of Tables vii

List of Figures viii

List of Abbreviations xiii

1 Introduction 1

1.1 Localization and Its Challenges . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Research Objectives and Contributions . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Uncontrolled Event-driven Localization . . . . . . . . . . . . . . . . 3

1.2.2 Localization and Tracking using Signature Distance . . . . . . . . . 5

1.3 Organization of the Manuscript . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Background and Related Work 7

2.1 Range-based Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Signal Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.1.1 Directly Infer Distance from RSS Measurements . . . . . . 8

2.1.1.2 RF Profiling and Fingerprint Matching . . . . . . . . . . . 10

2.1.2 Time of Fly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.2.1 Time of Fly of Acoustic Signals . . . . . . . . . . . . . . . 11

2.1.2.2 Time of Fly of RF Signals . . . . . . . . . . . . . . . . . . 13

2.1.3 Angle of Arrival . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.4 Radio Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.1.5 Remarks on Range-based Localization . . . . . . . . . . . . . . . . . 19

2.2 Range-free Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.1 Anchor Proximity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.2 Network Connectivity . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2.2.1 Centralized Methods . . . . . . . . . . . . . . . . . . . . . . 23

iii

2.2.2.2 Distributed Methods . . . . . . . . . . . . . . . . . . . . . . 26

2.2.2.3 Dealing with “Complex Shapes” and “Holes” . . . . . . . . 27

2.2.3 Localization Events . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.2.4 Remarks on Range-free Localization . . . . . . . . . . . . . . . . . . 33

3 Uncontrolled Event-driven Localization 34

3.1 Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.2 MSP: Multi-sequence Positioning . . . . . . . . . . . . . . . . . . . . . . . . 34

3.2.1 System Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.2.2 Basic MSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2.3 Advanced MSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.2.3.1 Sequence-based MSP . . . . . . . . . . . . . . . . . . . . . 39

3.2.3.2 Iterative MSP . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.2.3.3 Distribution-based Estimation (DBE MSP) . . . . . . . . . 42

3.2.3.4 Adaptive MSP . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.2.4 Overhead and Complexity Analysis . . . . . . . . . . . . . . . . . . . 46

3.2.5 Wave Propagation Example . . . . . . . . . . . . . . . . . . . . . . . 47

3.2.6 Practical Deployment Issues . . . . . . . . . . . . . . . . . . . . . . . 48

3.2.6.1 Incomplete Node Sequence . . . . . . . . . . . . . . . . . . 48

3.2.6.2 Localization without Time Synchronization . . . . . . . . 49

3.2.6.3 Sequence Flip and Protection Band . . . . . . . . . . . . . 50

3.2.7 Simulation Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.2.7.1 Performance of the Basic MSP . . . . . . . . . . . . . . . . 53

3.2.7.2 Improvements of Sequence-based MSP over Basic MSP . . 55

3.2.7.3 Improvements of Iterative MSP over Sequence-based MSP 57

3.2.7.4 Distribution-based Estimation over Iterative MSP . . . . . 57

3.2.7.5 Improvements of Adaptive MSP . . . . . . . . . . . . . . . 58

3.2.7.6 Simulation Summary . . . . . . . . . . . . . . . . . . . . . 60

3.2.8 Test-bed Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.2.8.1 Indoor System Evaluation . . . . . . . . . . . . . . . . . . . 61

3.2.8.2 Outdoor System Evaluation . . . . . . . . . . . . . . . . . . 64

3.2.9 Summary and Remarks on MSP . . . . . . . . . . . . . . . . . . . . 67

3.3 LUE: Localization with Uncontrolled Events . . . . . . . . . . . . . . . . . . 68

3.3.1 System Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.3.1.1 Concepts in Event-driven Localization . . . . . . . . . . . . 68

3.3.1.2 Localization with Uncontrolled Events . . . . . . . . . . . . 69

3.3.2 LUE Basic Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.3.2.1 Event Generation Parameter Estimation . . . . . . . . . . 71

3.3.2.2 Location Area Estimation . . . . . . . . . . . . . . . . . . . 73

iv

3.3.2.3 Localization Algorithm . . . . . . . . . . . . . . . . . . . . 76

3.3.3 LUE Advanced Design . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.3.3.1 Event Generation Parameter MLE . . . . . . . . . . . . . . 77

3.3.3.2 Final Position MLE . . . . . . . . . . . . . . . . . . . . . . 79

3.3.4 Overhead and Complexity Analysis . . . . . . . . . . . . . . . . . . . 81

3.3.5 Discussion on Wave Propagation Events . . . . . . . . . . . . . . . . 83

3.3.5.1 Basic Design with Wave-based Events . . . . . . . . . . . . 83

3.3.5.2 Advanced Design with Wave-based Events . . . . . . . . . 84

3.3.6 Simulation Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 85

3.3.6.1 Simulation for the Basic LUE Design . . . . . . . . . . . . 86

3.3.6.2 Event Generation Parameter MLE . . . . . . . . . . . . . . 87

3.3.6.3 Final Position MLE . . . . . . . . . . . . . . . . . . . . . . 88

3.3.6.4 Simulation Summary . . . . . . . . . . . . . . . . . . . . . 89

3.3.7 Test-bed Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.3.7.1 Localization Results . . . . . . . . . . . . . . . . . . . . . . 89

3.3.7.2 Discussion on Node Pair Flip . . . . . . . . . . . . . . . . . 90

3.3.7.3 Discussion on Localization Performance . . . . . . . . . . . 91

3.3.8 Summary and Remarks on LUE . . . . . . . . . . . . . . . . . . . . 91

4 Localization and Tracking with Signature Distance 93

4.1 Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.2 LBC: Range-free Localization Beyond Connectivity . . . . . . . . . . . . . . 94

4.2.1 Empirical Data as Motivation . . . . . . . . . . . . . . . . . . . . . . 94

4.2.1.1 Preliminary Experiments . . . . . . . . . . . . . . . . . . . 95

4.2.1.2 Large-scale Experiments . . . . . . . . . . . . . . . . . . . 95

4.2.1.3 Analysis and Discussion . . . . . . . . . . . . . . . . . . . . 97

4.2.2 Design: a Relative Distance . . . . . . . . . . . . . . . . . . . . . . . 98

4.2.2.1 Neighborhood Ordering as a Signature . . . . . . . . . . . 98

4.2.2.2 SD: Signature Distance . . . . . . . . . . . . . . . . . . . . 99

4.2.2.3 RSD: Regulated Signature Distance . . . . . . . . . . . . . 104

4.2.3 Design as a Supporting Layer . . . . . . . . . . . . . . . . . . . . . . 107

4.2.3.1 Connectivity-Based Schemes . . . . . . . . . . . . . . . . . 107

4.2.3.2 Design Embedding . . . . . . . . . . . . . . . . . . . . . . . 109

4.2.4 Complexity of RSD Embedding . . . . . . . . . . . . . . . . . . . . . 109

4.2.5 Test-bed Experimentation . . . . . . . . . . . . . . . . . . . . . . . . 109

4.2.5.1 Experiment I: Linear Network . . . . . . . . . . . . . . . . 110

4.2.5.2 Experiment II: Regular 2D Network . . . . . . . . . . . . . 114

4.2.5.3 Test-bed Evaluation Summary . . . . . . . . . . . . . . . . 117

4.2.6 Simulation Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 117

v

4.2.6.1 The Noise Model . . . . . . . . . . . . . . . . . . . . . . . . 117

4.2.6.2 RSD as a Metric of Proximity . . . . . . . . . . . . . . . . 118

4.2.6.3 The Effectiveness of RSD . . . . . . . . . . . . . . . . . . . 119

4.2.6.4 The Robustness of RSD . . . . . . . . . . . . . . . . . . . . 122

4.2.6.5 Simulation Summary . . . . . . . . . . . . . . . . . . . . . 124

4.2.7 Summary and Remarks on LBC . . . . . . . . . . . . . . . . . . . . 125

4.3 SBT: Sequence-based Tracking Under Unreliable Sensing . . . . . . . . . . . 125

4.3.1 System Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

4.3.2 Main Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

4.3.2.1 Division of the Map . . . . . . . . . . . . . . . . . . . . . . 128

4.3.2.2 Unreliable Detection Node Sequence . . . . . . . . . . . . . 129

4.3.2.3 The Sequence Distance . . . . . . . . . . . . . . . . . . . . 130

4.3.2.4 Neighborhood Graph . . . . . . . . . . . . . . . . . . . . . 132

4.3.2.5 Tracking as Optimal Path Matching . . . . . . . . . . . . . 133

4.3.2.6 Algorithm and Complexity Analysis . . . . . . . . . . . . . 135

4.3.3 Multi-dimensional Smoothing . . . . . . . . . . . . . . . . . . . . . . 136

4.3.3.1 Modality Domain Smoothing . . . . . . . . . . . . . . . . . 136

4.3.3.2 Time Domain Smoothing . . . . . . . . . . . . . . . . . . . 137

4.3.3.3 Space Domain Smoothing . . . . . . . . . . . . . . . . . . . 137

4.3.4 Issues in Practical Applications . . . . . . . . . . . . . . . . . . . . . 138

4.3.4.1 Issue on System Scalability . . . . . . . . . . . . . . . . . . 138

4.3.4.2 Issue on Multiple Targets . . . . . . . . . . . . . . . . . . . 139

4.3.4.3 Issues on Time Synchronization and Energy Efficiency . . . 139

4.3.5 Simulation Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 140

4.3.5.1 Noise Models . . . . . . . . . . . . . . . . . . . . . . . . . . 140

4.3.5.2 An Example by Figures . . . . . . . . . . . . . . . . . . . . 141

4.3.5.3 SBT Performance Evaluation . . . . . . . . . . . . . . . . . 141

4.3.5.4 Effectiveness of Smoothing . . . . . . . . . . . . . . . . . . 144

4.3.5.5 Impact of the Node Placement . . . . . . . . . . . . . . . . 144

4.3.5.6 Simulation Summary . . . . . . . . . . . . . . . . . . . . . 146

4.3.6 Test-bed Experimentation . . . . . . . . . . . . . . . . . . . . . . . . 147

4.3.7 A Brief Discussion on Mobile Tracking . . . . . . . . . . . . . . . . . 148

4.3.8 Summary and Remarks on SBT . . . . . . . . . . . . . . . . . . . . 149

5 Concluding Remarks 150

5.1 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

5.2 Future Research Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Bibliography 153

vi

List of Tables

2.1 Summary of Range-based Localization in WSN . . . . . . . . . . . . . . . . 20

2.2 Summary of Range-free Localization in WSN . . . . . . . . . . . . . . . . . 33

3.1 Default Simulation Configurations for MSP . . . . . . . . . . . . . . . . . . 53

3.2 Default Simulation Configurations for LUE . . . . . . . . . . . . . . . . . . 85

3.3 Comparison of Event-driven Localization Methods . . . . . . . . . . . . . . 91

4.1 Major Factors Affecting RSS Sensing . . . . . . . . . . . . . . . . . . . . . . 97

4.2 Statistics of the Linear Network . . . . . . . . . . . . . . . . . . . . . . . . . 110

4.3 Statistics of the 2D Network . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

4.4 Default Simulation Configurations for LBC . . . . . . . . . . . . . . . . . . 118

4.5 Default Simulation Configurations for SBT . . . . . . . . . . . . . . . . . . 140

vii

List of Figures

1.1 Localize the Thesis in the State-of-the-art . . . . . . . . . . . . . . . . . . . 3

2.1 Round-trip Time of Fly Measurements . . . . . . . . . . . . . . . . . . . . . 13

2.2 Example Patterns of the Received UWB Signal . . . . . . . . . . . . . . . . 14

2.3 Ranging with Radio Interferometry . . . . . . . . . . . . . . . . . . . . . . . 18

2.4 APIT: Triangular Coverage Based on Proximity . . . . . . . . . . . . . . . . 22

2.5 Estimate Inter-node Distance with Hop Count . . . . . . . . . . . . . . . . 23

2.6 Examples of Anisotropic Network Topology . . . . . . . . . . . . . . . . . . 28

2.7 The Ideas of REP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.8 The Asymmetric Architecture of the Spotlight System . . . . . . . . . . . . 31

2.9 The design of StarDust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.1 The MSP System Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.2 Obtaining Multiple Node Sequences . . . . . . . . . . . . . . . . . . . . . . 37

3.3 Elimination Rule in Sequence-based MSP . . . . . . . . . . . . . . . . . . . 39

3.4 Sequence-based MSP Example . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.5 Iterative MSP: Reprocessing the Node Sequence from Scan 1 . . . . . . . . 42

3.6 An Example of Joint Distribution Estimation . . . . . . . . . . . . . . . . . 43

3.7 The Idea of DBE MSP for Each Node . . . . . . . . . . . . . . . . . . . . . 43

3.8 Four Cases for Each Node in the DBE Process . . . . . . . . . . . . . . . . 43

3.9 Basic Architecture of Adaptive MSP . . . . . . . . . . . . . . . . . . . . . . 44

3.10 Adaptive MSP: Candidate Slops for Node 3 at Anchor 1 . . . . . . . . . . . 45

3.11 Example of the Wave Propagation Situation . . . . . . . . . . . . . . . . . . 48

3.12 Node Sequence without Time Synchronization . . . . . . . . . . . . . . . . . 49

3.13 The Problem of Sequence Flip . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.14 The Application of Protection Band . . . . . . . . . . . . . . . . . . . . . . 51

3.15 Basic MSP: Error vs. Number of Anchors . . . . . . . . . . . . . . . . . . . 53

3.16 Basic MSP: Error vs. Number of Scans . . . . . . . . . . . . . . . . . . . . 54

3.17 Basic MSP: Error vs. Number of Target Nodes . . . . . . . . . . . . . . . . 54

3.18 Sequence-based MSP: Error vs. Number of Anchors . . . . . . . . . . . . . 55

3.19 Sequence-based MSP: Error vs. Number of Scans . . . . . . . . . . . . . . . 56

3.20 Sequence-based MSP: Error vs. Number of Target Nodes . . . . . . . . . . 56

viii

3.21 Improvements of Iterative MSP . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.22 Improvements of DBE MSP . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.23 Adaptive MSP for a 200 by 200 Field . . . . . . . . . . . . . . . . . . . . . . 58

3.24 Adaptive MSP for a 500 by 80 Field . . . . . . . . . . . . . . . . . . . . . . 59

3.25 Impact of the Number of Candidate Events . . . . . . . . . . . . . . . . . . 59

3.26 The 360-node Mirage Test-bed (Light Beam Scan) . . . . . . . . . . . . . . 60

3.27 The 20-node Outdoor Experiments (Sound Wave Propagation) . . . . . . . 60

3.28 Number of Flips for Different Scan Speed . . . . . . . . . . . . . . . . . . . 61

3.29 Scanning Speed and Protection Band: Number of Unlocalized Nodes . . . . 62

3.30 Scanning Speed and Protection Band: Mean Localization Error . . . . . . . 62

3.31 Scanning Speed and Protection Band: Maximum Localization Error . . . . 62

3.32 MSP Methods and Protection Band: Number of Unlocalized Nodes . . . . . 64

3.33 MSP Methods and Protection Band: Mean Localization Error . . . . . . . . 64

3.34 MSP Methods and Protection Band: Maximum Localization Error . . . . . 64

3.35 Number of Anchors and Scans: Number of Unlocalized Nodes . . . . . . . . 65

3.36 Number of Anchors and Scans: Mean Localization Error . . . . . . . . . . . 65

3.37 Number of Anchors and Scans: Maximum Localization Error . . . . . . . . 65

3.38 The Experiment of Wave Detection . . . . . . . . . . . . . . . . . . . . . . . 66

3.39 Wave Detection: Ranks vs. Distances . . . . . . . . . . . . . . . . . . . . . 66

3.40 Localization Error (Sound Wave Propagation) . . . . . . . . . . . . . . . . . 67

3.41 LUE System Overview I: Node Sequence and Anchor Subsequence . . . . . 69

3.42 LUE System Overview II: Map Partition and Location Area Estimation . . 70

3.43 Estimate Angle Range by Intuition . . . . . . . . . . . . . . . . . . . . . . . 71

3.44 Extract the Joint Part of Estimations . . . . . . . . . . . . . . . . . . . . . 72

3.45 Example of Redundant Estimation Units . . . . . . . . . . . . . . . . . . . . 72

3.46 Example of Area Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.47 Example Joint Location Area for Node 3 . . . . . . . . . . . . . . . . . . . . 74

3.48 Example of Location Area Finding . . . . . . . . . . . . . . . . . . . . . . . 75

3.49 Comparison Between Two Possible Scan Angles . . . . . . . . . . . . . . . . 78

3.50 MLE for Final Position Selection . . . . . . . . . . . . . . . . . . . . . . . . 80

3.51 Basic LUE Design with Wave Propagation Events . . . . . . . . . . . . . . 84

3.52 Event Generation Parameter MLE with Wave Propagation Events . . . . . 85

3.53 Final Location MLE with Wave Propagation Events . . . . . . . . . . . . . 85

3.54 Impact of the Number of Anchors for Basic LUE Design . . . . . . . . . . . 86

3.55 Impact of the Number of Events for Basic LUE Design . . . . . . . . . . . . 86

3.56 Effectiveness of Event Generation Parameter MLE . . . . . . . . . . . . . . 87

3.57 Effectiveness of Final Position MLE . . . . . . . . . . . . . . . . . . . . . . 88

3.58 Testbed LUE Result Illustration . . . . . . . . . . . . . . . . . . . . . . . . 90

3.59 Time Gap vs. Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

ix

3.60 Node Pair Flip vs. Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.1 Experimental Results: RSS vs. Distance . . . . . . . . . . . . . . . . . . . . 95

4.2 Empirical Date for System Level RSS vs. Physical Distance . . . . . . . . . 96

4.3 Empirical Date for the Monotonicity from Each Node’s Point of View . . . 97

4.4 Neighborhood Ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

4.5 1 Explicit Node-Pair Flip . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

4.6 10 Implicit Node-Pair Flips . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.7 2 Possible Node-Pair Flips . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.8 The Physical Meaning of Node-Pair Flips . . . . . . . . . . . . . . . . . . . 102

4.9 Physical Distance vs. Bisector Lines Passing . . . . . . . . . . . . . . . . . . 103

4.10 Far-away Node Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

4.11 Motivation for SD Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.12 Bisector Lines and Small Regions . . . . . . . . . . . . . . . . . . . . . . . . 106

4.13 Correlation with Physical Distance − SD vs. RSD . . . . . . . . . . . . . . 107

4.14 RSD for Non-neighboring Nodes . . . . . . . . . . . . . . . . . . . . . . . . 107

4.15 RSD Design Embedding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.16 Test-bed Experiments I: Linear Network . . . . . . . . . . . . . . . . . . . . 110

4.17 Distance Correlation Comparison: RSD vs. Hop (Linear Network) . . . . . 111

4.18 Localization in Linear Networks: DV-Hop vs. DV-RSD . . . . . . . . . . . 112

4.19 Localization in Linear Networks: RPA-Hop vs. RPA-RSD . . . . . . . . . . 112

4.20 Localization in Linear Networks: MDS-Hop vs. MDS-RSD . . . . . . . . . . 113

4.21 Comparison: RSD vs. Hop Distance . . . . . . . . . . . . . . . . . . . . . . 113

4.22 Test-bed Experiments II: Regular 2D Network . . . . . . . . . . . . . . . . 114

4.23 Network Layout and Neighborhood Size . . . . . . . . . . . . . . . . . . . . 114

4.24 Distance Correlation Comparison: RSD vs. Hop (Regular 2D Network) . . 115

4.25 Localization Results of MDS-RSD and MDS-Hop . . . . . . . . . . . . . . . 116

4.26 The Correlation Coefficient between RSD and Physical Distance . . . . . . 118

4.27 Impact of Different σx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

4.28 Impact of Different β . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

4.29 Impact of Different Numbers of Anchors . . . . . . . . . . . . . . . . . . . . 121

4.30 Impact of Different Node Densities . . . . . . . . . . . . . . . . . . . . . . . 121

4.31 Different System Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

4.32 Example Spatial Distribution of the Radio Path Loss β . . . . . . . . . . . 123

4.33 Robustness of RSD for Spatially Unbalanced Radio Path Loss β . . . . . . 124

4.34 SBT System Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

4.35 Examples for Map Division after WSN Deployment . . . . . . . . . . . . . . 128

4.36 Detection Sequences v.s. Signature Sequences . . . . . . . . . . . . . . . . . 129

4.37 Examples for the Sequence Distance . . . . . . . . . . . . . . . . . . . . . . 130

4.38 Sequence Distance vs. Geographic Distance . . . . . . . . . . . . . . . . . . 130

x

4.39 Examples for SeqD Calculation with Wildcard Matching . . . . . . . . . . . 131

4.40 Neighbor Faces and Neighborhood Graph Building . . . . . . . . . . . . . . 133

4.41 Neighborhood Graph for Randomly Deployed 4, 8, 12 and 16 Nodes . . . . 134

4.42 Converting Optimal Path Matching to Shortest Path Searching . . . . . . . 134

4.43 SBT Allows Multi-modality Integration at the Sequence Layer . . . . . . . 136

4.44 Issues of System Scalability and Multiple Targets Tracking . . . . . . . . . 138

4.45 Demo of Reduced Candidate Path Graph H . . . . . . . . . . . . . . . . . . 139

4.46 A Tracking Example from Simulation . . . . . . . . . . . . . . . . . . . . . 142

4.47 Impact of the Sensing Noise to Tracking Error . . . . . . . . . . . . . . . . 143

4.48 Impact of the Number of Sensor Nodes . . . . . . . . . . . . . . . . . . . . . 144

4.49 Impact of the Number of Starting Faces . . . . . . . . . . . . . . . . . . . . 144

4.50 The Effectiveness of Smoothing . . . . . . . . . . . . . . . . . . . . . . . . 145

4.51 Regular Deployment: Matrix Shape . . . . . . . . . . . . . . . . . . . . . . 146

4.52 Regular Deployment: Cross Shape . . . . . . . . . . . . . . . . . . . . . . . 146

4.53 An Example of Random Deployment . . . . . . . . . . . . . . . . . . . . . . 146

4.54 Number of Faces in Different Placements . . . . . . . . . . . . . . . . . . . . 147

4.55 Error Distributions for Different Placements . . . . . . . . . . . . . . . . . . 147

4.56 Outdoor System Evaluation: Tracking A Mobile Robot . . . . . . . . . . . . 148

4.57 RF Signal Strength Based Tracking Results . . . . . . . . . . . . . . . . . . 148

xi

List of Abbreviations

AOA Angle of Arrival

AP Access Point

CCA Curvilinear Component Analysis

CCR Corner Cube Retro-Reflector

COG Center of Gravity

CRB Cramer-Rao bound

DOA Direction of Arrival

DSSS Direct-Sequence Spread Spectrum

ESPRIT Estimation of Signal Parameters by Rotational Invariance Techniques

ETOA Elapsed Time of Arrival

FPGA Field-Programmable Gate Array

GeoD Geographical Distance

GPS Global Position System

KTD Kendall Tau Distance

LBC Localization Beyond Connectivity

LLE Locally Linear Embedding

LOS Line of Sight

LP Linear Program

LS Least Squares

LUE Localization with Uncontrolled Events

MDS Multidimensional Scaling

ML Maximum Likelihood

MLE Maximum Likelihood Estimation

MSE Mean Squared Error

xii

MSP Multi-Sequence Positioning

MTT Multiple Target Tracking

MUSIC Multiple Signal Classification

PLM Positioning using Local Maps

PM Path Matching

PN Pseudo Noise

RF Radio Frequency

RFID Radio-Frequency Identification

RIM Radio Interferometry Measurement

RSD Regulated Signature Distance

RSS Radio Signal Strength

RT Ray Tracing

RWP Random Way-Point Model

SA Simulated Annealing

SBT Sequence Based Tracking

SD Signature Distance

SDP Semidefinite Programming

SeqD Sequence Distance

SVD Singular Value Decomposition

TDOA Time Difference of Arrival

TOA Time of Arrival

TOF Time of Flight

UDG Unit Disk Graph

UWB Ultra Wide Band

WSN Wireless Sensor Networks

xiii

Chapter 1

Introduction

Recent advancements in micro electronics, wireless communication, and low-cost sensor

technologies have enabled the emergence and evolution of wireless sensor networks (WSN)

as a new paradigm of computer networking [1]. A wireless sensor network is composed of

a number of low-cost, tiny sensor nodes that are capable of sensing, data processing, short

range wireless communication, and even actuation [2, 3]. Sensor nodes are deployed in areas

of interest to cooperatively monitor physical or environmental conditions, such as sound,

vibration, temperature, pressure, motion, electromagnetic disturbance, etc. Wireless sensor

networks have shown more and more popularity for both military tasks [4, 5, 6, 7, 8, 9] and

civil applications, including industrial process monitoring and control [10, 11, 12, 13, 14],

structure health monitoring [15, 16, 17, 18, 19], habitat and environment monitoring [20,

21, 22, 23, 24, 25], health-care applications [26, 27, 28, 29, 30, 31], home automation [32,

33, 34, 35, 36], vehicle networks and intelligent transportation systems [37, 38, 39, 40, 41].

1.1 Localization and Its Challenges

In many aforementioned applications, the location information of each sensor node in the

network is critical for the service. This is because users normally need to know not only

what happens, but also where interested events happen or where the target is. For example,

in battlefield surveillance [6, 7, 8], the knowledge of where the enemy comes from can be

much more important than only knowing the appearance of the enemy; in a disaster relief

operation using WSN to locate survivors in a collapsed building, it is critical that sensors

report monitoring information along with their location [23, 48, 52, 56]. On the other hand,

the position parameters of sensor nodes are assumed to be available in many operations for

network management, such as routing where a family of geographical algorithms have been

proposed [42, 43, 44], topology control that uses location information as a priori knowledge

to adjust network connectivity for energy saving [45, 46, 47], and security maintenance

where location information can be used to prevent malicious attacks [50, 52].

1

Localization, as one of the most fundamental and widely applied middle-ware service in

wireless sensor networks [72, 160], basically allows every node in the network to obtain its

location information, either the absolute geographic coordinates, or a relative position that

can be transformed to the absolute counterpart when necessary. Localization plays a key role

in many sensor network applications, however, itself is a tough problem [53, 54, 55], because

of the demanding requirements for low cost, high energy efficiency, and small footprint at

the resource constrained sensor node side, as well as practical issues associated with network

deployments. We list major difficulties that challenge accurate and efficient positioning in

wireless sensor networks in the following.

• Cost and energy constraints for every sensor node. The requirement for a low-cost and

low-energy design at each sensor node prohibits localization with additional hardware

support. For example, GPS (Global Position System [58]), which is the most widely

used technique in localization, can hardly be applicable for every sensor node in the

network [57, 72]. Similarly, extra ranging modules, such as directional antennas,

electronic compass, laser rangers, video cameras, etc, are severely limited due to their

incompatible size, considerable cost or excessive power consumption [2, 51, 55, 57].

This indicates that a localization solution must be sensor node friendly, where features

of low-cost, energy efficient, and small footprint are necessary.

• Scalability of the Network. A wireless sensor network could potentially be composed

of a large number of nodes [1, 2, 8, 53]. For instance, ExScal [62] and GreenOrbs [24]

have employed more than one thousand sensor nodes in their deployed networks. It

is also projected that future wireless sensor networks may include thousands or even

millions of nodes [63, 64, 65]. In all those networks, traditional per-node location pa-

rameters configuration [59, 60] could be extremely costly, if not impossible. Therefore,

a localization design must be network scalable, meaning that it should be cost-effective

with both small and large scale systems.

• Harsh working environments. Wireless sensor networks are likely to be randomly

deployed in inaccessible terrains and environments [1, 56, 61], such as battlefield and

conflict zone [6, 7], as well as inhabitable areas [23, 66, 67], etc. Furthermore, there is

normally no infrastructure (e.g., radio signals from wireless AP towers or power line

radiations as coordinate references) that can be used for localization purpose. In this

case, self-organized localization without close-in human interference and calibration is

essential. In other words, the localization mechanism is highly preferred to function

as an autonomous system that is free of in-field manual calibration and extensive

environment profiling.

Many ideas have been proposed for node localization in WSN [69, 70, 71, 72]. Based on

2

whether accurate ranging is required, there are generally two types of methods: (i) range-

based localization, and (ii) range-free localization. Range-based approaches could achieve

good accuracy but costly for requiring either per-node ranging hardware [76, 84, 100, 103,

107, 112, 119, 121, 157], or careful system calibration and environment profiling [81, 83,

97, 98], and thus are not appropriate for large-scale outdoor sensor networks. Range-free

designs localize senor nodes based on simple sensing, such as wireless connectivity [165,

166, 169, 170, 178, 179, 180, 190], anchor (beacon) proximity [158, 161, 162, 163, 164], or

localization events detection [191, 192, 194, 195]. Those methods feature reduced system

cost at the resource constrained sensor node side, however, with less accuracy depending

on network topology, anchor density, and event distribution.

Realizing the limitations of existing work for large-scale outdoor environments, we tried

to investigate practical solutions to bridge the gap between low cost and high accuracy for

range-free localization. In the following, we give an overview about objectives, designs and

contributions of this thesis.

1.2 Research Objectives and Contributions

Our work contributes two new types of range-free localization methods (i) uncontrolled

event-driven localization, and (ii) localization and tracking using signature distance. Fig. 1.1

gives an overview about the work of this thesis respect to the state-of-the-art, where filled

patches illustrate objectives and contributions of the above two methods.

Figure 1.1: Localize the Thesis in the State-of-the-art

1.2.1 Uncontrolled Event-driven Localization

The first contribution of this thesis is the releasing of a key precondition of range-free event-

driven localization. We evolve the event-driven localization from using precisely-controlled

3

events, through semi-controlled events, and finally to uncontrolled events, making it advance

substantially towards a practical system.

Event-driven localization makes use of events (e.g. ultrasound or air blast propagation,

optical or laser beam scan), that are generated and propagate across the network area.

With known time-spatial relationship embedded in the event distribution, the location of

each sensor node can be obtained by mapping the time of event detection with the event

position at that time instance. Traditional event-driven solutions (e.g., Spotlight [192]

and Lighthouse [191]) demonstrated that long range and highly accurate localization can

be achieved simultaneously with little additional cost at sensor nodes. These benefits,

however, come along with an implicit assumption that localization events can be precisely

generated and distributed to a specified location at a specific time instance. In practice,

accurate event control is difficult to achieve, especially in outdoor scenarios when the terrain

is uneven, or the event distribution device is not well calibrated and its position is difficult

to maintain (e.g., the helicopter-mounted case in [192]). We consider those methods as the

first generation of event-driven localization based on precisely-controlled events.

To address limitations of prior work, the first attempt in this thesis is a method called

multi-sequence positioning (MSP), for large-scale stationary sensor node localization in de-

ployments where an event source has line-of-sight to all sensors. The novel idea behind MSP

is to estimate each sensor node’s two-dimensional location by processing multiple easy-to-

get one-dimensional node sequences obtained through loosely-guided event distribution. As

the first to apply the concept of node sequence for localization in wireless sensor network,

MSP offers several benefits. First, compared to a range-based approach, the design does

not require additional costly hardware. It works using sensors typically used by sensor net-

work applications such as light and acoustic detectors that we specifically considered in our

design. Second, compared to other range-free methods, MSP requires only a small number

of anchors (theoretically as few as two), so high accuracy can be achieved economically

by introducing more events instead of more anchors. In other words, it provides a nice

trade-off between physical costs (anchors) and soft cost (events), while maintaining the de-

sired localization accuracy. Last but the most notable, compared to previous event-driven

approaches [191, 192], MSP does not need precise and sophisticated event distribution by

bringing in a small number of anchor nodes, an advantage that significantly simplifies the

system design and reduces calibration cost.

We define MSP as the second generation of event-driven localization which relaxes the

requirement from precisely-controlled events to semi-controlled events [196]. This is because

although MSP does not require precise event distribution control, it assumes the knowledge

of event generation. As an important step further, a followed project investigates node

localization with uncontrolled events, or LUE in short.

Localization with totally uncontrolled events has two obvious benefits. First of all,

simple event generation mechanisms can be applied to make the system very flexible and

4

convenient to work with. Secondly, non-artificial natural events could possibly be utilized

for localization purpose. The design of LUE extends and generalizes the methodology de-

veloped in previous MSP, by estimating both event generation parameters and the location

area of each sensor node via processing node sequences obtained from uncontrolled event

distribution [197]. Besides a basic design, this thesis also introduces two interesting tech-

niques to further extract statistic information embedded in node sequences collected under

two situations: (i) sensor node density is high; and (ii) abundant events are available,

respectively. The LUE design demonstrates the possibility of accomplishing event-driven

localization with uncontrolled events, and thus provides us a potential option of achieving

node positioning through long-term natural ambient events.

1.2.2 Localization and Tracking using Signature Distance

The second contribution of the thesis is the invention of signature distance (SD) to achieve

range-free localization beyond connectivity with sub-hop resolution.

Our work is motivated by the finding that localization by means of mere connectivity

may underutilize the proximity information available from neighborhood sensing [198]. Al-

though radio signal strength (RSS) is considered irregular in many situations due to the

unknown radio propagation loss, multi-path fading effects, hardware discrepancy, antenna

issues and so forth [97, 98, 216, 217, 218, 224], our empirical study shows that in the out-

door open-air scenario, radio signal strength weakens approximately monotonically with the

physical distance (in a statistic sense), especially from the viewpoint of a single node, where

RSS might provide some useful distance-related information telling about which neighboring

node is closer and which is further.

Starting from this finding, we propose the idea of signature distance (SD) and its en-

hanced version regulated signature distance (RSD), as metrics for describing the proximity

among 1-hop neighboring nodes. The design of signature distance nicely utilizes the fact that

common views (i.e., local sensing results) among different nodes imply geographic proximity.

It contributes a novel range-free approach to extracting relative distance information from

neighborhood orderings that can be obtained easily from simple sensing and serve as unique

high-dimensional location signatures for sensor nodes in the network. By applying RSD, for

the first time, distance relationships among neighboring nodes get quantified with sub-hop

resolution in a range-free manner. And with little additional cost, RSD can be conveniently

applied as a transparent supporting layer for many state-of-the-art connectivity-based lo-

calization solutions to achieve better accuracy. Moreover, the embedding of RSD provides

an interesting feature of robustness for localization under unevenly distributed radio prop-

agation path loss.

We then extend the concept of localization with sequence processing and the idea of

signature distance to mobile tracking applications. One of the major challenges in tracking

5

systems using wireless sensor networks is that nodes’ detections of the moving target could

be unreliable due to a combination of factors such as irregular signal patterns emitted from

the target, in-field environment noise, sensing irregularity and so on [219]. To address

this issue, this thesis proposes a new mobile target tracking mechanism that accomplishes

the tracking task by processing a series of detection node sequences that are utilized as

spacial signatures of the target in the map of monitored area. Instead of estimating each

position point separately in a movement trace, we convert the original tracking problem to

the problem of finding the shortest path in a graph [220], which is equivalent to the optimal

matching of a series of node sequences, by applying the space and time domain constraints

that are universally appropriate for any moving object.

As a range-free approach, localization by processing node sequences provides two unique

benefits. First of all, the system is more robust to random sensing noise. On one hand,

as a range-free solution, ordering of nodes according to their detections effectively prevents

errors from common sensing bias among nodes; on the other hand, single node’s sensing error

becomes less detrimental to the tracking system that depends on the statistical information

embedded in whole node sequence rather than sensing results from a single node. Secondly,

tracking by node sequence processing provides a layer of abstraction [198]. As long as the

node sequences obtained reflect the relative distance relationships among the target and the

sensor nodes with known positions, specific format of the physical sensing modality (e.g.,

infrared, isotope and radio radiation, acoustic or seismic wave) is irrelevant to the tracking

algorithm. Therefore, the design is quite generic, flexible, and compatible with different

sensing modalities.

1.3 Organization of the Manuscript

The rest of the thesis is organized as follows. Chapter 2 provides a survey about local-

ization in wireless sensor networks. Chapter 3 concentrates on the topic of event-driven

localization, and presents designs of (i) multi-sequence positing (MSP), and (ii) localization

with uncontrolled events (LUE). Their superior accuracy and flexibility over traditional

event-driven solutions are demonstrated through multiple test-bed experiments as well as

extensive simulation. Chapter 4 introduces the idea and application of signature distance

by presenting designs of (i) localization beyond connectivity (LBC), and (ii) sequence-based

tracking with unreliable sensing results (SBT). Results from simulation and system evalu-

ation validate the performance gain of our design comparing with previous work. Finally,

Chapter 5 provides concluding remarks, limitation discussion and an outlook on future

research directions.

6

Chapter 2

Background and Related Work

Localization in wireless sensor networks has attracted a lot of research efforts in recent

years [68, 69, 70, 71, 72]. The early common ground achieved is that GPS [58] is not an

almighty solution for sensor network based applications, because of its expensive cost, high

energy consumption, and rigid deployment constraints [57, 68, 71, 72, 158]. As a result,

researchers have continued investigating innovative ideas to realize practical, inexpensive,

flexible and robust localization in wireless sensor networks.

Most of the proposed localization solutions for WSN can be generally categorized into

two classes: (i) range-based localization and (ii) range-free localization. Their major dif-

ference lies in whether ranging-efforts are required at sensor nodes in the network. In

the following, we give a survey about techniques developed by range-based and range-free

positioning in Section 2.1 and Section 2.2, respectively.

2.1 Range-based Localization

The methodology of range-based localization, such as Cricket [100], Radar [81], APS [135]

PinPoint [121], TPS [103], RIPS [152], BeepBeep [108], SpinLoc [157], etc, depends on

accurate ranging results among in-field sensor nodes. In other words, most of those designs

are based on fine-grained point-to-point distance, angle, or relative velocity measurements to

identify nodes’ coordinates. After obtaining ranging results, geographical calculations such

as triangulation [53, 79, 81, 179], bilateration [73], multilateration [68, 76, 77, 78], and convex

optimization (e.g., Semidefinite Programming (SDP) [74, 75]) are applied to compute the

best-effort position estimations of sensor nodes in the network. In the following subsections,

we explain range-based methods from the perspective of four types of elementary ranging

modalities, including (i) signal strength, (ii) time of fly, (iii) angle of arrival, and (iv)

radio interferometry. Note that this classification does not prevent designs using hybrid

measurements for better accuracy performance and system flexibility [83, 157, 145].

7

2.1.1 Signal Strength

In many ways, radio signal strength (RSS) is considered as an appealing modality for range

estimation in wireless (sensor) networks, mostly because RSS information can be obtained

at almost no additional cost with each radio message sent and received [96, 98]. The major

challenge is that radio signal strength is so unpredictable [80, 216, 217, 218, 224, 225],

where reflecting and attenuating caused by objects in the environment can have much

larger effects on RSS than distance, making it difficult to infer distance from RSS without

a detailed model of the physical environment [96, 97, 98].

To effectively utilize RSS for localization, two directions have been investigated: (i)

directly infer distance from RSS measurements [82, 83, 85, 86], and (ii) radio profiling and

radio-frequency (RF) fingerprint matching [81, 87, 88, 89, 90, 93, 94]. In the following, we

summarize basic ideas for typical examples of the above two types of methods.

2.1.1.1 Directly Infer Distance from RSS Measurements

As a pioneering work of RSS-based localization, SpotOn [82] demonstrates mobile sensor

node (RFID tags) localization with simple RSS sensing results. This work considers that

the received signal strength (RSS) is a function of the physical distance (d) between the

mobile sensor and the powerful base station (radio readers) as

RSS(d) = 0.0236 · d2 − 0.629 · d + 4.781 (2.1)

which is derived from empirical data, and RSS in Eq. 2.1 is measured in an abstract unit [82].

Given RSS measurements and corresponding mapped distance estimations for multiple base

stations, a central server then triangulates the precise position of the tagged object. Spo-

tOn [82] provides a simple solution for indoor mobile localization with sub-meter accuracy.

As an early system, this system suffers from multiple problems such as requiring environ-

ment profiling, depending on a large number of base stations, and being sensitive to errors

caused by radio irregularity [80].

To overcome the uncertainty of RSS and reduce the system cost, Patwari, et al made

dual effectors in [86]. First of all, unlike Eq. 2.1, which is a deterministic model for RSS

under different distance, [86] applies a widely observed statistic model to describe radio

propagation. The expected received signal strength, denoted as P in [86], is related to the

distance d with

P (d) = Π0 − 10 · np · log10

(d

∆0

)(2.2)

where np is the radio path-loss factor (also called the fading factor or attenuation factor [221,

222, 225]), typically between 2 and 6 [86, 221, 225], and Π0 is the received power (in dBm)

at a short reference distance ∆0. Staring from Eq. 2.2, [86] derives a bias-corrected pseudo

8

maximum likelihood estimator (pseudo-MLE) for the distance as

δBCi,j =

∆0

C· 10

n0−Pi,j10·np , where C = exp

1

2 ·(

10·np

σdB ·log10

)2

(2.3)

In Eq. 2.3, Pi,j is the measured RSS with zero mean Gaussian noise of variance σ2dB .

The second contribution of this work is the application and comparison among three

manifold learning algorithms for sensor node localization [165, 170], including Isomap [165],

Laplacian Eigenmap [173] and dwMDS [85]. Those algorithms require less number of anchor

nodes that are used for coordinates rotation and scaling [86], and achieve better localization

accuracy throughout the network because of using aggregated information. Nevertheless,

those methods can not automatically recognize and remove measurement outliers during

processing, resulting in a degraded positioning performance.

To overcome the non-robustness to significant noise of previous designs, a recent work

SISR [95] proposes an error-tolerant method to automatically identify “bad nodes” and

“bad links” arising from these errors, so that they receive less weight in the least-square

localization process [83, 84]. The basic idea is to apply a residual shaping function to de-

emphasize the impact of measurement outliers in the overall cost function. Specifically,

instead of optimizing the sum of squared residues F , namely,

F =∑

i,j

r(i, j)2, where r(i, j) = di,j − di,j (2.4)

where di,j is the distance estimated by a least-squares estimator and di,j is the direct RSS-

to-distance measurement between node i and node j. SISR solves an optimization problem

F =∑

i,j

s(i, j), where s(i, j) =

{αr(i, j)2 if |r(i, j)| < τ

ln(|r(i, j)| − u) − v otherwise(2.5)

In the above, u = τ − 12ατ , v = ln( 1

2ατ ) − ατ2. α and τ are parameters to be configured to

control the overall shape of the cost function. Based on Eq. 2.5, SISR [95] is able to suppress

and even discount the influence of measurement outliers and achieve notable performance

gain while adding little ultra cost at the sensor node side.

To determine values of α and τ in Eq. 2.5, simulations in [95] suggest iterative refinement

that is relatively costly in terms of computation. In addition, as most of previous work,

SISR depends on in-field calibration to determine environmental parameters for converting

RSS values to actual physical distance for unknown radio fading factor a and bias b in the

following Eq. 2.6 [95]

RSSI(d) = 10 · log10(da) + b (2.6)

9

2.1.1.2 RF Profiling and Fingerprint Matching

Motivated by the fact that direct distance estimation from received signal strength is found

to be ineffective in the indoor scenario [81], many localization solutions use RSS for po-

sitioning by employing a technique called RF profiling [81, 87, 88, 89, 90, 93, 94]. Those

methods work by constructing a map of signal strength about the overage area during the

deployment phase of the network. The RSS values recorded at each position in the area

are collected from all available anchor nodes. The record for a particular position is called

the RF fingerprint of that position. At a later time, a node with unknown location can be

localized by matching the detected RF fingerprint at its current position to the profiles of

the positions recorded in the map.

When localizing a target node, RADAR [81] searches the map of RSS profiles to pick

the location that best matches the observed signal strength of the target node. The metric

used for RF fingerprint comparison is the Euclidean distance in a special signal space. For

example, for a candidate position j in the map, the distance between the measured RSS

values from N anchor nodes (i.e., {RSS′i} | i = 1, 2, · · ·N) and the RF profile for position

j in the map (i.e., {RSSji } | i = 1, 2, · · ·N), denoted as Dj , can be computed with

Dj =

N∑

i=1

√(RSSj

i − RSS′i)

2 (2.7)

where N is the number of in-filed anchors available at j. By applying the empirical method,

RADAR can provide a good localization performance with the median distance error ranging

from 2 to 3 meters [81].

Building an empirical map can be tedious and costly. RADAR provides an alterna-

tive of constructing a virtual map by applying carefully derived radio propagation models.

Specifically, a Wall Attenuation Factor (WAF) model is proposed in [81] as follows

P (d) = P (d0) − 10 · n · log(

d

d0

)−{

nW · WAF nW < C

C · WAF nW ≥ C(2.8)

where n is the attenuation factor; P (d0) is the signal power at a reference distance d0; d

is the transmitter-receiver separation distance; C is the maximum number of obstructions

(walls) up to which the attenuation factor makes a difference; nW is the number of obstruc-

tions (walls) between the transmitter and the receiver; and WAF is the wall attenuation

factor [137, 222]. Unfortunately, results in [81] reported that the empirical method out-

performed the use of virtual map. The key weakness of the alternative strategy is that

the estimated map from proposed radio propagation model may not fit well the actual

environment.

To overcome difficulties with the RADAR system, Ji, et al developed a more sophis-

ticated indoor localization system called ARIADNE [90]. ARIADNE advances the radio

10

profiling based design in both map generation and localization searching.

In ARIADNE [90], a new radio propagation model is developed from the ray tracing

(RT) method [91], which uses a finite number of isotropic rays emitted from a transmitting

antenna, to approximate the radio propagation in the indoor area. By considering the

distance-dependent path loss, attenuation due to reflections and transmission, ARIADNE

defined and verified a radio propagation model as follows

P =

Nr,j∑

i=1

(P0 − 20 · log10(di) − λ · Ni,ref − α · Ni,trans) (2.9)

where Nr,j is the total number of rays received at receiver j; di, Ni,ref , and Ni,trans represent

the transmission distance, the number of reflections and the number of (wall) transmissions

of the ith ray, respectively. λ is the reflection coefficient, and α is the transmission coefficient.

ARIADNE assumes that the layout of the area is available [90] to determine di,Ni,ref , and

Ni,trans in Eq. 2.9. Values of λ and α are estimated by the simulated annealing (SA) [92]

algorithm. The benefit of applying SA is that in theory the generation of an accurate signal

strength map requires only one set of RSS measurements [90].

ARIADNE also proposes a clustering-based search algorithm for localization. It is com-

posed of two phases. In the first phase of cluster preparation, a set of candidate locations

with lower mean square error than a threshold are selected and preprocessed with the pur-

pose to neglect isolated locations from the set; then in the second phase, the remaining

candidate locations are grouped into several clusters and the center of the largest cluster is

chosen as the final estimate. ARIADNE is proved to be more cost-effective than RADAR for

indoor localization with reduced profiling cost, quick adaptation to dynamic radio behavior,

and enhanced accuracy [90].

2.1.2 Time of Fly

Many high-accuracy localization systems rely on time of fly measurements of acoustic or

radio signals to achieve precise ranging. The methodology is simple: given the speed of

signal propagation, the elapsed time from signal emitter to a receiver indicates the dis-

tance between them. Generally speaking, acoustic systems can achieve centimeter-level

high accuracy, but require dense deployment of sensor nodes because of limited effective

range at each node [99, 100, 108, 110]; on the other hand, a RF-based design can have

a wider coverage, however it normally provides low accuracy from several feet to tens of

meters [118, 119, 121, 126].

2.1.2.1 Time of Fly of Acoustic Signals

Acoustic signal propagates much slower than the radio, making it ideal for sensor nodes with

limited timing and computation capabilities. The major challenge is that the transmitter

11

and receiver may not be accurately synchronized. Continuous time synchronization with

high precision is by no means an easy task in wireless sensor networks [113, 114]. So, the

problem of how to conduct time of fly measurements without synchronization attracts much

attention, and two types of techniques have been developed to achieve a synchronization-

free system: (i) signals with different speeds [83, 84, 99, 100, 101]; and (ii) round-trip time

transfer and delay cancellation [103, 107, 109, 111, 108, 112].

As an early design based on time-of-flight of ultrasonic signal, the Bat system [99]

demonstrated an accuracy up to 3 centimeters. This system relies on an infrastructure that

is an irregular matrix of networked, ultrasonic receivers daisy-chained together above the

ceiling of the room. A base station periodically sends out a radio message, causing the

corresponding Bat device (essentially a sensor node) to emit a short pulse of ultrasound.

Simultaneously, ultrasound receivers on the roof are reset to wait for incoming ultrasound.

Thus, the measured time-of-flight of the ultrasound pulse from the Bat to receivers can be

converted to the corresponding Bat-receiver distances for positioning.

The Cricket location system [100] introduces an Ad hoc design without any infrastruc-

ture. It removes transmitter-receiver synchronization by employing concurrent radio and

acoustic signal transmission from the sender node, where the radio signal is essentially used

as a reference at the receiver to indicate the starting instance of transmission. Then, the

differential time of arrival between two signals is used to infer the distance as follows.

d = vsound · (tsound − tradio) = vsound · ∆t (2.10)

where ∆t is just the time difference of arrival at the receiver node. The Cricket system

can achieve good ranging accuracy with specially designed hardware and careful system

calibration. However, it has an effective range of only a couple of meters [100].

In addition to TDOA (time difference of arrival) between different modalities, TPS [103]

and UPS [107] present an interesting TDOA design with only acoustic signal propagation.

In UPS [107], four anchor nodes (can be more for enhanced accuracy) broadcast acoustic

beacons one after another in an ordered manner, so that the distance between the target

node and each anchor can be calculated with pre-known anchor coordinates and the mea-

sured time gaps between detections at the target node and those at every anchor during

several rounds of transmissions. Like Cricket [100], TPS and UPS do not require time syn-

chronization among nodes. Their advantage is that one modality (sound) is sufficient to

localize, however, at the cost of anchor density and significant communication overhead. It

is notable that localization with detections of time (difference) of arrival (TOA/TDOA) at

multiple sensors can be formulated as hyperbolic positioning [102, 103] that is investigated

to be solved by a class of spherical interpolation methods [104, 105, 106].

BeepBeep [108] and ARTL [112] stand for another class of methods that apply carefully

designed back-and-forth transmissions to achieve effective “ETOA” (i.e., elapsed time of

12

arrival) measurements. Their ideas are similar to some round-trip time synchronization

protocols (e.g., TPSN [115], Tiny-Sync [116]), where the first transmission from the sender

node is utilized as a reference time and the reply from the receiver helps to eliminate the

non-determinism of communication and detection delays.

Figure 2.1: Round-trip Time of Fly Measurements

As an example, Fig. 2.1 illustrates ranging process of the BeepBeep design [108]. At

first, node A emits a sound signal with its speaker at time tA0 that is respect to the time

frame of tA. This signal gets detected by its own microphone at tA1 as well as the receiver

B at tB1. Then, B echoes back at tB2. This signal is also recorded and time-stampled by

both nodes as shown in the figure. Despite the arbitrary span between two transmissions,

as marked in Fig. 2.1, after mathematical permutation, the distance between two nodes can

be estimated with the following equation,

d =1

2· (dA→B + dB→A) =

vsound

2· ((tA3 − tA1) − (tB3 − tB1)) + LA + LB (2.11)

where LA and LB are the distances between the speaker and microphone on node A and

node B, respectively. Integrating other noise mitigation approaches, BeepBeep [108] reports

1 cm and 2 cm average ranging accuracy with less than 2 cm standard deviations for

typical indoor and noisy outdoor environments, respectively. One remark here is that the

mechanism depicted by Fig. 2.1 and Eq. 2.11 is actually quite general, and also works

without self-recording. The difference is that tA0 and tA1 converge to one time instance (so

do tB2 and tB3) that can be obtained by using low-layer time-stamping techniques [115, 117].

Also in such case, we have LA = LB = 0.

2.1.2.2 Time of Fly of RF Signals

Measuring time of fly for radio signals is extremely challenging in wireless sensor networks.

The difficulty comes from three aspects (i) the unbeatable speed of light (radio), (ii) the

relatively short distance among nodes in the network, and (iii) the hardware constraints of

sensor nodes that prohibit timing with ultra-high resolution. To the best of our knowledge,

designs in this category require either specially designed radio chips [118, 119, 126, 128]

13

or high speed clocks and processors [120, 121, 126] to accomplish the ranging task with

reasonable accuracy (e.g., 1 ∼ 10 meters).

To use radio as the modality for ranging, the time domain resolution of the signal is the

first parameter that determines the localization accuracy of the system. Two mostly used

technologies for time of fly measurements with radio are UWB (ultra wide band [125]) and

DSSS (direct-sequence spread spectrum [122]), both of which are wide-band or ultra-wide-

band signals with enhanced time domain resolution.

The DSSS signal has been used in ranging systems for many years (e.g., the GPS [58]).

In such a system, a signal coded by a pseudo-noise (PN) sequence is transmitted by a

transmitter. Then a receiver cross-correlates the received signal with a locally generated

PN sequence using a sliding correlator or a matched filter [123, 221]. The distance between

the transmitter and receiver is calculated from the arrival time of the first correlation

peak. The resolution of TOA estimation in DSSS ranging systems is roughly determined

by the chip width of PN sequence, or equivalently the signal bandwidth [123]. For example,

if a bandwidth of 100 MHz is used, distance estimation errors are about or less than 3

meters under ideal LOS (line of sight) conditions [124]. However, this requires that the PN

generator at the sender and the correlator at the receiver both have a time resolution of at

least 10 ns. In other words, high speed clocks and dedicated hardware (e.g., FPGA) are

required in the system [118, 119, 120].

As mentioned before, signal bandwidth is one of the key factors that affect TOA estima-

tion with radio signals. The wider the bandwidth, the higher the ranging accuracy. Ultra

wide band (UWB [125]) systems, that employ bandwidths more than 1 GHz, have attracted

considerable attention, especially for indoor geolocation applications [128]. It has been

shown that the UWB signal is not seriously affected by multi-path fading [127, 128, 129],

Multi-path delayed signals

Figure 2.2: Example Patterns of the Received UWB Signal

14

which is because of the compact footprint of its plus-shaped signal in the time domain that

allows differentiation among delayed replicas as shown in Fig. 2.2 (borrowed from [130] by

Jourdan). From this figure, we can see that signal peaks can be clearly identified along the

time line. However, integrating such a system on sensor nodes is quite challenging, because

it demands highly sophisticated hardware and software designs to provide accurate edge

detecting, swift sampling and precise timing.

One remark here is that methods used by acoustic system for synchronization-free local-

ization, e.g., round-trip time transfer and delay cancellation, mostly can also be applied in

the radio scenario. For instance, Youssef, et al proposed a “four-way” timestamp exchange

approach to detect the time of fly without synchronization [121], the concept of which is

essentially similar to that in Fig. 2.1. Nevertheless, as many other radio based system, a

300 MHz clock is used in [121] for accurate timing.

2.1.3 Angle of Arrival

Another class of range-based localization is the use of angular estimates instead of dis-

tance estimates. The angle of arrival (AOA) data are typically gathered using radio or

microphone arrays [83, 223, 131], which allows a receiver to determine the direction of a

transmitter. At the concept level, AOA is not a new idea. Phased array radars [133] and

smart antennas [134], which function based on the AOA methodology, have been widely

used in military and civil applications. However, the use of AOA for localization in wireless

sensor networks is not a trivial “technology transfer” when considered from the perspective

of a practical system. This is because angles are simply much harder and more expensive

to measure than distance for sensor nodes with tremendous constraints in cost, form factor

and energy. For example, the need of spatial separation between microphones or antennas

is difficult to be accommodated in small sized nodes such as Berkley motes [3, 51].

To perform localization with AOA, the angles between sensor nodes and multiple anchors

(also called landmarks in many literatures) are measured. Given the position information

of anchors, sensor nodes’ location coordinates can be easily calculated with geometrical

methods. Detailed descriptions about the basics of AOA-based localization in wireless sensor

networks can be found in [135] and [136]. On the other hand, researchers have contributed

many efforts in multiple aspects of AOA localization in WSN, including (i) practical angle

measurements [83, 132, 157, 194]; (ii) effective noise mitigation [145, 147, 143, 144, 141];

and (iii) anchor placement and limitations of AOA [148, 149]. In the following, we give a

brief introduction about above work.

Cricket Compass [132] developed by Priyantha et al at MIT, and the Medusa platform

reported in [83] are among the first designs investigating AOA with practical sensor nodes.

The cricket compass system builds an indoor infrastructure with ultrasound-RF beacon

nodes attached on the ceiling of a room. By attaching a compass device to a target in the

15

room, orientation of the target can be obtained from the compass device that estimates and

analyzes angles of arrival of acoustic signals emitted from beacons on the ceiling. The system

achieves an accuracy of 5◦ for orientation detection, when angles lay between ±40◦ [132].

Medusa, used in the AHLos project [83] at UCLA, is another wireless senor node that

integrates several ultrasound receivers facing different directions for AOA measurements.

The design of Medusa allows angle of arrive detection without extensive infrastructures.

Although the Cricket Compass and the Medusa platform have various limitations, these

incipient implementations convey the message that it is feasible to get AOA capability in a

small package for future pervasive ad hoc networks. Recent work [157] and [194] make use of

radio interferometry and laser scanning events, respectively, to determine the angles among

nodes and anchors in the network. These two hybrid designs will be further explained in

Section 2.1.4 and Section 2.2.3, respectively.

The accuracy of AOA measurements is affected by a combination of factors, including

the directivity of signal emitter and receiver, multi-path reflections, background noise, etc.

Many AOA designs depend on a LOS path from the transmitter to the receiver [83, 132, 136].

Furthermore, a multi-path component may appear as a signal arriving from an entirely

different direction, leading to large errors in angle estimation. To overcome those difficulties,

researchers have investigated many robust designs that help to reduce AOA measurement

noise as well as its impact to localization results.

For AOA measurements based on sensor array DOA (direction of arrival) estimation

(e.g., an array of antennas, microphones, light sensors, etc) , multi-path problems are sug-

gested to be addressed by applying maximum likelihood (ML) algorithms [138, 137, 139, 140,

141, 142]. ML estimation can be classified into deterministic (or conditional) and stochastic

(or unconditional) methods, depending on assumptions about the statistical characteristics

of the signal [70]. A lot of theoretical research has been done in this direction, and a survey

and comparative study can be found in [138]. Another class of AOA estimators are built on

sub-space based algorithms [70], such as MUSIC (multiple signal classification) [143] and

ESPRIT (estimation of signal parameters by rotational invariance techniques) [144], both

of which are typical methods for parameter estimation in statistical signal processing. In

addition to estimator designs, one important contribution from aforementioned work is the

analysis about the Cramer-Rao bound (CRB) (with unbiased estimators) that gives clear

error uncertainty evaluation for AOA measurments.

Basu, et al [145] analyze the problem of network localization with noisy angle and dis-

tance measurements at sensor nodes. They prove that when in the presence of a small

amount of noise, the network localization problem can be NP-hard [145]; localization with

accurate distance information and relative angle information can be also hard [145]. Mo-

tivated by these observations, approximation schemes (approximating convex constraints)

and linear programs (LP) are proposed to localize nodes in the network under noisy ranging

measurements. The formation of the problem in [145] also provides the upper and lower

16

bounds on the location uncertainty. Rong, et al [146] reveal that by considering the angle

of arrival information between neighbor nodes and beacon information multiple hops away,

additional constraints can be applied to achieve enhanced localization performance despite

inaccurate angle measurements and only a small number of beacons. However, they assume

that every node in the network has the AOA capability. In [147], Bishop, et al investigate

and derive geometric constraints among nodes in the network. By formulating localization

as a geometric optimization problem, their work makes sure that the positioning solution

is consistent with the underlying geometry of the network, which helps to improve the

accuracy performance under unreliable angle detections.

On the other hand, Dogancay, et al study an interesting issue of optimal sensor place-

ment for AOA localization [148]. They report the angular separation requirements for

achieving angle-of-arrival positioning with best mean squared error (MSE) performance,

and point out that (i) path planning for mobile anchors (or beacons), e.g., unmanned aerial

vehicles (UAVs), is critical for localization angular separation; (ii) optimal angular sensor

separation is in general not unique; (iii) when all sensors are equidistant from the beacon

emitter, there may exist optimal sensor configurations with non-uniform angular sensor

separation in addition to equiangular separation.

Bruck, et al look into localization in sensor network with only local angle information

under the UDG (unit disk graph) theoretical radio model [149]. Their study shows that it is

NP-hard [150] to find a valid embedding in the plane such that neighboring nodes are within

distance 1 from each other and non-neighboring nodes are at least distance√

2/2 away.

For localization, [149] introduces an embedding algorithm with local angle information by

solving a linear program. In addition, it is shown that though angle information is not

sufficient to derive the global geometry, it is sufficient for many topology control designs

assuming location information.

2.1.4 Radio Interferometry

We list localization designs making use of radio interferometry measurements (RIM) as a

separate type of methods despite the fact that RIM values are usually obtained through

RSS (received signal strength) sampling in practical systems [152, 153, 154, 155, 156, 157].

This is because this technology is fundamentally different from other ranging approaches in

terms of physical and theoretical foundation.

Radio interferometry has long been used in the astronomy research [151], however, its ap-

plication for localization in wireless sensor networks is first proposed by Maroti, et al at Van-

derbilt University with the RIPS (radio interferometric positioning system) project [152].

RIPS utilizes two transmitters (anchor nodes) to create the interference signal at receiver

nodes (target nodes to be localized). It is proved in [152] that if the frequencies of the two

emitters are almost the same, the composite signal will have a low frequency envelope that

17

can be measured by cheap and simple hardware, e.g., a mote in wireless sensor networks.

By using the relative phase offset of the signal at two receivers, which is a function of the

relative positions of the four nodes involved and the carrier frequency (or equivalently, the

wave length λcarrier), an equation containing the coordinates of target nodes as unknown

variables can be established. To better illustrate the idea, we borrow a figure from [152] as

Fig. 2.3, where four nodes A,B,C,D form a “q-range” equation as shown in the figure.

Phase Offset = 2π (dAD − dBD) + (dBC − dAC)

λcarrier

(mod 2π )

Figure 2.3: Ranging with Radio Interferometry

It is also proved in [152] that there are at most 32(n−2)(n−3) independent interference

measurements in a network of n nodes. In other words, when n = 4 for three anchors with

known positions and one target node, a number of three equations are available, sufficient

to solve target coordinates in 3D space. The most notable feature of this system is its large

effective range and good accuracy. [152] reports an estimation of 160 m effective range on

Mica2 nodes (more than twice of the communication range), and 3 cm localization accuracy

in an 8-node prototype system [152].

Kusy, et al [153] reveal that the original RIPS [152] design suffers from significant ranging

errors at large distances. Further analysis concludes two reasons: (i) “q-range ambiguity”

caused by the particular choice of wavelengths in RIPS, and (ii) “multi-path effects” where

radio signal gets 180◦ phase shifted after ground reflection. To address these problems, [153]

presents an interleaved and iterative localization algorithm, in which current localization

results are used to constrain the search space of q-range estimation in the next localization

phase, so as to iteratively refining the result. Results in [153] confirm a 170 m maximum

range (4X of communication range), while keeping ranging errors down to a few centimeters.

A follow-up work inTrack [154] applies the radio-interferometric ranging technique for

mobile target tracking applications. Later, inTrack gets extended and upgraded to mTrack

18

[155], which provides simultaneous multiple target tracking (MTT). The main difference

between inTrack and mTrack is essentially roles the tracked objects and the infrastruc-

ture nodes play. In inTrack, the target is on of the two transmitters, e.g., a “target-as-

transmitter” pattern [154]. While mTrack follows a reversed “target-as-receiver” pattern.

This means that only infrastructure nodes transmit in mTrack and consequently, the num-

ber of tracked objects is not limited by instant channel access. Another important idea

in mTrack is the introduction of utilizing Doppler effects to measure the instant velocity

difference (a vector value) observed from two anchors (i.e., infrastructure nodes) about the

same target node, i.e., the “q-speed” [155]. This idea is actually the starting point of a

more sophisticated tracking design proposed in [156], where tracking is modeled as a non-

linear optimization problem and an extended Kalman filter (CNLS-EKF) is used to solve

it accurately under the assumption of Gaussian measurement noise.

Chang, et al develop an indoor localization system called SpinLoc [157] inspired by pre-

vious work on radio interferometry [152, 154] and Doppler effects [155, 156]. The innovative

idea behind SpinLoc is to let the base station “move” fast enough so as to generate Doppler

efforts for stationary target nodes. Specifically, a base station includes a Mica2 beacon

node that is attached to a spinning arm driven by a motor to create frequency shifted radio

signals. The polar angle between a stationary target node and a reference node to the

spinning beacon determines the observed Doppler effects at the target. As a result, this

angle can be measured by detecting the frequency (phase) difference at the target node.

With angle measurements respect to multiple base stations, the target node can simply be

localized with AOA-based calculation.

Localization using radio interferometry provides a large ranging coverage and high accu-

racy simultaneously. Nevertheless, all above systems have several shortcomings, including

(i) requiring highly accurate time synchronization among nodes, (ii) demanding extensive

system tuning and in-field calibration, (iii) depending on certain type of radio chips that

support precious carrier frequency adjustment, module configuration, and stream-based

transition (all above projects use the same CC1000 radio solution).

2.1.5 Remarks on Range-based Localization

To summarize, Table 2.1 lists pros and cons of different types of range-based localization

methods. From this table, we can observe that radio and acoustic signals are the most

investigated modalities for range-based localization in wireless sensor networks.

Generally speaking, systems based on acoustic signals own the advantages of a neat sys-

tem design with high localization accuracy. However, they suffer from very limited effective

range and extra cost for per-node ranging components (e.g., speakers or microphones). On

the contrary, radio based systems can provide a large coverage, but ask for either extensive

environmental profiling (e.g., RSS maps) and system tuning (e.g., frequency fine tuning in

19

Table 2.1: Summary of Range-based Localization in WSN

Range-based Methods Pros Cons

RSS

Direct Inferring

low-cost sensor nodes, scalable,

omni-directional, low computa-

tion overhead for ranging

low positioning accuracy, envi-

ronment sensitive, in-field cali-

bration for accuracy

Map Profiling

low-cost sensor nodes, enhanced

accuracy, omni-directional, low

computation at nodes

extensive environment profiling

and calibration, unscalable, high

background computation cost

TOF

Acoustic Signal

high accuracy, low timing require-

ments, low computation and com-

munication overhead

limited effective range, direc-

tional, extra sensing hardware,

high anchor (landmark) density

Radio Signal

better accuracy than RSS direct

inferring, large effective range

than acoustic systems

ultra-high timing requirements,

expensive hardware, heavy com-

putation for signal processing

AOAadditional channel of ranging, ori-

entation information

hardware constraints, computa-

tion for effective estimation

RIM

large effective range, low-cost sen-

sor nodes, high accuracy, resis-

tant to multi-path fading

careful system tuning, synchro-

nization sensitive, hardware de-

pendent, processing overhead

RIM), or special hardware systems (e.g., FPGA circuits for RF TOA measurements) to

realize a good ranging performance.

From all the above analysis, we conclude that (i) range-based methods can provide sound

localization results concerning accuracy; (ii) however, it would be costly for the operation of

ranging, in the form of either hard cost (additional hardware) or soft cost (time and efforts)

at each in-field sensor nodes.

2.2 Range-free Localization

The methodology of range-free localization, such as Centroid [158], APIT [162], MDS-

MAP [166], DV-hop [178], RPA [179], Spotlight [192], Stardust [195], etc, tries to localize

sensor nodes without costly ranging efforts. Those methods have applied many smart ideas

to pursue a low-cost system design. Early range-free solutions make use of the proximity

information respect to 1-hop anchors with known positions [158, 162]. Then, researchers

investigate connectivity-based localization which uses local neighborhood sensing to build

hop-based virtual distances for large-scale sensor network localization [166, 178]. Recent

study proposes another type of range-free approaches, called event-driven localization, in

which artificially events (e.g., laser or light beam scan, sound blast, etc) are generated to

distribute over the network area. Localization can be accomplished by analyzing simple

event detections at low-cost sensor nodes.

20

2.2.1 Anchor Proximity

When ranging is difficult and costly, proximity sensing becomes a degraded substitution to

describe the geolocation relationships among nodes. The insight behind localization with

proximity is simple. If node A senses node B’s existance via any modality (e.g., radio,

acoustic, infrared, magnetic field, etc), node A obtains the information that node B is in its

vicinity. In other words, two nodes are located close to each other with distance dAB ≤ RA,

where RA is the maximum sensing range of node A. In such a way, a binary ranging result,

i.e., “0” for out of RA and “1” for within RA can be obtained in a range-free manner, which

then be used for localization.

Centroid [158] is a typical implementation of the above idea for localization in WSN.

The target sensor node j selects a number of k neighboring anchor nodes with most reliable

communication link quality. Then, the location of the target node, denoted with (xj , yj), is

calculated as the gravity center of the selected k anchor nodes, namely,

(xj, yj) =

(k∑

i=1

Xi/k,k∑

i=1

Yi/k

)(2.12)

where (Xi, Yi) are the coordinates of anchor node i.

LANDMARC [159], MSL [160] and WCL [161] improve the Centroid design by proposing

the Weighted Centroid approach. They share similar design philosophy: the anchor close to

the target node should occupy more weight in position estimation. LANDMARC [159] and

WCL [161] both use radio signal strength (RSS) to infer the distance parameters among

nodes. For example, WCL applies the following position estimation scheme

(xj , yj) =

∑ki=1 wij · (Xi, Yi)∑k

i=1 wij

where wij =

(Pref · 10

RSSij20

)g

(2.13)

where RSSij is the measured radio signal strength from (or at) anchor i at (or from) node

j, Pref is a reference power of the radio system, and g is a parameter to ensure that remote

anchors with weak RSS still impact the position determination. MSL [160] proposes a

more complex design to determine the location of a static or mobile target node. It applies

a partial filter process to iteratively infer the position of target node, by evaluating the

impacts (weights) of 1-hop and 2-hop anchors to candidate positions obtained for previous

step of sampling. Evaluation shows that weighted centroid outperforms the original design

in terms of localization accuracy.

APIT [162] is another interesting work making use of anchor proximity. We borrowed

a figure from [162] as Fig. 2.4 to better explain the design. The main idea of APIT is to

perform node location estimation by segmenting the area into a large number of triangular

regions with different sets of anchor nodes. The target sensor node receives beacon messages

from those anchors to identify possible triangles that cover its true position, as shown in

21

Estimated Area for Sensor Location

Figure 2.4: APIT: Triangular Coverage Based on Proximity

Fig. 2.4. The overlapping area extracted from all these triangles is considered as the possible

location area of the target node, which is depicted as a small gray triangle in the figure.

The final position estimation is obtained by computing the center of gravity of this area,

marked as a black-filled cycle in the figure.

To determine whether the target node is located in a triangle made by three anchors, a

PIT (Point-In-Triangulation) [162] test is conducted based on geometry. For a given triangle

constructed by anchor A,B and C, a node M is evaluated outside of ∆ABC if there exists

a direction such that a position point adjacent to node M is further or closer to anchor A,B

and C simultaneously. Otherwise, M is inside ∆ABC. Considering that node M may not

be able to move in practical systems, an approximate PIT test is proposed based on two

assumptions: (i) RSS measurements are monotonic with physical distance; (ii) a sufficient

node density is available for mimicking node movements (using neighboring nodes to sense

nearby radio signal strength).

Centroid [158] and APIT [162] demonstrate that proximity based range-free designs

allow extremely low cost sensor nodes to be localized. However, to achieve high position-

ing accuracy, a large number of anchors need to be placed in the network appropriately.

Bulusu, et al [163] address this problem by proposing two algorithms, i.e., HEAP and

STROBE, to promote anchor self-placement and optimization in medium and dense de-

ployments. The HEAP algorithm deploys anchor nodes in a network step by step that

resembles growing a tree. Candidate positions of new anchors are determined by the cover-

age of deployed anchors for minimum redundancy. The design of STROBE aims at tuning

off spare anchors in a dense network for lifetime extension. In STROBE, each anchor node

periodically switches over three states, and enters the “sleep” state whenever sufficient

active anchors exist in its neighborhood.

On the other hand, Shrivastava, et al explore the fundamental performance limits of

localizing and tracking a target in a d-dimensional space (d ∈ {1, 2, 3}) using only binary

proximity sensors [164]. Their conclusion reveals that the achievable spatial resolution in

localizing a targets trajectory is of the order of 1ρRd−1 , where R is the ideal sensing radius,

and ρ is the sensor density per unit space.

22

2.2.2 Network Connectivity

Extending the proximity idea to network level localization, researchers have found “hop

count” to be a useful metric to describe inter-node distances. The local connectivity infor-

mation provided by the radio communication defines an unidirectional graph, where vertices

are wireless sensor nodes and edges represent radio links between nodes. We borrow a figure

from [165] as Fig. 2.5 to show an example. In this figure, we can observe that in a randomly

deployed network with considerable node density, the shortest path between two nodes can

be a good indicator of their physical distance.

Figure 2.5: Estimate Inter-node Distance with Hop Count

Methods using network connectivity for sensor node localization can be divided into two

types: (i) centralized methods [175, 166, 168, 184, 169], and (ii) distributed methods [177,

179, 78, 180, 174], depending on where the location estimation computation is conducted

− at a centralized localization server, or at each sensor node locally. Note that many

algorithms in those methods are also applicable for range-based localization where physical

distance, in addition to hop distance, is available.

2.2.2.1 Centralized Methods

In centralized methods, the connectivity information is collected in a server either within

or out of the network. Localization algorithms run at this server to give position estimation

for all target nodes involved. Centralized methods usually can output globally optimized

results, however, they require plentiful computation capability.

Isomap (isometric feature mapping) by Tenenbaum, et al [165] paves the foundation

for a series of MDS-based designs [86, 166, 168, 169] using network connectivity for sensor

node localization. In Isomap, the physical distance di,j between node i and j is replaced by

another “distance” δi,j that is defined as the number of hops along the shortest path between

two nodes in the network. The rational behind the substitution is that the shortest path in

the neighborhood connectivity graph, as exampled in Fig. 2.5, is a good approximation to

23

the shortest distance on the manifold (i.e., the physical distance). Then, for a network of

n nodes (including both anchors and target nodes), location estimation is considered as an

optimization problem for the following cost function.

minimize CIsomap =n∑

i=1

n∑

j=1

(δ2i,j − ‖zi − zj‖2

)2(2.14)

where zi is the estimated vector coordinates of node i, and ‖ · ‖2 is the Euclidean norm.

To obtain the optimal location estimation zi (i ∈ {1, 2, · · · n}) that satisfies Eq. 2.14, a

standard MDS technique [167] can be applied with a distance matrix A as input, where aij

(the value at the ith row and the jth column in A) equals δi,j. Specifically, a relative map

of all nodes, denoted as Z ′ = [z′1, z′2, · · · , z′n] where z′i is the relative coordinates of node i,

can be calculated in several steps from Eq. 2.15 to Eq. 2.19.

D = [a2ij] (2.15)

H = In − 1

n· eeT where en×1 = [1, · · · , 1]T (2.16)

B = −0.5 · HDH (2.17)

(U,Λ, V ) = SV D(B) where Λ = diag(λ1, · · · , λn) (2.18)

U = [U1, · · · , Un], Ui is a n × 1 vector

Z ′ = diag(λ1/21 , λ

1/22 )[U1, U2] (2.19)

In Eq. 2.18, matrices U,Λ, V are obtained from the singular value decomposition of matrix

B, namely, B = UΛV ∗ (or B = UΛV T in this case for a real V ). After obtaining the

relative coordinates Z ′, the “absolute map” can then be computed by scaling and rotating

the “relative map” according to the absolute coordinates built with at least three anchor

nodes in the network, namely,

Z = T (Z ′, {zj}), j ∈ {1, · · · ,m} (2.20)

where zj is the true coordinates of anchor node j, and T (·) is a frame transform function.

The design of MDS-based methods makes full of the connectivity information in the

network. In addition to the local embedding that is achieved by considering 1-hop con-

nectivity [170, 175], hop-based distances among all non-neighboring node pairs also get

utilized to provide more constraints that help to optimally determine the network layout.

Simulation results in [166] show that connectivity based MDS methods achieve an aver-

age localization error of 0.31R, where R is the UDG radio range, in a randomly deployed

network with mean 1-hop connectivity of 12.1 (i.e., average degrees ).

The computation cost of the above MDS process is O(n3) [86, 166], mostly from the

SVD step in Eq. 2.18, which makes the algorithm not possible to execute on low-power

24

sensor nodes, and not very scalable for large scale systems. To overcome this problem,

[168, 169] improve MDS-based designs by investigating revisions for enhanced scalability.

Ji, et al propose a distributed version of the MDS algorithm in [168]. In their design, a

series of local maps of adjacent sensors along the route from a starting anchor to an ending

anchor are computed first with the MDS algorithm. Then, local maps are pieced together

to get the global view of the whole map, which has a reduced computation complexity of

O(n2) using the LS (least squares) methods. By aligning the calculated positions and the

true positions of all anchor nodes, the positions of target nodes in the stitched map can be

be effectively calibrated simultaneously. [168] mentioned that in addition to the benefits of

scalability and distributed processing, this map-stitch design works better for networks with

irregular shapes and obstacles, which is essentially an problem about “holes and complex

shapes” investigated heavily later [184, 185, 187, 190].

Shang, et al then push forward distributed MDS to an extreme by introducing the PLM

(positioning using local maps) concept [169]. In PLM, each node builds its local map with

hop radius Rlm = 1, 2, or 3, depending on the system configuration. Then, the global map

is obtained by stitching and aligning all local maps as that in [168]. [169] demonstrates that

PLM is robust to an irregular network layout, e.g., a “C”-shaped topology.

MDS is actually one classic technique for dimensionality reduction [170]. Some similar

techniques, such as the LLE (locally linear embedding) [170, 171, 172], Laplacian Eigen-

maps [173], and CCA (curvilinear component analysis) [174] are also proposed for localiza-

tion in sensor networks. Their basic model is that given n input vectors xi (i = 1, · · · , n),

where each vector xi is of p dimensions, dimensional reduction looks for n output vectors

yi (i = 1, · · · , n) , where each yi is of q dimensions (q < p). The condition is that the dis-

tance between input vectors xi and xj (can be Euclidean or other definitions) is preserved

between output vectors yi and yj.

In LLE [170], local connectivity results are treated as a high-dimensional observation

at each node (where each neighbor occupies one dimension), resembling that nodes obtain

local snap shots of the map. Given high-dimensional data from all nodes, a search algo-

rithm is first used to identify the neighborhood of each node. Then, a weighted LS fitting

problem is solved by eigenvalue decomposition [171], which gives the location estimation of

all nodes. Local manifold embedding normally has reduced computation complexity than

MDS. However, with less constraints, localization performance given by those methods may

be inferior to that of MDS, especially for a regular-shaped network.

Similarly to the manifold embedding approach, researchers have investigated convex

optimization algorithms such as SDP to localize sensor nodes based on link constraints in

the network connectivity graph [175, 176]. The theory behind SDP based localization can be

found at [75], and comprehensive tutorials and research papers about convex optimization

and SDP-based localization are available at http://www.convexoptimization.com/.

25

2.2.2.2 Distributed Methods

In distributed methods, each target sensor node collects its connectivity information for self-

localization. Localization algorithms running at a target node only give position estimation

for this node itself. Distributed designs usually are quite scalable with low computation

cost, however, their accuracy is inferior to centralized methods with global optimization.

Many centralized designs also provide distributed versions as mentioned before, such as

[168, 169, 174, 176] where local processing is essentially a miniature version of the original

method. In spite of reduced computation, we still consider them as centralized designs to

differentiate from distributed designs surveyed in this section.

DV-hop [177, 178] localizes the sensor nodes in two steps. First, anchor nodes flood

beacon messages through out the network to exchange location information with each other

and probe the number of hops among them. Once anchors obtain these two pieces of

information, they estimate the average size (physical distance) for one hop as follows,

dhop =

∑i6=j dis(vi, vj)∑i6=j hop(vi, vj)

(2.21)

where d(vi, vj) and hop(vi, vj) are the physical distance and the minimum number of hops

between anchor vi and vj , respectively. Then in the second step, an arbitrary node ui can

estimate it physical distances to anchors with

dis(ui, vi) = dhop · hop(ui, vi) (2.22)

that can be used to perform triangulation. [177] reports 0.2 ∼ 0.45 R localization errors in

an isotropic network of 100 nodes with an average node degree of 7.6.

RPA [179] uses a similar mechanism of hop-based distance estimation called Hop-

TERRAIN as its first step. In addition, it introduces an iterative refinement step for

position adjustment based on local sensing results. Specifically, at iteration k, the position

of node ui is recomputed based on the estimated positions of its neighbors obtained from it-

eration k−1 as well as updated neighborhood sensing results. Simulation results reported in

[179] show that the refinement step can effective enhance localization performance compar-

ing with Hop-TERRAIN alone. Besides, [179] summarizes three guidelines for connectivity

based positioning: (i) a high connectivity (i.e., ≥ 10), (ii) a reasonable fraction of anchors

(i.e., ≥5%), (iii) an appropriate anchor placement (i.e., at the boundary of the network).

The Amorphous [180] design, proposed independently from DV-hop by Nagpal, et al,

employs a similar algorithm to estimate sensor positions from hops to remote anchor nodes.

Different from DV-hop, Amorphous estimates the hop distance using the following equation

26

given by Kleinrock and Silvester [181],

dhop = R · (1 + e−nlocal −∫ 1

−1e−

nlocalπ

(arccos(t)−t·√

1−t2)dt) (2.23)

where R is the UDG radio radius, nlocal is the average neighborhood size. The insight behind

Eq. 2.23 is that dhop depends only on the expected neighborhood nlocal rather than the total

number of sensors in the network. Amorphous also introduces a smoothing mechanism to

improve hop-based distance estimation as follows,

s(vi, ui) =

∑vj∈N(vi)

hop(vj , ui) + hop(vi, ui)

|N(vi)| + 1− 0.5 (2.24)

where s(vi, ui) is the smoothed hop distance between target node vi and anchor ui, N(vi) is

the 1-hop neighbor set of vi. Evaluation shows that Amorphous benefits from its refinement

step with improved localization accuracy.

Recently, Langendoen, et al [182] give a performance comparison among DV-hop [177],

RPA [179] and N-hop [78] (that is more like a range-based approach), and provide sugges-

tions about which type of localization designs to deploy under difference situations. [182]

also theoretically proves an interesting conclusion. For n sensors and m anchors distributed

uniformly at random in a [0; 1]d hypercube, where m ≥ d + 1, the localization error from

Hop-TERRAIN based methods is bounded by

‖zi − zi‖ ≤ r1

R+ O(R) (2.25)

where r1 =d · r0

2√

3, R > r0 and r0 = 8

√3d

3

2 ·(

log(n)

n

) 1

d

Eq. 2.25 tells that node density and radio range play important roles in such connectivity-

based range-free localization.

2.2.2.3 Dealing with “Complex Shapes” and “Holes”

Most of the above connectivity based localization methods assume network topology to

be “isotropic”, meaning that the proximity measurements (e.g., the physical distance for

each hop) are statistically identical in all directions throughout the network, as exampled

in Fig. 2.5. In practice, this assumption usually does not hold due to a number of fac-

tors [184] such as obstacles in the field, radio irregularity, non-uniform node density, etc.

As a result, “holes” and “complex shapes” of the topology may appear as shown in Fig. 2.6.

Fig. 2.6(a) illustrates a single hole in the network where the red-dashed line indicates the

physical distance between a pair of nodes, and the black-solid curve shows the shortest path

between them. Fig. 2.6(b) gives an example of irregular topology, and Fig. 2.6(c) shows a

more complicated case with distorted network boundary and multiple holes marked as gray

27

Figure 2.6: Examples of Anisotropic Network Topology

ellipses, as well as unbalanced node density. In those cases, the hop-based distance could

be quite ineffective for inferring the physical distance.

[168, 169, 174] deal with the anisotropic problem in a passive manner, by developing

distributed versions of centralized designs that omit this issue. The insight behind those

methods is that although the whole network is anisotropic, the local map can be considered

isotropic in small regions. However, an appropriate choice of the size of small regions may

be difficult, which greatly affects the localization performance. On the contrary, [184, 185,

187, 190] address the holes and complex topology actively with dedicated designs.

PDM [184] develops a linear transformation T that optimally projects the proximity

measures (in hops) into the geographic distance (in meters) despite anisotropic topology.

With m anchors, a proximity matrix P and a distance matrix L can be organized as

P = [p1, · · · , pm], pi = [pi1, · · · , pim]T (2.26)

L = [l1, · · · , lm], li = [li1, · · · , lim]T (2.27)

where pij and lij are the hop distance and physical distance between anchor i and j, re-

spectively. Then the PDM transformation matrix T is obtained by minimizing the square

error ǫi for every anchor defined as follows,

ǫi =

m∑

k=1

(lik − tipk)2, i = {1, · · · ,m} (2.28)

where the row vector ti has a theoretical solution ti = lTi P T (PP T )−1. With all anchors,

the optimal transformation matrix T can be expressed as

T = LP T (PP T )−1 (2.29)

where the numerically stable form of Eq. 2.29 is computed by SVD on P [184].

In matrix T , tij essentially represents the contribution of proximity to anchor j on the

geographic distance to anchor i. After obtaining T , the distance estimation of a target node

28

s to all anchors, denoted as a column vector ls, can be calculated with

ls = Tps (2.30)

where ps is the hop distance vector from node s to all anchors. Eq. 2.30 essentially estimates

the distance from s to an anchor by a weighted sum of proximities to all anchors. Finally,

the location of node s is estimated with LS methods according to ls and the available

coordinates of anchor nodes. [184] shows that PDM is superior to DV-hop [178] and MDS-

MAP [169]. Nevertheless, later studies reveal that PDM is inferior to REP [187], which

explores geometric characteristics of a hole to correct distance estimation, and sensitive to

the number of in-field anchor nodes as well as their placement in the network.

Wong, et al propose DHL (density-aware hop-count localization) [185], a design for

localization in non-uniform and sparse networks. In DHL, the hop-count measurement

incorporates density information so that it provides more accurate distance estimation.

Specifically, a confidence threshold is used to regulate the maximum number of hops to

reach anchor nodes. In addition, a range ratio is defined and utilized to refine the hop size

estimation under different node densities. DHL achieves better localization performance

than DV-hop in node density unbalanced networks, however, it assumes that the network

diameter is available as well as an UDG radio with constant 1-hop range.

REP [187] by Li, et al presents a path rendering technique to remove the impact of holes

in the network. To illustrate basic ideas, we borrow several figures from [187] as Fig. 2.7.

In Fig. 2.7(a), a hole exists in the network and the shortest path distance between node s

Figure 2.7: The Ideas of REP

and t gets distorted because of the hole. REP augments and renders the shortest path by

creating a supplemental circle with center at o that is a point at the boundary of the hole,

as depicted in Fig. 2.7(b). Then, the straight-line distance between s and t can be easily

computed based on the law of cosines for ∆sot in Fig. 2.7(c) with

dst =√

d21 + d2

2 − 2 · d1 · d2 · cos(α) (2.31)

where α = 2π − dab

r− arccos(

r

d1) − arccos(

r

d2) (2.32)

29

α in Eq. 2.31 is calculated with Eq. 2.32 by exploring the geometrical relationships embedded

in Fig. 2.7(d), where dab is the line length of the arc from a to b; r is the radius of the

supplemental circle with focal point at o.

Simulation shows that REP is significantly better than DV-hop [178] and APIT [162] for

isotropic networks. It also outperforms PDM [184] for networks with sub-30 anchor nodes.

Unfortunately, REP makes a critical assumption of high node density, so that (i) accurate

boundary recognition [186, 188, 189] can be accomplished; (ii) the shortest path between

two nodes in the network is close to a straight line if there is no holes in between; and (iii)

the length of an arc can be estimated from node connectivity along the circle boundary.

Lederer, et al address the hole and complex shape issue in a different manner [190], by

effectively partitioning the network and placing anchors nodes. The localization algorithm

selects landmarks on network boundaries with sufficient density [186]. Then it constructs

the landmark “Voronoi” diagram and its dual combinatorial “Delaunay complex” on these

landmarks [190] (in the form of triangles). Because the combinatorial Delaunay complex

is provably rigid and has a unique realization in the plane, an embedding of landmarks by

simply gluing Delaunay triangles can properly recover the faithful network layout. With

the landmarks nicely localized, the rest of the nodes can easily localize themselves by tri-

lateration to nearby landmark nodes.

The state-of-the-art tells that holes and irregular shapes of the network can be detri-

mental to connectivity based localization. It is difficult and remains as an open problem,

especially for large scale networks with median and low node densities.

2.2.3 Localization Events

An emerging category of range-free localization methods makes use of localization events

that are generated and propagate across the area where sensor networks are deployed [191,

192, 194, 195]. The major objective of those designs is to reduce the overhead at the resource

constrained sensor node side, by applying an asymmetric system design where senor nodes

only need to conduct simple operations of event detection and reporting.

As a pioneering event-driven design, the Lighthouse system [191] derives the distance

between a sensor node (equipped with optical detector) and the localization device (gener-

ates a parallel rotating optical beam) by measuring the time duration that the sensor node

dwells in the light beam. Suppose that the angular velocity of beam rotation is ω, and the

parallel light beam has a width of b, then the distance d between the target sensor node

and the beam generator can be estimated with

d =b

2sin(α/2)and α = ω · ∆t (2.33)

where ∆t is the interval at which the senor node continuously senses the existence of illumi-

nation. To extend from 2D to 3D, the event generator (base station) is proposed to generate

30

three mutually perpendicular parallel optical beams to locate all sensor nodes within the

range and line-of-sight (LOS) of the light beams in R3. The Lighthouse system demon-

strates around 10 cm accuracy in a 5 m × 5 m square space. However, it requires a complex

localization device with careful system calibration, especially in the 3D case.

Different from the Lighthouse system, where sensor nodes take the responsibility for

range measurements and localization computation, Spotlight [192] tries to remove all ex-

pensive and energy depletion functions for the localization from the sensor node side to an

external spotlight device. As shown in Fig. 2.8, the localization device generates some from

of localization events according to certain well defined “event function”, and then it receives

the detection report from the sensor nodes. According to the time-spacial relationship em-

bedded in the event function, the spotlight device is able to get the location information of

each node, which is then feedback to those nodes, so that every node in the network obtains

its location.

Event Detection

Function D(e)

Sensor Node i

Event Distribution

Function E(t)

Spotlight Device

Localization

Function L(T)

e(t)

T = {t1, t2, ...}

Pi(x, y, z)

Figure 2.8: The Asymmetric Architecture of the Spotlight System

The idea of asymmetric structure introduced and summarized by Spotlight[192] achieves

the goal of low cost at each node, which actually determines the whole cost of the net-

work [193]. The powerful computing capability and abundant energy supply of the Spotlight

device realize the configurable high accuracy of the localization. However, in the Spotlight

system, the event distribution needs to be both accurate as to time and precise about the

space, which adds system cost and results in slow localization speed. Precise event distribu-

tion is difficult to achieve without careful calibration, especially when the event-generating

devices require certain mechanical maneuver or the terrain is uneven.

LaserScan [194] functions in a similar way to the Spotlight system − an asymmetric

architecture that shifts most of the complexities and hardware requirements from each

node to a single powerful centralized device. In [194], laser-beam line scans are applied as

localization events. With synchronized scan operations conducted at multiple anchor devices

(e.g., identical scan angular speeds, predefined scan directions and starting phases), sensor

nodes’ detections about the time gaps between events from different anchors embed relative

31

angle information. With measured angles respect to anchors, localization estimation carries

out with traditional AOA computation [194]. LaserScan demonstrates a nice combination

of range-based methods (e.g., AOA, TDOA) and range-free methods (localization events),

however, it also requires precise event manipulation as that in the Spotlight system [192],

which would be very costly for outdoor large scale networks.

StarDust [195] proposed by Stoleru, et al works much faster than most of the other

event-driven localization systems. StarDust requires sensor nodes attached with cheap

corner cube retro-reflectors (CCR) as shown in Figure 2.9(a) and (b). CCR can reflect the

light back to its coming direction. A flashing light spot is generated to illuminate the area

with sensor nodes, which is shown Fig. 2.9(c), and simultaneously a picture of this area is

taken. By computer image processing, a result shown in Fig. 2.9(d) can be obtained. This

figure indicates that the locations of sensor nodes can be determined. StarDust employs

label relaxation algorithms to match light spots reflected from CCRs with nodes using

various kinds of constraints. Unfortunately, label relaxation algorithms converge only when

a sufficient number of robust constraints are obtained. In addition, due to the environmental

impact on the optical event and the RF connectivity constraints, StarDust is shown to be

less accurate than Spotlight [192].

Figure 2.9: The design of StarDust

Compared with ranging-based methods and other ranging-free designs, event-driven

localization provides an option of shifting system overhead out of low cost sensor nodes. As

an relatively new kind of method, event-driven sensor node localization is now attracting

more and more attention from the researchers, and considered as a promising solution

in many scenarios that require trade-offs among system cost, localization accuracy and

deployment flexibility.

32

2.2.4 Remarks on Range-free Localization

To summarize, Table 2.2 lists pros and cons of different types of range-free localization

methods. From this table, we can observe that range-free methods depend only on simple

sensing at low-cost sensor nodes, e.g., radio connectivity and localization events. Therefore,

range-free localization can achieve reduced overall system cost.

Table 2.2: Summary of Range-free Localization in WSN

Range-free Methods Pros Cons

Anchor Proximity

low-cost sensor nodes, low

communication and computa-

tion overhead

low accuracy, short effective

range, more anchors for larger

networks

Connectivity

Centralized

low-cost sensor nodes, a small

number of anchors, improved

accuracy than the distributed

methods in regular networks,

scalable for large networks

relatively low accuracy, com-

munication overhead, extra

processing center, sensitive to

anisotropic topology, not suit-

able for sparse networks

Distributed

low-cost sensor nodes, scalable

for large networks, reduced

computation than the central-

ized methods, more robust to

anisotropic topology

lower accuracy than central-

ized methods in regular net-

works, communication cost,

may need more anchors, not

suitable for sparse networks

Localization Events

low-cost sensor nodes, trade-off

between accuracy and cost, low

communication and computa-

tion overhead at target nodes

expensive localization device,

in-field device calibration, pre-

cise event manipulation, envi-

ronment sensitive

Generally speaking, range-free localization based on anchor proximity features extremely

low overhead for communication and computation, however, it suffers from low accuracy,

and a growing number of anchors for improved accuracy performance or for a larger sys-

tem. Connectivity based methods provide good scalability, but incur more communication

and computation. In addition, they face the difficulty of anisotropic network topology.

Event-driven localization, as an emerging research direction, can achieve a nice balance

between low-cost sensor nodes and high localization accuracy. Nevertheless, methods ap-

plying localization events mostly require rigid and precise control over event generation and

distribution, which could be very costly and difficult in practical outdoor scenarios.

From all the above analysis, we conclude that (i) range-free localization can provide

localization service for low-cost sensor nodes without ranging capability; (ii) however, it is

lack of accuracy, or requires a large number of anchors, extra efforts for topology recognition,

and expensive localization device with precise event manipulation.

33

Chapter 3

Uncontrolled Event-driven

Localization

3.1 Chapter Introduction

Traditional event-driven sensor node localization (e.g., Spotlight [192] and Lighthouse [191])

demonstrated that long range and highly accurate localization can be achieved simultane-

ously with little additional cost at sensor nodes. These benefits, however, come along with

an implicit assumption that localization events can be precisely generated and distributed

to a specified location at a specific time instance. In practice, accurate event control is

difficult to achieve, especially in outdoor scenarios when the terrain is uneven, or the event

distribution device is not well calibrated and its position is difficult to maintain (e.g., the

helicopter-mounted case in [192]). We consider those methods as the first generation of

event-driven localization based on precisely-controlled events.

In this chapter, we release this key precondition of range-free event-driven localization

by evolving from using precisely-controlled events, through semi-controlled events (i.e., MSP

introduced in Section 3.2), and finally to uncontrolled events (i.e., LUE introduced in Sec-

tion 3.3), making the event-driven localization advance substantially towards a practical

system with reduced overhead, convenient deployment, and improved localization accuracy.

3.2 MSP: Multi-sequence Positioning

To address the limitation of precise contral in current envent-driven localization, in this

section we present a multi-sequence positioning (MSP) method for large-scale stationary

sensor node localization in deployments where an event source has line-of-sight to all sen-

sors. The novel idea behind MSP is to estimate each sensor node’s two-dimensional loca-

tion by processing multiple easy-to-get one-dimensional node sequences obtained through

loosely-guided event distribution. This design offers several benefits. First, compared to

34

a range-based approach, MSP does not require additional costly hardware. It works us-

ing sensors typically used by WSN applications such as light and acoustic sensors which

we specifically consider in this work. Second, compared to a range-free approach, MSP

needs only a small number of anchors (theoretically as few as two), so high accuracy can

be achieved economically by introducing more events instead of more anchors. And third,

compared to Spotlight [192], MSP does not require precise and sophisticated event distri-

bution, an advantage that significantly simplifies the system design and reduces calibration

cost. Besides these high-level advantages of MSP, the intellectual contributions of this work

include the following:

• We are the first to localize sensor nodes using Multi-Sequence Processing. Each se-

quence is an ordered list of sensor nodes, sorted by the detection time of a dissem-

inated event. We demonstrate that making full use of the information embedded in

one-dimensional node sequences can significantly improve localization accuracy. In-

terestingly, we discover that (i) in addition to anchor nodes that are traditionally used

for localization, normal target nodes can also contribute to the positioning task; (ii)

repeated reprocessing of one-dimensional node sequences can further enhance local-

ization accuracy.

• We propose a distribution-based location estimation strategy that obtains the final

location of sensor nodes using marginal probability of joint distribution among adja-

cent nodes within a sequence. This new algorithm outperforms the widely adopted

Centroid method [158, 162].

• To the best of our knowledge, this is the first work to improve the localization accuracy

by introducing adaptive events. The generation of later events is guided by localization

results from early events.

• We evaluate line-based MSP on our indoor Mirage test-bed that can support as many

as 360 nodes working simultaneously, and wave-based MSP in outdoor environments.

Through system implementation, we discover and address several interesting issues

such as partial sequence and sequence flips. To reveal the performance of MSP at

scale, we also provide analytic results as well as extensive simulation study.

The rest of this section is organized as follows. Section 3.2.1 presents an overview of

the MSP localization system. In Section 3.2.2 and Section 3.2.3, the basic MSP and four

advanced processing methods are introduced, respectively. Section 3.2.4 analyzes the cost

of MSP computation. Then, Section 3.2.5 describes how MSP can be applied in a wave

propagation scenario. Section 3.2.6 discusses several issues in practical systems using MSP.

Section 3.2.7 presents simulation results, and Section 3.2.8 reports implementation and

evaluation of MSP on the Mirage test-bed and an outdoor test-bed. Finally, Section 3.2.9

summarizes the design of MSP.

35

3.2.1 System Overview

MSP works by extracting relative location information from multiple simple one-dimensional

orderings of nodes. Fig. 4.34(a) shows the layout of a sensor network with anchor nodes

and target nodes. Target nodes are defined as nodes to be localized. Briefly, the MSP

system works as follows. First, events are generated one at a time in the network area

(e.g., ultrasound propagations from different locations, laser scans with diverse angles). As

each event propagates, as shown in Fig. 4.34(a), nodes detect the event sequentially at

different time instances. For a single event, we call the ordering of nodes based on their

sequential event detections a node sequence. Each node sequence includes both target nodes

and anchor nodes as shown in Fig. 4.34(b). Second, a multi-sequence processing algorithm

helps to narrow the possible location of each node to a small area depicted in Fig. 4.34(c).

Finally, a distribution-based estimation method estimates the exact location of each sensor

node, as shown in Fig. 4.34(d).

1

A

B2

34

5

1A 5 3 B2 4

1

2

3

5

4

(b)

(c)(d)

(a)

Anchor node Target node

Event 1

Event 2

Event 3

Event 4Node sequence from event 1

Node sequence from event 2

1 A2 5A 43

1A25B4 3

1 A2 5B 4 3

Node sequence from event 3

Node sequence from event 4

Figure 3.1: The MSP System Overview

From above, we can see that node sequences can be obtained more economically than

accurate pairwise distance measurements in traditional range-based approaches. In addi-

tion, this system does not require a rigid time-space relationship during localization event

distribution, which is critical but hard to achieve in state-of-the-art event driven solutions

(e.g., Spotlight [192] and LaserScan [194]).

In fact, using node sequence instead of absolute sensing results owns several extra ben-

efits: (i) node ordering in a sequence features better robustness to sensing noise; (ii) node

sequence recording the timing relationship among detections at different nodes significantly

alleviates the requirement of network-level time synchronization (detailed in Section 3.2.6);

(iii) node sequence is more resistant to irregular event propagation velocity. For exam-

ple, in some situations, the time interval between two nodes’ event detections may not be

36

monotonic with the distance between them, which violates the assumptions made in some

works [199], while node ordering in this case remains correct. In the following, for the sake

of clarity, we present the system design in two cases:

• Ideal Case, in which all the node sequences obtained from the network are complete

and correct, and nodes are time-synchronized [117].

• Non-Ideal Case, in which, (i) node sequences can be partial (incomplete), (ii) the

elements in the sequences could flip (i.e. the order obtained is reversed from reality),

and (iii) nodes are not time synchronized.

In the following, to introduce the MSP algorithm, we first consider a simple straight-line

scan scenario. Then, we describe how to implement straight-line scans as well as other types

of event, such as sound wave propagation.

3.2.2 Basic MSP

The top-level idea of basic MSP is to split the whole area where nodes deployed into small

pieces by processing node sequences. Given knowledge of anchors and localization events, a

target node’s rankings in node sequences can determine where it is possibly located. Fig. 3.2

gives an example showing the concepts in basic MSP.

1

A

2

3

4

5

B

C

6

7

8

9

Straight-line Scan 1

Straight-line Scan 2

Target node

Anchor node

Node Sequence Obtained From Scan 1: 8 1 5 A 6 C 4 3 7 2 B 9

Node Sequence Obtained From Scan 2: 3 1 C 5 9 2 A 4 6 B 7 8

Figure 3.2: Obtaining Multiple Node Sequences

In Fig. 3.2, we use numbered circles to denote target nodes and numbered hexagons to

denote anchor nodes. Suppose that two straight lines scan the area from different directions

one by one, treating each scan as an event. All the nodes react to the event and generates

two node sequences: for vertical scan 1, the node sequence is (8, 1, 5, A, 6, C, 4, 3, 7, 2,

B, 9); for horizontal scan 2, the node sequence is (3, 1, C, 5, 9, 2, A, 4, 6, B, 7, 8), as

shown in the figure. Given locations of anchors and the scan angles, the whole area can be

37

vertically and horizontally divided into totally 16 parts. And the rankings of a target node

in both sequences actually indicate which small part this node is located. For example, in

the node sequence from event 1, node 8 ranks in front of anchor A, meaning that it detected

the vertical scan event earlier than anchor A did. This indicates that node 8 locates above

node A in the map. Similarly, from the node sequence for scan 2, node 8 detected scan 2

later than anchor B did, meaning that node 8 should be on the right of anchor B. Combine

above, node 8 can be localized to be in the top-right rectangle in Fig. 3.2.

To extend this process, suppose that we have M anchor nodes and perform d times

of scan from different angles, obtaining d node sequences and dividing the area into many

small parts. Obviously, the number of parts is a function of the number of anchors M ,

the number of scans d, anchors’ locations and the slope k of each scan. According to the

pie-cutting theorem [200], an area can be divided into O(M2 ·d2) parts. When M and d are

appropriately large, the polygon for each node could be sufficiently small and as a result

accurate localization can be achieved. We emphasize that the accuracy is affected not only

by the number of anchors M , but also by the number of events d. In other words, MSP

provides a tradeoff between the physical cost of anchors and the soft cost of events.

Algorithm 1: Basic MSP Process

input : Node sequences from eventsoutput: Estimated location of each node

repeat1

GetOneUnprocessedSequence() ;2

repeat3

GetOneNodeFromSequenceInOrder() ;4

GetBoundaries() ;5

UpdateMap() ;6

until all target nodes are updated ;7

until all node sequences are processed ;8

repeat9

GetOneUnestimatedNode() ;10

CentroidEstimation() ;11

until all target nodes are estimated ;12

Algorithm 1 gives the processing flow of basic MSP. Each node sequence is processed

within line 1 to 8. For each node, GetBoundaries() in line 5 searches for the predecessor and

successor anchors in the sequence so as to determine the boundaries of this node’s location

area. Then UpdateMap() at line 6 shrinks the location area of this node according to newly

obtained boundaries. After processing all sequences, Centroid estimation (line 11) set the

center of gravity of the final polygon as the estimated location of a sensor node.

Basic MSP only makes use of the order information between a target node and anchors

in each sequence. In fact, we can extract much more information from node sequence.

38

Section 3.2.3 introduces the design of advanced MSP including four novel optimizations

that significantly improve localization performance.

3.2.3 Advanced MSP

Four improvements to basic MSP are proposed in this section: (i) sequence-based MSP, (ii)

iterative MSP, (iii) DBE MSP, and (iv) adaptive MSP. The first three improvements do not

need additional sensing and communication in the networks but require only slightly more

off-line computation. The objective of all these improvements is to make full use of the

information embedded in the node sequences. The results we have obtained empirically in-

dicate that the implementation of the first two methods can dramatically reduce localization

error, and that the third and fourth methods are helpful for some system deployments.

3.2.3.1 Sequence-based MSP

We note that in the basic MSP design, only anchor nodes are used to narrow down the

polygon (location area) of each target node, although there is more information in the node

sequence that can be utilized.

1

2

1 2

1

2

Lower boundary of 1 Upper boundary of 1

Lower boundary of 2 Upper boundary of 2New sequence

New upper boundary of 1

New Lower boundary of 2

Event Propagation

Figure 3.3: Elimination Rule in Sequence-based MSP

Let’s first look at a simple example shown in Fig. 3.3. Suppose that previous scans

narrow the locations of target node 1 and node 2 to two dashed rectangles as shown in

the left part of the figure. Then a new scan obtains an additional sequence (1, 2). With

knowledge of the scan direction, it is easy to tell that node 1 is located to the left of node

2. Thus, we can further narrow the location area of node 2 by eliminating the shadowed

part in node 2’s rectangle. This is because node 2 is located on the right of node 1 while

the shadowed area is out of the left boundary of node 1. Similarly, the location area of

node 1 can be narrowed by eliminating the shadowed part to the right of node 2’s right

boundary. We call this processing progress sequence-based MSP meaning that the whole

node sequence needs to be processed node by node in order. Specifically, sequence-based

MSP follows the following processing rule:

Elimination Rule: along a scan direction, the lower boundary of the successor’s area shall

be equal or larger than the lower boundary of predecessor’s area, and the upper boundary of

predecessor’s area shall be equal or smaller than the upper boundary of successor’s area.

39

In the case of Fig. 3.3 for example, along the scan direction, node 2 is the successor of

node 1 and node 1 is the predecessor of node 2. According to the elimination rule, node

2’s lower boundary (i.e., the left boundary in this specific example) cannot be smaller than

node 1’s lower boundary and node 1’s upper boundary (i.e., the right boundary in this

example) cannot exceed node 2’s upper boundary.

Algorithm 2 gives the pseudo code of the sequence-based MSP. Each node sequence is

processed within line 3 and 12 with two steps:

Step 1 (line 3 to 7): compute the lower boundary of each target node by increasing order

in the node sequence. Each node’s lower boundary is determined by the lower boundary of

its predecessor node in the sequence. Thus the processing must start from the first node

in the sequence and by increasing order. Then update the map according to the newly

obtained lower boundary.

Step 2 (line 8 to 12): compute the upper boundary of each target node by decreasing

order in the node sequence. Each node’s upper boundary is determined by the upper

boundary of its successor node in the sequence. Thus the processing must start from the

last node in the sequence and by decreasing order. Then update the map according to the

newly obtained upper boundary.

After processing all node sequences, for each target node, a polygon bounding its pos-

sible location area has been found. Then, center-of-gravity-based estimation is applied to

compute the exact location of each node (line 14 to 17).

Algorithm 2: Sequence-based MSP Process

input : Node sequences from eventsoutput: Estimated location of each node

repeat1

GetOneUnprocessedSequence() ;2

repeat3

GetOneNodeByIncreasingOrder() ;4

ComputeLowbound() ;5

UpdateMap() ;6

until all target nodes are updated ;7

repeat8

GetOneNodeByDecreasingOrder() ;9

ComputeUpbound() ;10

UpdateMap() ;11

until all target nodes are updated ;12

until all node sequences are processed ;13

repeat14

GetOneUnestimatedNode() ;15

CentroidEstimation() ;16

until all target nodes are estimated ;17

40

1

A

2

3

4

5

B

C

6

7

8

9

Straight-line Scan 1

Straight-line Scan 2

Straight-line Scan 3

Target node

Anchor node

Node 3's area cut by

node 6's boundary

Node 4 and node 7's

areas cut by node 2's

boundary

Node 2's area cut by

node 7's boundary

Node Sequence Obtained From Scan 3: B 9 2 7 4 6 3 8 C A 5 1

Figure 3.4: Sequence-based MSP Example

An example of this process is shown in Fig. 3.4, a third scan generates node sequence

(B, 9, 2, 7, 4, 6, 3, 8, C, A, 5, 1). In addition to the anchor split lines, because nodes 4 and

7 is ranked after node 2 in the sequence, polygons of node 4 and node 7 can be narrowed

according to the lower boundary of node 2 (the lower right-shaded area); similarly, the

shaded area in node 2’s rectangle could be eliminated since this part is beyond node 7’s

upper boundary. Similar eliminating can be performed for node 3 as shown in the figure.

From above, we can see that sequence-based MSP makes use of the information embed-

ded in every sequential node pair in the node sequence. The polygon boundaries of target

nodes obtained in prior could be used to further split other target nodes’ areas. Our evalu-

ation in Sections 3.2.7 and Section 3.2.8 shows that sequence-based MSP can considerably

enhances system accuracy.

3.2.3.2 Iterative MSP

Sequence-based MSP is preferable to basic MSP because it extracts more information from

the node sequence. Actually, additional information is still available! In sequence-based

MSP, a sequence processed later benefits from information produced by previously processed

sequences. However, the first several sequences can hardly benefit from other scans in this

way. Inspired by this phenomenon, we propose iterative MSP. The basic idea of iterative

MSP is to process all the sequences iteratively several times so that the processing of each

single sequence can benefit from the results of other sequences.

To illustrate the idea more clearly, Fig. 3.4 shows the results of three scans that have

provided three sequences. Now if we process the sequence (8, 1, 5, A, 6, C, 4, 3, 7, 2, B,

9) obtained from scan 1 again, we can get new information as depicted in Fig. 3.5. The

41

1

A

2

34

5

B

C6

7

8

9

Straight-line Scan 1

Straight-line Scan 2

Straight-line Scan 3

Virtually Perform Scan 1 Again

Target node

Anchor node

Node 3's area cut by

node 7's boundary

Node 4 area cut by

node 7's boundary

Reprocess Sequence From Scan 1: 8 1 5 A 6 C 4 3 7 2 B 9

Figure 3.5: Iterative MSP: Reprocessing the Node Sequence from Scan 1

reprocessing of node sequence 1 provides information in the way an additional vertical scan

would. From the sequence-based MSP, we know that the bottom boundaries of node 3 and 4

along the scan direction must not beyond the bottom boundary of node 7, and therefore we

can eliminate the grid part of node 3 and node 4 as shown in Fig. 3.5. From this example,

we can see that iterative processing of sequences could help further shrink the polygon of

target nodes, and thus enhance localization accuracy.

The implementation of iterative MSP is straightforward: process all the sequences mul-

tiple times with sequence-based MSP. Like sequence-based MSP, iterative MSP introduces

no additional event cost. In other words, reprocessing does not actually repeat the scan

physically. Evaluation results in Section 3.2.7 will show that iterative MSP contributes no-

ticeably to a lower localization error. Further empirical results show that after 5 iterations,

improvements become less significant. In summary, iterative processing can achieve better

performance with only a little computation overhead.

3.2.3.3 Distribution-based Estimation (DBE MSP)

After determining the location area polygon for each node, estimation is needed for a final

decision. Previous research mostly applied the Center of Gravity (COG) method [158, 162,

52] which minimizes average error. If every node is independent with each other, COG is

statistically the optimal solution. In MSP, however, each node may not be independent.

For example, two neighboring nodes in a sequence could have overlapping polygon areas.

In this case, if the marginal probability of joint distribution is used for estimation, better

statistic results can be achieved. Fig. 3.6 shows an example in which node 1 and node 2 are

located in the same polygon. If COG is used, both nodes are localized at the same position

42

(a) Center of Gravity (b) Joint Distribution

1 2

2

1 1

2

1

2 2

1

1 2

2

1 1

2

Figure 3.6: An Example of Joint Distribution Estimation

…...

vmap[0]

vmap[1]

vmap[2]

vmap[3]

Combine

map

Figure 3.7: The Idea of DBE MSP for Each Node

(as shown in Fig. 3.6(a)). However, the node sequences obtained from two scans indicate

that node 1 should be to the left and above node 2 (as shown in Fig. 3.6(b)).

The high-level idea of distribution-based estimation proposed for MSP, which we call

DBE MSP, is illustrated in Fig. 3.7. The distributions of each node under the i th scan (for

the i th node sequence) is estimated in node.vmap[i ] that is a data structure for remembering

the marginal distribution over scan i. Then all the vmaps are combined to get a single map

and weighted estimation is used to obtain the final location.

Pre node’s area

Predecessor node exists:

conditional distribution based on

predecessor node’s area

Alone: Uniformly Distributed

Suc node’s area

Successor node exists:

conditional distribution based

on successor node’s area

Suc node’s area

Both predecessor and successor

nodes exist: conditional

distribution based on both of them

Pre node’s area

Figure 3.8: Four Cases for Each Node in the DBE Process

For each scan, all the nodes are sorted according to their gap, which is defined as

the diameter of the location area polygon along the direction of the scan, to produce a

second gap-based node sequence. Then, final location estimation starts from the node with

43

the smallest gap. This is because it is statistically more accurate to assume a uniform

distribution of the node with smaller gap. For each node processed in order from the

gap-based node sequence, there are four cases as illustrated and interpreted in Fig. 3.8).

Specifically, either if no neighbor node in the original event-based node sequence shares an

overlapping area, or if neighbors have not been processed yet due to bigger gaps, a uniform

distribution is applied to this isolated node (the Alone case in Fig. 3.8). If the distribution of

its neighbors with over-lapped areas has been processed, we calculate the joint distribution

for the node as the other three possible cases, depending on whether the distribution of the

overlapping predecessor and/or successor nodes have/has already been estimated. In the

figure, the darkness of each position point in the location area depicts the probability of the

sensor node’s being at the corresponding position.

The estimation’s strategy of starting from the most accurate node (with smallest gap)

reduces the problem of estimation error propagation. The results in the evaluation section

indicate that applying distribution-based estimation gives statistically better results than

the traditional COG method.

3.2.3.4 Adaptive MSP

So far, all the enhancements to basic MSP focus on improving the multi-sequence processing

algorithm given a fixed set of scan directions. All these enhancements require only more

computing time without any overhead at sensor nodes. In fact, it is also possible to optimize

how events are generated. For example, in military situations, artillery or rocket-launched

mini ultrasound bombs can be used for event generation at some selected locations. In

adaptive MSP, we carefully generate each new localization event so as to maximize the con-

tribution of a new event to the refinement of localization, based on feedback from previous

events. Fig. 3.9 depicts the basic architecture of adaptive MSP. Through previous localiza-

tion events, the whole map has been partitioned into many small location areas. The idea

of adaptive MSP is to generate the next localization event to achieve best effort elimination

that ideally could shrink the location area of individual node as much as possible.

Map Partitioned by Previous

Localization Events

Diameter of

Each Area

Trigger Next

Localization Evet

Candidate

Localization Events

Evaluation

Figure 3.9: Basic Architecture of Adaptive MSP

We use a weighted voting mechanism to evaluate candidate localization events. Every

44

2

3

Diameter D3

1

1

3k

2

3k

3

3k

4

3k

5

3k6

3k

1

3k2

3k3

3k6

3k4

3k5

3k

Weight

el

smalli

opt

i

j

ii

j

iS

SDkkDfkWeight

arg

),(,()( ⋅=∆=

1

3

optk

Target node

Anchor node

Gravity Center

Node 3's area

Figure 3.10: Adaptive MSP: Candidate Slops for Node 3 at Anchor 1

node wants the next event to split its area evenly that would shrink the area fast. Therefore,

every node votes for the parameters of the next event (e.g., the scan angle k of the straight-

line scan event). Since the area map is maintained centrally, the vote can be done virtually

without real nodes’ participation. After gathering all the voting results, event parameters

with the most votes win the election. There are two factors that determine the weight of

each vote:

• The vote for each candidate event is weighted according to the diameter D of the voter

node’s location area. Nodes with larger location areas speak louder in the voting, since

overall system error is reduced mostly by splitting larger areas.

• The vote for each candidate event is also weighted according to their elimination

efficiency for a location area, which is defined as how equally in size (or in diameter)

an event can cut an area. In other words, an optimal scan event cuts an area evenly

in size, since this cut shrinks the area quickly and thus effectively reduces localization

uncertainty.

Combining the above, the weight for each voting is computed as follows:

Weight(kji ) = f(Di,△(kj

i , kopti )) (3.1)

where kji is node i’s j th supporting parameter for next event generation; Di is the diameter

of node i’s location area; △(kji , k

opti ) is the distance between kj

i and the optimal parameter

kopti for node i. Note that △(kj

i , kopti ) should be defined to fit specific applications.

Fig. 3.10 presents an example for node 3’s voting for the slops of the next straight-

line scan. In the system, there are a fixed number of candidate slopes for each scan (e.g.,

k1, k2, k3, k4 · · · ). The location area of target node 3 is shown in the figure. Candidates

events k13 , k

23 , k

33 , k

43 , k

53 , k

63 are evaluated according to their effectiveness for area cutting

comparing with the optimal event kopt3 shown as a dotted line. For this specific example, as

45

is illustrated in the right part of Fig. 3.10, f(Di,△(kji , k

opti )) is defined as

Weight(kji ) = f(Di,△(kj

i , kopti )) = Di ·

Ssmall

Slarge(3.2)

where Ssmall and Slarge are the sizes of the smaller part and larger part of the area cut by

a candidate line, respectively. In this case, node 3 votes 0 for candidate lines that do not

across its location area, because Ssmall = 0.

We show later that adaptive MSP improves localization accuracy in WSNs with irreg-

ularly shaped deployment areas.

3.2.4 Overhead and Complexity Analysis

This section provides a complexity analysis of the MSP design. We emphasize that MSP

adopts an asymmetric design in which sensor nodes only need to detect and report the

events. They are blissfully oblivious to the processing methods proposed in previous sec-

tions. About the total time needed for localization, one major factor may relate to the speed

of event dissemination in the network, which essentially is dependent on specific applica-

tions. In terms of communication cost, the slim footprint of node sequence allow it to be

efficiently piggybacked on normal traffic in the network. And considering that localization

usually is only a one time job, we did not expand more along this direction. Instead, in this

subsection, we analyze the computational complexity of the MSP algoirthms.

According to Algorithm 1, the computing complexity of basic MSP is O(d · N · S); the

memory space required is O(N · S), where d is the number of events, N is the number of

target nodes and S is the area size. In Algorithm 2, the computing complexity of sequence-

based MSP and iterative MSP can be expressed as O(c · d ·N · S) where c is the number of

iterations and c = 1 for sequence-based MSP; the memory space required is O(N ·S). Both

the computing complexity and the memory cost are equal to or within a constant factor of

basic MSP.

The computation complexity of distribution-based estimation (DBE MSP) is higher.

The major overhead comes from joint distribution computation when both predecessor and

successor nodes exist. In order to calculate the marginal probability, MSP needs to enumer-

ate all possible locations of the predecessor node and the successor node. For example, node

A has predecessor node B and successor node C, then the marginal probability PA(x, y) of

node A’s being at location (x, y) is:

PA(x, y) =∑

i

∑

j

∑

m

∑

n

(1

NB,A,C· PB(i, j) · PC(m,n)

)(3.3)

where NB,A,C is the number of valid locations for node A satisfying the sequence (B, A, C)

when B is at (i, j) and C is at (m,n); PB(i, j) is the available probability of node B’s being

46

located at (i, j); PC(m,n) is the available probability of node C’s being located at (m,n).

A naive algorithm to compute equation (3.3) has a complexity of O(d · N · S3). However,

since the marginal probability indeed comes from only one dimension along the scanning

direction (e.g., a line), the complexity can be reduced to O(d · N · S1.5) after algorithm

optimization. In addition, final location areas for sensor nodes are usually much smaller

than the original field with size S, therefore, in practice, DBE MSP can be computed much

faster than O(d · N · S1.5).

3.2.5 Wave Propagation Example

So far, the description of MSP has been solely in the context of straight-line scan events.

However, we note that MSP is conceptually independent of how the event is propagated as

long as node sequences can be obtained. Clearly, we can also support wave-propagation-

based events (e.g. ultrasound propagation, air blast propagation), which are polar coordi-

nate equivalences of the straight-line scan in the Cartesian coordinate system. This section

illustrates the implementation of MSP in the wave propagation-based situation. For easy

modeling, we have made the following assumptions:

• The wave propagates uniformly in all directions, therefore the propagation has a

circular frontier. Since MSP does not rely on an accurate space-time relationship, a

certain distortion in wave propagation is tolerable. If any directional wave is used,

the propagation frontier can be modified accordingly.

• Under the situation of line-of-sight, we allow obstacles to reflect or deflect the wave.

Reflection and deflection are not problems because each node reacts only to the first

detected event. Those reflected or deflected waves come later than the line-of-sight

waves. The only thing the system needs to maintain is an appropriate time interval

between two successive localization events.

• We assume that background noise exists, and therefore we run a band-pass filter to

listen to a particular wave frequency. This reduces the chances of false detection.

The parameter that affects localization event generation here is the source location of

the event. The distance between a node and the event source determines its rank in the

node sequence. Using the node sequences, the MSP algorithm divides the whole area into

many non-rectangle areas as shown in Fig. 3.11. In this figure, stars represent the source

locations of two events triggered. Previous event propagations split the whole map into

many of areas by those dashed circles that pass one of the anchors. Each node is located

in one of the small areas. Since sequence-based MSP, iterative MSP and DBE MSP make

no assumption about the type of location events and the shape of location area, all three

optimization algorithms can be applied for the wave propagation scenario.

47

Figure 3.11: Example of the Wave Propagation Situation

However, adaptive MSP needs more explanation. Fig. 3.11 shows an example of nodes’

voting for next event source location. Unlike the straight-line scan, the critical parameter

in this situation is the location of the event source, because the distance between each node

and the event source determines the rank of the node in the sequence. In Fig. 3.11, if the

next event breaks out along or close to the solid thick gray line that perpendicularly bisects

the solid dark line between anchor C and the center of node 9’s area (the gray area), the

wave would reach anchor C and the center of gravity of node 9’s area at roughly the same

time, which would lead to a relatively equal division of node 9’s area. Thus, node 9 prefers

to vote for the positions around the thick gray line. Note that there are totally three such

gray lines for node 9 and each of them corresponding to one anchor in field. For clarity, we

did not draw all three lines in the figure.

3.2.6 Practical Deployment Issues

For the sake of clarity, until now we have described MSP in an ideal case where complete

node sequences can be obtained with accurate time synchronization. In this section we

describe how to make MSP work well under more realistic conditions.

3.2.6.1 Incomplete Node Sequence

For diverse reasons, such as sensor malfunction or natural obstacles, nodes in the network

could fail to detect the localization events. In such cases, node sequences will not be

complete but partial. This problem has two versions:

• Anchor nodes are missing from a sequence. If some anchor nodes fail to respond to

localization events, then the system has fewer anchors. In this case, the solution is to

generate more events to compensate for the loss of anchors for desired accuracy.

48

• Target nodes are missing from a sequence. There are two consequences when target

nodes are missing. First, if these nodes are still be useful to sensing applications, they

need to use other backup localization approaches (e.g., Centroid [158]) to localize

themselves with help from their neighbors who have already learned their locations

from MSP. Secondly, since in advanced MSP each node in the sequence may contribute

to the overall system accuracy, dropping target nodes from sequences could also reduce

localization accuracy. Thus, proper compensation procedures such as adding more

localization events need to be launched.

3.2.6.2 Localization without Time Synchronization

In a sensor network without time synchronization support, nodes cannot be ordered into

a sequence using timestamps. For such cases, we can either apply the “post-facto” timing

strategy [201] or follow a listen-detect-assemble-report protocol proposed in the following

that is able to function independently without time synchronization.

Figure 3.12: Node Sequence without Time Synchronization

listen-detect-assemble-report requires that every node listen to the channel for the node

sequence transmitted from its neighbors. Then when a node detects a localization event,

it assembles itself into the newest node sequence it has heard and reports the updated

sequence to other nodes. Fig. 3.12 (a) illustrates an example of the listen-detect-assemble-

report protocol. For simplicity, in this figure, we did not differentiate target nodes from

anchor nodes. A solid line between two nodes stands for a communication link. Suppose

that a straight line scans from left to right. Node 1 detects the event and it broadcasts

a sequence (1) into the network. Node 2 and node 3 receive this sequence. When node 2

detects the event, node 2 adds itself into the sequence and broadcast (1, 2). The sequence

49

propagates in the same direction as the scan, shown in Fig. 3.12 (a). Finally, node 6 obtains

a complete sequence (1, 2, 3, 5, 7, 4, 6).

In the case of ultrasound propagation, because the event propagation speed is much

slower than that of radio, the listen-detect-assemble-report protocol can work well in a

situation where node density is not high. For instance, if the distance between two nodes

along one direction is 10 meters, the 340m/s sound needs 29.4ms to propagate between

them. While the normally the communication data rate is 250Kbps in the WSN (e.g.,

CC2420 [203]), it takes only about 2 ∼ 3 ms to transmit an assembled packet.

One problem that may occur with the listen-detect-assemble-report protocol is multiple

partial sequences as shown in Fig. 3.12 (b). Two separate paths in the network may result

in two sequences that could not be further combined. In this case, two sequences can only

be processed separately for one event. As a result some ordering information is lost and

localization performance could decrease.

The other problem is the sequence flip issue. As shown in Fig. 3.12 (c), because node 2

and node 3 are too close to each other along the scan direction, they detect the scan almost

simultaneously. Due to the uncertainty in media access delay, two messages could transmit

out of order. For example, if node 3 sends out its report message first, then the order of

node 2 and node 3 gets flipped in the final node sequence. In fact, sequence flip could show

up even in an accurately synchronized system due to random jitter in node detection and

processing delay, when an event arrives at multiple nodes almost simultaneously. A method

addressing the sequence flip problem is presented in the following.

3.2.6.3 Sequence Flip and Protection Band

The problem of sequence flip can be solved with and without time synchronization. We start

with a scenario where time synchronization is available. Existing solutions for time synchro-

nization [117, 202] can easily achieve sub-millisecond accuracy. For example, FTSP [117]

achieves 16.9 µs (microsecond) average error for a two-node single-hop case. Therefore, we

can comfortably assume that the network is synchronized with a maximum error of 1 ms

(millisecond) among nodes. However, when multiple nodes are located close to each other

along the event propagation direction, even when accurate time synchronization is achieved

in the network, sequence flip may still occur. For example, in the wave propagation case, if

two nodes are less than 0.34 meters apart, the time interval between their detections would

be less than 1 ms.

We find that sequence flip could not only damage system accuracy, but also might cause

a fatal error in the MSP algorithm. Fig. 3.13 illustrates both detrimental results. In the left

side of Fig. 3.13, suppose that node 1 and node 2 are so close to each other that it costs less

than 0.5 ms for the localization event to propagate from node 1 to node 2. Unfortunately,

node sequence is mistaken to be (2, 1). So node 1 is expected to be located to the left

of node 2 such as at the position of the dashed node 1. According to the eliminating rule

50

1

2

12

2

Lower boundary of 1 Upper boundary of 1

Flipped Sequence Fatal Elimination Error

Event Propagation

1 1

Fatal Error

1

Figure 3.13: The Problem of Sequence Flip

in sequence-based MSP, the left part of node 1’s location area is cut off as shown in the

right part of Fig. 3.13. This is a potentially fatal error, because the real position of node

1 has been eliminated by mistake. During the subsequent eliminations introduced by other

events, node 1’s area might be cut off completely, and as a result node 1 could consequently

be erased from the map! Even in cases where node 1 still survives, its location area actually

does not cover its true position. Another problem is not fatal but lowers the localization

accuracy. If we get the right node sequence (1, 2), node 1 has a new upper boundary which

can narrow the area of node 1. However, due to the sequence flip, node 1 loses this new

upper boundary.

In order to address the sequence flip problem, especially to prevent nodes from being

erased from the map, we propose a protection band compensation approach. The basic idea

of protection band is to extend the boundary of the location area a little bit so as to make

sure that the node will never be erased from the map. This solution is based on the fact that

nodes have a high probability of flipping in the sequence if they are near to each other along

the event propagation direction. If two nodes are apart from each other more than some

distance, saying B, they rarely flip unless nodes are faulty. The width of a protection band

B is largely determined by the maximum time synchronization error and the propagation

speed of localization events.

1

2

12

2

Lower boundary of 1 Upper boundary of 1

Flipped Sequence Safe Elimination

Even

t Pro

pag

atio

n

1 1

New lower boundary of 1

1

B

B: Protection band

Figure 3.14: The Application of Protection Band

Fig. 3.14 presents the application of the protection band. In stead of eliminating the

dashed part in Fig. 3.13 for node 1, the new lower boundary of node 1 is set by shifting the

original lower boundary of node 2 to the left by a distance of B. In this case, node 1 is still

in its location area and protected from being erased. In a practical implementation, suppose

that ultrasound localization events are used. If the maximum error of time synchronization

is 1 ms, two nodes might get flipped if the time interval between their detections is smaller

51

or equal to 1 ms. Accordingly, we set the protection band B as 0.34 m (the distance sound

can propagate within 1 ms). By adding the protection band, we reduce the chances of fatal

errors, although at the cost of localization accuracy. Empirical results obtained from our

physical test-bed verified this conclusion.

In the case of applying the listen-detect-assemble-report protocol, the only change is to

select the protection band according to the maximum delay uncertainty introduced by the

MAC operation and the event propagation speed. To bound MAC delay at the node side,

a node can drop its report message if it experiences excessive MAC delay. This converts

the sequence flip problem to the incomplete sequence problem that can be addressed by

methods proposed in Section 3.2.6.1.

3.2.7 Simulation Evaluation

Our evaluation of MSP was conducted on three platforms: (i) an indoor MSP system with

46 MICAz motes using straight-line scan, (ii) an outdoor MSP system with 20 MICAz motes

using sound wave propagation, and (iii) an extensive simulation under various settings. In

order to understand the behavior of MSP under numerous situations, we start our evaluation

with simulations. System evaluation is presented later in Section 3.2.8.

In simulation, we assume that all the node sequences are perfect so as to reveal the

achievable performance of MSP in the absence of incomplete node sequences or sequence

flips. In our simulations, all anchor nodes and target nodes are assumed to be deployed

at random following uniform distribution. The mean and maximum localization errors are

averaged over 50 runs to obtain high confidence (the localization error of each node is

defined as the distance between the estimated location and the real position). For legibility

reasons, we do not plot the confidence intervals here. All the simulations are based on the

straight-line scan example. We implement three scan strategies:

• Random Scan: the slope of the scan line is randomly chosen each time;

• Regular Scan: the slope is predetermined to rotate uniformly from 0◦ to 180◦. For

example, if the system scans 6 times, then the scan angle would be: 0◦, 30◦, 60◦, 90◦,

120◦, and 150◦ respectively.

• Adaptive Scan: the slope of each scan is determined based on the localization results

from previous scans (i.e. adaptive MSP).

We start with basic MSP and then demonstrate the performance improvements one

step at a time by adding (i) sequence-based MSP, (ii) iterative MSP, (iii) distributed-based

estimation, namely DBE MSP, and (iv) adaptive MSP.

52

3.2.7.1 Performance of the Basic MSP

The evaluation starts with basic MSP, where we compare the performance of random scan

and regular scan under different configurations. We intend to illustrate the impact of the

number of anchors M , the number of scans d, and target node density (number of target

nodes N in a fixed-size region) on the localization error. Table 3.1 shows the default simula-

tion parameters. We note that by default we only use three anchors, which is considerably

fewer than existing range-free solutions [158, 162].

Table 3.1: Default Simulation Configurations for MSP

Parameter Description

Field Area S 200×200 (in grid unit)

Scan Type Regular(default)/Random Scan

Number of Anchors 3(default)

Number of Scans 6(default)

Number of Target Nodes 100

Statistics Error Mean/Max

Random Seeds 50 runs

Impact of the Number of Anchors

In this experiment, we compare the regular scans with random scans under different

number of anchors from 3 to 30 in steps of 3. The results shown in Fig. 3.15 indicate that

(i) as the number of anchor nodes increases, localization error decreases, and (ii) statistically,

regular scans obtains better results than random scans with the same number of anchors.

Impact of the Number of Scans

In this experiment, we compare regular scan with random scan under different number

of scans from 3 to 30 in steps of 3. The number of anchors is 3 by default. Results in

Fig. 3.16 indicates that: (i) as the number of scans increases, localization error decreases

significantly. For example, localization errors drop more than 60% from 3 scans to 30 scans.

0 5 10 15 20 25 300

10

20

30

40

50

60

Mean Error and Max Error vs. Number of Anchors

Number of Anchors

E

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Max Error of Random Scan

Max Error of Regular Scan

Mean Error of Random Scan

Mean Error of Regular Scan

Figure 3.15: Basic MSP: Error vs. Number of Anchors

53

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90

Mean Error and Max Error vs. Number of Events

Number of Scan Events

E

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Max Error of Random Scan

Max Error of Regular Scan

Mean Error of Random Scan

Mean Error of Regular Scan

Figure 3.16: Basic MSP: Error vs. Number of Scans

0 50 100 150 20010

20

30

40

50

60

70

Mean Error and Max Error vs. Number of Target Nodes

Number of Target Nodes

E

rro

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un

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Max Error of Random Scan

Max Error of Regular Scan

Mean Error of Random Scan

Mean Error of Regular Scan

Figure 3.17: Basic MSP: Error vs. Number of Target Nodes

(ii) statistically, regular scans achieve better performance than random scans with identical

number of scans. However, the performance gap reduces when the the number of scan

increases. This is expected since a large number of random numbers converge to a uniform

distribution. Fig. 3.16 also demonstrates that MSP requires only a small number of anchors

to perform very well, compared to existing range-free solutions [158, 162]. By combining

Fig. 3.16 and Fig. 3.15, we can conclude that MSP allows a flexible tradeoff between physical

costs (anchor nodes) and soft costs (localization events).

Impact of the Number of Target Nodes

In this experiment, we confirm that the density of target nodes has no impact on the

accuracy for basic MSP, which motivated the design of sequence-based MSP. In this exper-

iment, we compare the regular scan with random scans under different number of target

nodes from 10 to 190 in steps of 20, while maintaining 3 anchors. Results in Fig. 3.17 show

that mean localization errors remain constant across different node densities. However,

when the number of target nodes increases, the maximum error increases.

54

Basic MSP Simulation Summary

From the above experiments, we can conclude that in basic MSP (i) increasing either

anchor nodes or localization events can enhance the localization performance; (ii) for square

shaped map, regular scan are better than random scan under different numbers of anchors

and scan events. This is because regular scans uniformly cut the map from different direc-

tions, while random scans would obtain sequences with redundant overlapping information

when two scans choose similar scan slopes.

3.2.7.2 Improvements of Sequence-based MSP over Basic MSP

This section evaluates the benefits of exploiting the order information among target nodes

by comparing sequence-based MSP with basic MSP. In this and the following sections,

regular scan is used for straight-line scan event generation. The purpose of using regular

scan is to keep the scan events and the node sequences identical for both sequence-based

MSP and basic MSP, so that the only difference between them is the sequence processing

procedure.

Impact of the Number of Anchors

In this experiment, we use different number of anchors from 3 to 30 in steps of 3. As

shown in Fig. 3.18, the mean error and maximum error of sequence-based MSP is much

smaller than that of basic MSP. Especially when there is limited number of anchors in the

system. For example, for 3 anchors, the errors were almost halved by using sequence-based

MSP. This phenomenon has an interesting explanation: the cutting lines created by anchor

nodes are exploited by both basic MSP and sequence-based MSP, so as the number of anchor

nodes increases, anchors tend to dominate the contribution. Therefore, the performance gap

lessens when more anchors are available in the system.

0 5 10 15 20 25 300

5

10

15

20

25

30

35

40

45

50

Basic MSP vs. Sequence Based MSP I

Number of Anchors

E

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Max Error of Basic MSP

Max Error of Seq MSP

Mean Error of Basic MSP

Mean Error of Seq MSP

Figure 3.18: Sequence-based MSP: Error vs. Number of Anchors

55

0 5 10 15 20 25 300

10

20

30

40

50

60

70

Basic MSP vs. Sequence Based MSP II

Number of Scans

E

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Max Error of Basic MSP

Max Error of Seq MSP

Mean Error of Basic MSP

Mean Error of Seq MSP

Figure 3.19: Sequence-based MSP: Error vs. Number of Scans

0 50 100 150 2005

10

15

20

25

30

35

40

45

50

55

Basic MSP vs. Sequence Based MSP III

Number of Target Nodes

E

rro

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rid

un

it) Max Error of Basic MSP

Max Error of Seq MSP

Mean Error of Basic MSP

Mean Error of Seq MSP

Figure 3.20: Sequence-based MSP: Error vs. Number of Target Nodes

Impact of the Number of Scans

In this experiment, we compare sequence-based MSP with basic MSP under different

number of scans from 3 to 30 in steps of 3. Fig. 3.19 indicates significant performance

improvement in sequence-based MSP over basic MSP across all scan settings, especially

when the number of scans is large. For example, when the number of scans is 30, errors in

sequence-based MSP are only about 20% of that of basic MSP. We conclude that sequence-

based MSP performs extremely well when there are many scan events

Impact of the Number of Target Nodes

Fig. 3.20 demonstrates the benefits of exploiting order information regarding target

nodes. Since sequence-based MSP makes use of the information among target nodes in

sequence, more target nodes contributes to the overall system accuracy. As a result, with

increasing number of target nodes, localization error decreases for sequence-based MSP.

Sequence-based MSP Simulation Summary

56

From the above experiments, we can conclude that exploiting ordering information

among target nodes can significantly improve localization accuracy, especially in the sit-

uations when we have abundant events but limited anchor nodes.

3.2.7.3 Improvements of Iterative MSP over Sequence-based MSP

In this experiment, the same node sequences were processed iteratively multiple times. In

Fig. 3.21, two single marks are results from basic MSP, since basic MSP doesn’t perform

iterations. Two curves present the performance of iterative MSP under different number

of iterations, i.e. c. We note that when c = 1, iterative MSP degrades to sequence-based

MSP. Therefore, Fig. 3.21 compares the three methods together to one another.

0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

50

Basic MSP vs. Iterative MSP

Number of Iterative Processing

E

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Max Error of Iterative Seq MSP

Mean Error of Iterative Seq MSP

Max Error of Basic MSP

Mean Error of Basic MSP

Figure 3.21: Improvements of Iterative MSP

Fig. 3.21 shows that the second iteration can reduce localization error significantly.

Applying iterative MSP, the maximum and mean error can be reduced by approximately

83% and 80% from those of basic MSP, respectively. However, the performance gain reduces

dramatically over iterations, e.g., when c > 5, there is almost no gain for further iterative

processing. This is because the second iteration allows earlier scans to exploit the new

boundaries created by later scans in the first iteration, while such exploitation decays quickly

over iterations.

3.2.7.4 Distribution-based Estimation over Iterative MSP

Fig. 3.22, in which we augment the iterative MSP with distribution-based estimation, shows

that distribution-based estimation (DBE) can bring in statistically better performance.

Fig. 3.22 presents the cumulative distribution of localization errors. In general, two curves

of DBE MSP lay slightly to the left of that of non-DBE MSP, indicating that DBE MSP

has a smaller statistical mean error and averaged maximum error than non-DBE MSP. We

note that because DBE is augmented on top of the best solution so far, the performance im-

provement is not significant. When we apply DBE on basic MSP methods, the improvement

57

0 2 4 6 8 10 12 14 160

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

DBE vs. Non−DBE

Error

C

um

ula

tiv

e D

istr

ub

uti

oin

Fu

nc

tio

ns

(C

DF

)

Mean Error CDF of DBE MSP

Mean Error CDF of Non−DBE MSP

Max Error CDF of DBE MSP

Max Error CDF of Non−DBE MSP

Figure 3.22: Improvements of DBE MSP

would be much more significant. We omit these results because of space constraints.

3.2.7.5 Improvements of Adaptive MSP

This section illustrates the performance of adaptive MSP over non-adaptive MSP. We note

that the feedback-based adaptation can be applied to all MSP methods, since it only affects

how events are generated but not sequence processing. In this experiment, we evaluated

how adaptive MSP can improve the best solution so far (regular scans in iterative MSP

with DBE). The default angle granularity (i.e. step) for adaptive searching is set to be 5◦

in the simulation.

The Impact of Area Shape

First, if system settings are regular, the adaptive method can hardly contributes to the

results. For a square shaped area (regular), the performance of adaptive MSP and regular

scans are very close and almost overlapping with each other as shown in Fig. 3.23. However,

0 20 40 60 80 1000

5

10

15

20

25

Adaptive MSP for 200by200

Number of Target Nodes

E

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Max Error of Regular Scan

Max Error of Adaptive Scan

Mean Error of Regular Scan

Mean Error of Adaptive Scan

Figure 3.23: Adaptive MSP for a 200 by 200 Field

58

0 20 40 60 80 1000

10

20

30

40

50

60

70

Adaptive MSP for 500by80

Number of Target Nodes

E

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Max Error of Regular Scan

Max Error of Adaptive Scan

Mean Error of Regular Scan

Mean Error of Adaptive Scan

Figure 3.24: Adaptive MSP for a 500 by 80 Field

0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Mean Error CDF at Different Angle Steps in Adaptive Scan

Mean Error

C

um

ula

tiv

e D

istr

ub

uti

oin

Fu

nc

tio

ns

(C

DF

)

5 Degree Angle Step Adaptive

10 Degree Angle Step Adaptive

20 Degree Angle Step Adaptive

30 Degree Step Regular Scan

Figure 3.25: Impact of the Number of Candidate Events

if the shape of the area is not regular, e.g. not a square, adaptive MSP helps to choose

the appropriate localization events to compensate. Therefore, adaptive MSP can achieve a

better mean error and maximum error as shown in Fig. 3.24. For example, adaptive MSP

improves localization accuracy by 30% when the number of target nodes is 10.

The Impact of Target nodes Number

Fig. 3.24 shows that when node density is low, adaptive MSP brings more benefit than

when node density is high. This phenomenon makes statistical sense since the law of large

numbers tells us that node placement approaches a uniform distribution as the number of

nodes increases. Adaptive MSP has an edge when network layout is not uniform.

The Impact of Number of Candidate Events

Fig. 3.25 shows that smaller adaptive searching step gives better statistical performance

in terms of mean localization error. The rational is clear: more candidate scan angles

provide MSP more opportunity to choose the best one approaching the optimal angle.

59

3.2.7.6 Simulation Summary

Starting from the basic MSP, we have demonstrated step-by-step how four optimizations can

be applied on top of each other to improve the localization performance. In other words,

these optimizations are compatible with each other and can jointly improve the overall

performance. We note that our simulation was done under assumption that complete node

sequences can be obtained without sequence flips. In the next section, we present two

versions of system implementation that reveal and address practical issues.

3.2.8 Test-bed Evaluation

In this section, we present system implementation of MSP on two test-beds. The first

one is called Mirage, a large indoor test-bed we built over a six-month period that can

support up to 360 nodes working simultaneously under multiple voltages. The whole test-

bed is composed of six 4-feet by 8-feet boards, illustrated in Fig. 3.26. Each board in the

system can be used as an individual sub-system that be powered, controlled and metered

separately. We use three high-end HITACHI CP-X1250 projectors, connected through a

MATROX Triplehead2go graphics expansion box, to create an ultra-wide integrated display

on six boards. Fig. 3.26 shows that a long tilted line is generated by the projects. We have

implemented all five versions of MSP on the Mirage test-bed, running 46 MICAz motes.

Figure 3.26: The 360-node Mirage Test-bed (Light Beam Scan)

Figure 3.27: The 20-node Outdoor Experiments (Sound Wave Propagation)

60

In the outdoor system, a DELL A525 SPEAKER is used to generate a 4700 Hz beep

as shown in Fig. 4.56. We place 20 MICAz motes in the backyard of a house. Since the

location is not completely open, sound wave are reflected, scattered and absorbed by various

objects in the vicinity, causing a multi-path effect. Due to the limitation of experimental

hardware, we tested the design with a relatively small scale outdoor system. For networks

deployed in a large outdoor area, we consider that firstly MSP can work by using more

powerful event generators [192]; and in addition, regional localization results for different

parts of the network could be obtained individually and then merged easily.

3.2.8.1 Indoor System Evaluation

During indoor experiments, we encountered several real-world problems that are not re-

vealed in the simulation. First, sequences obtained were partial due to sensing errors and

message losses. Second, elements in the sequences could flip due to detection delay, un-

certainty in media access or time synchronization error. We show that these issues can be

addressed by using the protection band method described in Section 3.2.6.3. In the follow-

ing, unless mentioned otherwise, the default setting of the system is 3 anchors and 6 scan

events with scanning line speed of 8.6 feet/s.

On Scanning Speed and Protection Band

In this experiment, we studied the impact of the scanning speed and the length of the

protection band on the performance of the localization. In general, with increasing scanning

speed, nodes have less time to respond to the event and the time gap between two adjacent

nodes shrinks, leading to an increasing number of partial sequences and sequence flips.

Fig. 3.28 shows the node flip situations for six scans with distinct angles under different

scan speeds. The X-axis shows the distance in terms of rank between the flipped nodes

0 5 10 15 200

20

40

(3) Flip Distribution for 6 Scans at Line Speed of 14.6feet/s

F

lip

s

Node Distance in the Ideal Node Sequence

0 5 10 15 200

20

40

(2) Flip Distribution for 6 Scans at Line Speed of 8.6feet/s

F

lip

s

0 5 10 15 200

20

40

(1) Flip Distribution for 6 Scans at Line Speed of 4.3feet/s

F

lip

s

Figure 3.28: Number of Flips for Different Scan Speed

61

0 0.2 0.4 0.6 0.8 10

2

4

6

8

10

12

14

16

18

20

Unlocalized Nodes vs. Protection Band

Protection Band (in feet)

U

nlo

ca

lize

d N

od

es

Scan Line Speed: 14.6feet/s

Scan Line Speed: 8.6feet/s

Scan Line Speed: 4.3feet/s

Figure 3.29: Scanning Speed and Protection Band: Number of Unlocalized Nodes

0 0.2 0.4 0.6 0.8 10.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Mean Error(Line Scan at Different Speed)

Protection Band (in feet)

E

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ee

t)

Scan Line Speed:14.6feet/s

Scan Line Speed: 8.6feet/s

Scan Line Speed: 4.3feet/s

Figure 3.30: Scanning Speed and Protection Band: Mean Localization Error

0 0.2 0.4 0.6 0.8 11.5

2

2.5

3

3.5

4

Max Error(Line Scan at Different Speed)

Protection Band (in feet)

E

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ee

t)

Scan Line Speed: 14.6feet/s

Scan Line Speed: 8.6feet/s

Scan Line Speed: 4.3feet/s

Figure 3.31: Scanning Speed and Protection Band: Maximum Localization Error

in a correct node sequence (obtained from the true locations of all nodes). Y-axis shows

the total number of flips in six scans. This figure tells that faster scan brings in not only

increasing number of flips, but also long distance flips that require bigger protection band

62

to prevent fatal elimination errors.

Fig. 3.29 shows the effectiveness of the protection band in terms of reducing the number

of unlocalized nodes. When we use a moderate scan speed (4.3 feet/s), the chance of

flipping is rare, therefore we can achieve 0.45 feet mean accuracy (Fig. 3.30) with 1.6 feet

maximum error (Fig. 3.31). With increasing scan line speed, the protection band needs to

be set to a larger value to deal with flipping. An interesting phenomenon can be observed

in Fig. 3.29, 3.30 and 3.31: on one hand, applying protection band can sharply reduce

the number of unlocalized nodes; on the other hand, protection band enlarges the location

area where a target would potentially reside, introducing more uncertainty. Thus there is

a concave curve for both mean and maximum error when the scan speed is at 8.6 feet/s.

On MSP Methods and Protection Band

In this experiment, we show improvements resulting from three different methods.

Fig. 3.32 shows that a protection band of 0.35 feet is sufficient for the scan speed 8.57

feet/s. Fig. 3.33 and Fig. 3.34 show clearly that iterative MSP (with adaptation) achieves

best performance. For example, Fig. 3.33 shows that when we set the protection band to be

0.05 feet, iterative MSP achieves 0.7 feet accuracy that is 42% more accurate than the basic

design. Similarly, Fig. 3.33 and Fig. 3.34 show the double-side effects of protection band on

the localization accuracy. In addition, by comparing Fig. 3.32, Fig. 3.33 and Fig. 3.34, we

can see an interesting phenomenon: although advanced MSP (e.g. sequenced-based MSP

and iterative MSP) owns better performance in terms of localization accuracy, it might leave

slightly more nodes unlocalized. This result is expected since advanced MSP aggressively

shrink the localization area of each node and thus with higher probability of erasing the

node from the map.

On Number of Anchors and Scans

In this experiment, we show a tradeoff between hardware cost (anchors) with soft cost

(events). Fig. 3.35 shows that with more cutting lines created by anchors, the chance of

unlocalized nodes increases slightly. We note that with a 0.35 feet protection band, the

percentage of unlocalized nodes is very small, e.g. in the worst-case with 11 anchors, only

2 out of 46 nodes are not localized due to flipping. Fig. 3.36 and Fig. 3.37 show a tradeoff

between number of anchors and the number of scan events. Obviously, with the increasing

number of anchors, localization error drops significantly. With 11 anchors we can achieve

an accuracy as low as 0.25 ∼ 0.35 feet, which is nearly a 60% improvement. Similarly, with

increasing number of scans, localization error drops significantly as well. We can observe

about a 30% performance gain across all anchor settings when we increase the number of

scans from 4 to 8. For example, with only 3 anchors, we can achieve 0.6-foot accuracy with

a number of 8 scans.

63

0 0.2 0.4 0.6 0.8 10

2

4

6

8

10

12

14

16

18

20

Unlocalized Nodes (Scan Line Speed 8.57feet/s)

Protection Band (in feet)

U

nlo

ca

lize

d n

od

es

ou

t o

f 4

6

Unlocalized node of Basic MSP

Unlocalized node of Sequence Based MSP

Unlocalized node of Iterative MSP

Figure 3.32: MSP Methods and Protection Band: Number of Unlocalized Nodes

0 0.2 0.4 0.6 0.8 1

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

Mean Error (Scan Line Speed 8.57feet/s)

Protection Band (in feet)

E

rro

r (i

n f

ee

t)

Mean Error of Basic MSP

Mean Error of Sequence Based MSP

Mean Error of Iterative MSP

Figure 3.33: MSP Methods and Protection Band: Mean Localization Error

0 0.2 0.4 0.6 0.8 11.5

2

2.5

3

3.5

4

Max Error (Scan Line Speed 8.57feet/s)

Protection Band (in feet)

E

rro

r (i

n f

ee

t)

Max Error of Basic MSP

Max Error of Sequence Based MSP

Max Error of Iterative MSP

Figure 3.34: MSP Methods and Protection Band: Maximum Localization Error

3.2.8.2 Outdoor System Evaluation

The outdoor system evaluation contains two parts: (i) effective detection ordering evalua-

tion, which shows that sequences can be readily obtained, and (ii) sound propagation based

64

3 4 5 6 7 8 9 10 110

0.5

1

1.5

2

2.5

Unlocalized Nodes (Protection Band: 0.35 feet)

Number of Anchors

U

nlo

ca

lize

d N

od

es

4 Scan Events at Speed 8.75feet/s

6 Scan Events at Speed 8.75feet/s

8 Scan Events at Speed 8.75feet/s

Figure 3.35: Number of Anchors and Scans: Number of Unlocalized Nodes

3 4 5 6 7 8 9 10 110.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Mean Error (Protection Band: 0.35 feet)

Number of Anchors

E

rro

r (i

n f

ee

t)

Mean Error of 4 Scan Events at Speed 8.75feet/s

Mean Error of 6 Scan Events at Speed 8.75feet/s

Mean Error of 8 Scan Events at Speed 8.75feet/s

Figure 3.36: Number of Anchors and Scans: Mean Localization Error

3 4 5 6 7 8 9 10 110.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

Max Error (Protection Band: 0.35 feet)

Number of Anchors

E

rro

r (i

n f

ee

t)

Max Error of 4 Scan Events at Speed 8.75feet/s

Max Error of 6 Scan Events at Speed 8.75feet/s

Max Error of 8 Scan Events at Speed 8.75feet/s

Figure 3.37: Number of Anchors and Scans: Maximum Localization Error

localization, which verifies propagation-based localization.

Detection Ordering Evaluation

65

Figure 3.38: The Experiment of Wave Detection

1 2 3 4 50

5

10

15

20 2 feet group distance

Ra

nk

Group Index1 2 3 4 5

0

5

10

15

20 3 feet group distance

Ra

nk

Group Index

1 2 3 4 50

5

10

15

20 4 feet group distance

Ra

nk

Group Index1 2 3 4 5

0

5

10

15

20 5 feet group distance

Ra

nk

Group Index

Figure 3.39: Wave Detection: Ranks vs. Distances

We evaluate the sequence flip phenomenon in wave propagation. As shown in Fig. 3.38,

20 motes were placed as five groups in front of the speaker (four nodes in each group at

roughly the same distance to the speaker). The gap between each group is tested with 2, 3,

4 and 5 feet respectively in four experiments. Fig. 3.39 shows the detection results. The X-

axis in each subgraph indicates the group index and four nodes in each group are depicted

with 4 bars. The Y-axis shows the detection rank of each node in corresponding node

sequence. We can see from the figure: as the distance between each group increases, the

number of flips in the resulting node sequence decreases. For example, in 2 feet subgraph,

there are quite a few flips among nodes in adjacent and even non-adjacent groups, while in

5 feet subgraph, flips between different groups almost disappear.

Sound Propagation Based Localization

As shown in Fig. 4.56, 20 motes are placed as a grid including five rows with 5 feet

between each row, and four columns with 4 feet between each column. Six 4700 Hz beep

events are generated around the mote grid by a speaker. Fig. 3.40 shows the localization

66

0

2

4

6

8

10

12

14

16

18

20

22

24

0 2 4 6 8 10 12 14

Y-D

imensio

n (

feet)

X-Dimension (feet)

Node

0

2

4

6

8

10

12

14

16

18

20

22

24

0 2 4 6 8 10 12 14

Y-D

imensio

n (

feet)

X-Dimension (feet)

Anchor

Figure 3.40: Localization Error (Sound Wave Propagation)

results with iterative MSP (three times of iterative processing) with protection band of 3

feet. The average error of the localization results is 3 feet and the maximum error is 5 feet

with only one unlocalized sensor node.

We found that sequence flip in wave propagation is more severe than that in the indoor

line-based test. This is expected due to (i) the high propagation speed of sound; and (ii)

random detection delays at the acoustic sensor of each node. In addition, the speaker we use

is not a perfect omnidirectional acoustic source, which causes many partial node sequences.

Currently we use MICAz mote equipped with a low quality microphone. We believe that if

use a better speaker with more events, the system can yield better localization accuracy.

3.2.9 Summary and Remarks on MSP

We present the first work that exploits the concept of Multi-Sequence Processing to localize

sensor nodes. It is demonstrated that the localization performance can be greatly improved

by making full use of the information embedded in multiple easy-to-get one-dimensional

node sequences. Four optimization methods are proposed for exploiting order and marginal

distribution among non-anchor nodes as well as the feedback information from available

localization results. Importantly, these optimization methods can be used together and

improve accuracy additively. Practical issues of partial node sequence and sequence flip were

identified in two test-beds and addressed accordingly. MSP is evaluated at scale through

simulation and testbed experiments. Results show that requiring neither per-node hardware

nor precise event distribution, MSP achieves sub-foot accuracy with a few anchors provided

sufficient events. In fact, MSP offers an optional tradeoff between hardware cost (anchors)

and soft cost (events). When anchors are scarce, more events can be used for compensation,

vise versa. Therefore, MSP provides nice flexibility among diverse applications.

67

3.3 LUE: Localization with Uncontrolled Events

MSP presented in previous section successfully relaxes the rigid requirement of precisely-

manipulated events to semi-controlled events, by bringing in a small number of anchor

nodes. As an important step further, this section investigates the possibility and perfor-

mance of localization with uncontrolled events, which owns two obvious benefits. Firstly,

the event generation mechanism can be greatly simplified to make the system flexible and

convenient to work with. Secondly, non-artificial natural events could potentially be utilized

for localization purpose.

Despite of benefits, uncontrolled events impose a major challenge of significant infor-

mation loss, comparing with previous precisely controlled events (e.g., Lighthouse [191],

Spotlight [192]). To overcome this difficulty, our earlier work [197] firstly introduced the

concept of node localization using totally uncontrolled events, while in this section we refined

the idea of estimating parameters of events and the location of sensor nodes simultaneous,

by deeply processing node sequences easily obtained from event distributions. Besides the

basic design, two important improvements based on maximum likelihood estimation (MLE)

were proposed to further extract location information embedded in node orderings for two

scenarios: (i) node density is high; and (ii) abundant events are available. We evaluated the

design with extensive simulation and testbed experiments including 41 MICAz motes. Re-

sults revealed that with only randomly generated events, our design can effectively localize

nodes with great flexibility, while adding little extra overhead at the resource constrained

sensor nodes side.

This section is organized as follows. Section 3.3.1 provides some background and an

overview of the design. Section 3.3.2 and 3.3.3 present the basic design and enhancements

as the advanced design. We give discussions on computation overhead and explanations for

wave propagation based events in Section 3.3.4 and 3.3.5, respectively. Then, Section 3.3.6

and 3.3.7 report simulation results as well as a system evaluation on our Mirage testbed.

Finally, Section 3.3.8 concludes our design of LUE and suggests future works.

3.3.1 System Overview

In this part, we first review basic concepts about event-driven localization. Then, we give

an overview about the proposed localization scheme with uncontrolled events.

3.3.1.1 Concepts in Event-driven Localization

In event-driven localization, events (e.g., ultrasound or air blast propagation, optical or

laser beam scans) are generated to distribute over the network area for positioning purpose.

Sensor nodes detect events and report detections to a localization server that also serves as

the event disseminator. Given the information about event distribution, for example, the

68

position of an event at any specific time instance, localization sever can efficiently pinpoint

the coordinates of a node according to its reported detection timestamp for this event.

In theory, such an event-driven mechanism allows accurate localization, however, it

comes with an implicit assumption that events can be precisely distributed to a desired

location at a specified time instance. In practice, in order to satisfy the above assumption,

the event disseminator needs to accomplish two levels of control over localization events: (i)

control over event generation, and (ii) control over event distribution. For example, Fig. 3.26

shows a snapshot of a straight-line light beam scan event generated by projectors of our

Mirage testbed. In this case, the control over event generation determines the scan angle

and scan direction; while the control over event distribution, for instance, can help maintain

a constant line-speed of the light beam on the testbed. Unfortunately, both aforementioned

controls could be costly to realize in practical outdoor systems, especially at large scale

when the terrain is uneven, or the event generation device is not well calibrated and its

position is difficult to maintain.

3.3.1.2 Localization with Uncontrolled Events

Uncontrolled events bring in maximum flexibility, however, previous localization mechanism

fails to work. The idea we propose in this and following sections is to estimate the generation

parameters of uncontrolled events with a small number of anchor nodes in the field, and

then shrink the possible location area of each normal node according to its ranking in node

sequences obtained from the event detections.

Event 1

Event 2

Normal node

Anchor node

Node Sequences Obtained

Scan 1: 3 A 1 6 4 8 C 2 B 7 5

Scan 2: 2 1 C 5 3 A 4 B 8 7 6

Scan 3: 2 5 C B 7 1 4 8 3 A 6

Scan 4: 7 6 8 B 4 5 A C 3 2 1

Event 4

Event 3

(a) Node sequences obtained from uncontrolled events

1 A

2

3

B

C

4

6

75

8

Event Parameter Estimation

Angle range of scan 1 = ACB

Angle range of scan 2 = CAB

Angle range of scan 3 = CBA

Angle range of scan 4 = BAC

Anchor Subsequence

Scan 1: A C B

Scan 2: C A B

Scan 3: C B A

Scan 4: B A C

(b) Event parameter estimation using anchors in the sequences

X

Y

Figure 3.41: LUE System Overview I: Node Sequence and Anchor Subsequence

Fig. 3.41 and Fig. 3.42 give an overview for the design. First of all, certain type of

events are generated in the network, for example straight-line laser beam scans with un-

controlled angles, directions and speeds. As an event propagates, sensor nodes detect the

69

event sequentially at different time instances that naturally gives an ordering of related

nodes, called a node sequence. For instance, in Fig. 3.41(a), a top-down scan (i.e., Event

1) generates node sequence (3 A 1 6 4 8 C 2 B 7 5). Here we use uppercase letters (e.g.,

A, B, C) to denote anchor nodes and numbers (e.g., 1, 2, 3) to denote normal nodes to be

localized. Note that without precise event distribution control, a node sequence essentially

embeds the information on relative positions among nodes along the propagation direction

of the event.

Second, given a node sequence, an algorithm is developed to estimate generation pa-

rameters for the corresponding event (e.g., possible scan angles), by processing the ordered

anchor subsequence that can be extracted directly from a node sequence, as shown in

Fig. 3.41(b). The rational behind this step is that the ordering of anchor nodes in a node

sequence reflects possible range of the event generation parameter.

Node Seq. + Est. Angles

Scan 1: 3 A 1 ... 5 + ACB

Scan 2: 2 1 C ... 6 + CAB

Scan 3: 2 5 C ... 6 + CBA

Scan 4: 7 6 8 ... 1 + BAC

Each event contributes

a map division

Location estimation

from joint areas

Estimated location

1 A

2

3

B

C

4

6

75

8

A

B

C

4

6

75

8

2

13

Figure 3.42: LUE System Overview II: Map Partition and Location Area Estimation

Then, as depicted in the left of Fig. 3.42, the whole map can be divided into lots of

small parts after processing a node sequence with corresponding estimated event generation

parameter. Each normal node obtains a possible location area composed of one or multiple

parts in the map according to its rank in the node sequence. With multiple events, the final

location area of a normal node can be shrunk dramatically by extracting joint regions of

possible location areas from different node sequences (events), as illustrated in the right of

Fig. 3.42. As a result, the final estimated position of a normal node can be obtained from

a relatively small area. As a range-free approach, the above design applying node sequence

instead of direct sensing results in localization considered the following advantages:

• The scheme with node sequences does not require high accuracy of time synchroniza-

tion among nodes, as long as the orderings in sequences are mostly correct.

• A node sequence features better robustness than a single sensing result under noise and

hardware errors. The majority of node-pair orderings in the sequence could remain

unchanged under single node’s sensing error or universal biased environmental noise.

• Localization by processing node sequences provides a useful layer of abstraction that

makes the design generic and compatible with different sensing modalities. Given

node sequences, specific sensing signals are transparent to the localization algorithm.

70

In the following, for the sake of clarity, we firstly use the straight-line scan as an example

localization event to convey ideas as it is done for MSP in Section 3.2. Later, we explain

how other types of events (e.g., sound wave propagation) can be processed similarly.

3.3.2 LUE Basic Design

This section explains the basic design of localization with uncontrolled events. We introduce

the system in two steps: (i) event generation parameter estimation (Section 3.3.2.1), and (ii)

location area estimation (Section 3.3.2.2). After that, we provide an intergraded algorithm

in Section 3.3.2.3.

3.3.2.1 Event Generation Parameter Estimation

Sensor nodes’ sequential detection of an event gives an ordering of those nodes, namely a

node sequence. By utilizing the ordered anchors in the node sequence, event generation

parameters can be estimated.

Taking the straight-line scan event as an example, the event generation parameters

include the scan angle as well as the scan direction. Given three anchors not in a line, their

ordering actually embeds the information for both scan direction and possible range of the

scan angle. For instance, as illustrated in Fig. 3.43, if a straight-line scans from top to

bottom, a node sequence (3 A 1 6 4 8 C 2 B 7 5) can be obtained. Reversely, given this

node sequence, an anchor ordering subsequence (A C B) can be extracted directly. With

the location information of anchor nodes, by careful observation, we can conclude that (i)

the scan must be conducted from top to bottom in Fig. 3.43; (ii) the scan angle must be

within the range of θ = (θ1, θ2), i.e., ∠ACB, since any angle beyond θ should not output

anchor ordering (A C B).

Node Sequences: 3 A 1 6 4 8 C 2 B 7 5

Straight-line Scan

Anchor Subsequence: A C B

Possible Angle Range: θ = (θ1 , θ2)θ1

θ2

θ

1A

2

3

B

C

4

6

75

Normal nodeAnchor node

8

Figure 3.43: Estimate Angle Range by Intuition

From above , we can see that for a straight-line scan event, a three-anchor ordering is

sufficient to give an estimation about the possible range of the scan angle. We call such

a three-anchor ordering as an estimation unit for the straight-line scan event. If multiple

anchors exist in a node sequence, each combination of three anchors creates an estimation

unit that outputs an angle range. Therefore, the final result for event parameter estimation

71

can be obtained by extracting the joint part of results given by all estimation units in the

node sequence.

A

B

C

D

Estimation unit (A B C) outputs θRange1

Estimation unit (D E F) outputs θRange2

θRange1

θRange2

θRange1 ∩ θRange2

E

F

θRange2

θRange1

(a) (b)

Joint part θRange1 ∩ θRange2

shrinks the estimation range

Figure 3.44: Extract the Joint Part of Estimations

An example is shown in Fig. 3.44. Suppose that an anchor subsequence (A B C D E F)

is extracted from a node sequence. Estimation unit (A B C) gives a scan angle estimation

θRange1, and another estimation unit (D E F) contributes a different range θRange2, as

illustrated in Fig. 3.44(a). Then the joint part θRange1 ∩ θRange2 is an estimation with

smaller interval (uncertain range), as shown in Fig. 3.44(b). We can imagine that with

increasing number of anchors, more estimation units help shrink the uncertain range and

thus better estimations could be achieved.

With increasing number of anchors, the computation complexity for event generation

parameter estimation seems to enlarge quickly. A naive conclusion is that for a node se-

quence with n anchors, there are C3n = n3−3n2+2n

6 = O(n3) different three-anchor estimation

units. In fact, only O(n) among those O(n3) estimation units are helpful and thus need to

be processed. To explain this observation, we redraw Fig. 3.44 as Fig. 3.45 in the following.

Node Sequence

(… A … B … C … D … E … F ... )

θRange1

A

C

DE

F

Example Effective Estimation Unit

(A B C)

Example Redundant Estimation Unit

(A B D), (A B E), (A B F)

Anchor Subsequence

( A B C D E F)

B

Figure 3.45: Example of Redundant Estimation Units

Suppose that anchor A and B are chosen as the first two anchors of a three-anchor

estimation unit, then only selecting anchor C, which is the next element after B in anchor

subsequence (A B C D E F), generates an effective estimation unit. This is because esti-

mation units composed of A, B and any other anchors beyond C in the anchor subsequence

72

would give a wider angle range that covers θRange1 given by estimation unit (A B C), as

shown in Fig. 3.45. For instance, ∠ABD, ∠ABE, and ∠ABF , given by estimation unit (A

B D), (A B E) and (A B F), respectively, are all redundant due to their wider range than

∠ABC. Therefore, only three consecutive anchor nodes form an effective estimation unit

for the straight-line scan event.

In general, if l anchors are required to form an estimation unit, with n anchors in a node

sequence, the number of effective estimation units is at most n− l+1. In other words, only

O(n) estimation units are necessary for computation.

Algorithm 3: Event Generation Parameter Estimation

input : A node sequence: NodeSeqoutput: Estimated event generation parameter: θ

θ = All possible values of the parameter ;1

repeat2

Uniti = GetUnusedEstimationUnit(NodeSeq) ;3

θi = EventParameterEstimation(Uniti) ;4

θ = θ ∩ θi ;5

until all effective estimation units in NodeSeq are used ;6

Algorithm 3 depicts the computation architecture for the above parameter estimation.

For each node sequence, all effective estimation units are processed independently, and the

final result θ is obtained through extracting the joint part of all individual estimations.

Specifically, line 1 initializes θ to be the scope of all possible values of the event generation

parameter. For example, (−π2 ,+π

2 ) for the angle of line scan event. Effective estimation

units are processed between line 2 and 6. Line 3 gets an unused estimation unit Uniti from

the node sequence NodeSeq, and line 4 computes an estimation θi from Uniti. Then, θ gets

shrunk based on previous estimation θ and newly obtained θi at line 5.

3.3.2.2 Location Area Estimation

With estimated event generation parameter, i.e., θ from Algorithm 3, and cooperating with

the original node sequence, the interested area can be divided into multiple parts. For each

normal target sensor node, its rank in the node sequence determines a possible location area

in which it is located.

Explanation about the Location Area

Fig. 3.46 shows an example for area partition from a straight-line scan event. Node

sequence (3 A 1 6 4 8 C 2 B 7 5) was obtained from the scan event, and the angle range

θ = θ was determined by anchor subsequence (A C B). Now, according to the location

information of anchors and estimated angle range θ, the whole area can be divided into 8

73

1A

Normal nodeAnchor node

Node Sequences: 3 A 1 6 4 8 C 2 B 7 5

Angle Range: θ

Segment Location Area

3 : I + II + III + IV

1, 6, 4, 8 : I + II + V + IV + VI

2: I + VIII + V + IV + VI

7, 5: I + VIII + VII + VI

Straight-line Scan

θI

II

3

2

5

4

7

8

6

III

V

VIII

VII

VI

IV

C

B

Figure 3.46: Example of Area Division

parts marked as I, II, · · · , VIII in the figure. Considering normal node 3 as an example, it

is ranked ahead of anchor A in the node sequence, meaning that node 3 detected the event

earlier than A did. Therefore, we can conclude that node 3 should be located in a region

that is the union of part I, II, III and IV, because if node 3 was located outside of this

region, it is impossible to satisfy the obtained node sequence.

For a system containing n anchor nodes, according to the pie-cutting theorem [200], the

whole area gets cut into O(4n2) small parts by a straight-line scan event, e.g., I, II, III,

· · · , in Fig. 3.46. On the other hand, a node sequence can be divided into at most n + 1

segments by n anchors. For example, three anchors A, B, C divide the node sequence (3

A 1 6 4 8 C 2 B 7 5) into four segments: {3}, {1 6 4 8}, {2}, and {7, 5}. Normal nodes

within the same segment essentially share the same possible location area in terms of this

cut. Note that the possible area for each segment is a combination of multiple contiguous

small parts as indicated in the right part of Fig. 3.46.

Figure 3.47: Example Joint Location Area for Node 3

Given multiple node sequences from different events, each normal node obtains a number

of possible location areas composed of diverse parts in the map. Then, the joint region

among them is the final location area of this normal node. Fig. 3.47 shows an example

for obtaining a localization area for node 3 after two events. Fig. 3.47(a) and Fig. 3.47(b)

give possible location regions for node 3 according to the node sequence obtained from each

event, and then Fig. 3.47(c) depicts the overlapping area as a better estimation. Following

74

this example, we can imagine that with increasing number of anchors and events, the size

of the final location area gets shrunk dramatically, and effective sensor node localization

can be achieved.

Computation with Grid-based Sampling

Following the intuitive explanation above, this section details the computation algorithm

for location area estimation. We model the whole network area with a grid map, a pixel

in the map stands for a differentiable position point. Given a node sequence, the task is to

identify the location areas in the map for segments of the node sequence.

For segment S from a node sequence, all position points in the map are examined. Con-

sidering any position point, say P , we firstly calculate a hypothetic parameter θ satisfying

the requirement that if normal nodes locate at P , they would appear in the segment S for

a event generated with parameter θ. Then, this hypothetic event generation parameter θ

is compared with the obtained estimation θ. If they have overlapping portions, it indicates

that the true event also satisfies θ, therefore point P is considered as a possible position for

nodes in segment S. Otherwise, P is excluded from the location area of S.

Specifically, there are two cases for processing a segment:

• A segment locates between two anchors in the node sequence, for example, segment

{1 6 4 8} in the following Fig. 3.48;

• The first segment and the last segment that have only one neighboring anchor in the

node sequence, for example, segment {3} and segment {7 5} in Fig. 3.48.

A

θI

II

III

V

VIIIVII

VI

IV

C

B

A

θI

II

III

V

VIIIVII

VI

IV

C

B

θ1

θ2

θ1

θ2

P1

P2

P1

P2

(a) Segment between two anchors

θ1∩θ ≠ Ø, θ2∩θ = Ø

(b) First segment example

θ1∩θ ≠ Ø, θ2∩θ = Ø

Node Sequences: 3 A 1 6 4 8 C 2 B 7 5

Angle Range: θ

Figure 3.48: Example of Location Area Finding

Fig. 3.48(a) shows an example for determining the location area of segment {1 6 4 8}(between anchor A and C) following the first case. Two position points P1 and P2 are

investigated. First, anchor ordering (A C B) gives θ = θ as shown in the figure. For point

P1’s being ranked between anchor A and C in a node sequence, the hypothetic angle range

is θ = θ1. Since θ1 ∩ θ 6= ∅, namely θ ∩ θ 6= ∅, P1 is a possible position for the segment

{1 6 4 8}. While for point P2, the hypothetic angle range is θ = θ2. θ2 ∩ θ = ∅, namely

θ ∩ θ = ∅, therefore P2 is not a possible location for nodes in segment {1 6 4 8}.

75

Fig. 3.48(b) shows an example for the second case. P1 and P2 are investigated for

segment {3} that has only one neighboring anchor A. The scheme used here for this case

is a little bit tricky because one anchor is not sufficient to give an angle range. Imaging

there is another dummy anchor located far far away above anchor A in the map, then this

dummy anchor can be regarded as the other neighboring anchor for segment {3}. This is

because if it were there, it would be ranked ahead of node 3 in the sequence for any event

satisfying scan angle range θ. Thus a vertical line can be used for the other boundary of θ.

Similarly as before, because θ1 ∩ θ 6= ∅ and θ2 ∩ θ = ∅, we can conclude that P1 is valid

for segment {3} while P2 is not.

Algorithm 4: Location Area Estimation

input : A segment in a node sequence SegmentEstimated event generation parameter θ

output: Estimated location area for this segment Area

Area = ∅ ;1

Anchor1 = PreAnchor(Segment) ;2

Anchor2 = SucAnchor(Segment) ;3

repeat4

P = GetUnprocessedPositioinPoint(Map) ;5

θ = Hypothetic(Anchor1, P, Anchor2) ;6

if θ ∩ θ 6= ∅ then7

Area = Area ∪ P ;8

end9

until all position points in the map are processed ;10

Algorithm 4 shows steps for finding the possible location area of a segment. First,

the possible area is initialized to be ∅ at line 1. Line 2 and 3 get the predecessor and

successor anchors for this segment in the node sequence (one of them might be a dummy

anchor). Then from line 4 to 10, each position point in the Map is examined. Specifically,

line 6 computes the hypothetic event generation parameter θ. If the true event generation

parameter is within the range of θ, a normal node at this position point P would be ranked

between the predecessor anchor and the successor anchor in the node sequence. Line 7 to

9 express that if θ has common part with estimated parameter θ, P is a possible location

for this segment and thus be added to Area. Otherwise, continue to check another position

point in the map.

3.3.2.3 Localization Algorithm

Combining Algorithm 3 for event generation parameter estimation and Algorithm 4 for seg-

ment location area finding, we give an integrated design as Algorithm 5. The input of the

localization algorithm is node sequences obtained from uncontrolled event detections. The

76

Algorithm 5: Localization with Uncontrolled Events

input : Multiple node sequences: NodeSeqsoutput: Estimated coordinates of normal nodes

repeat1

NodeSeq = GetUnprocessedSequence(NodeSeqs) ;2

θ = Algorithm 3(NodeSeq) ;3

repeat4

Segment = GetUnproessedSegment(NodeSeq) ;5

Area = Algorithm 4(Segment, θ) ;6

repeat7

Node = GetUnprocessedNode(Segment) ;8

LocationAreaShrink(Node, Area) ;9

until all normal nodes in the Segment are processed ;10

until all segments in NodeSeq are processed ;11

until all node sequences in NodeSeqs are processed ;12

repeat13

Node = GetUnprocessedNode(NodeSeq) ;14

CentroidEstimation(Node) ;15

until all normal nodes in NodeSeq are estimated ;16

output is the estimated location coordinates of normal nodes. Line 1 to 12 process each

node sequence one by one to shrink the possible location area of each normal node. Specif-

ically, line 2 gets an unprocessed node sequence, and line 3 estimates the event generation

parameter for this node sequence with Algorithm 3. Line 4 to 11 process each segment in

the node sequence with two steps. First, line 6 estimates the location area for this segment

with Algorithm 4. And then, from line 7 to 10, each node within this segment refresh its

location area by extracting the joint part of its previous area and the newly obtained area.

At last, center of gravity is used to determine the final estimated positions of normal nodes

between line 13 and 16.

Note that Algorithm 5 is a general computation structure for localization with uncon-

trolled events. And further interpretations for this algorithm will be provided in later

sections concerning events other than the straight-line scan example .

3.3.3 LUE Advanced Design

This section presents system enhancements for two scenarios: (i) sensor nodes are randomly

deployed with high density; and (ii) a large number of events are available.

3.3.3.1 Event Generation Parameter MLE

This subsection introduces a method for further estimating the event generation parameter

based on maximum likelihood estimation (MLE).

77

Suppose that a node sequence (4 A 1 C 2 7 11 3 5 9 10 B 6 8) is obtained from a straight-

line scan event. Three anchors A, C, B divide the node sequence into four segments: {4},{1}, {2 7 11 3 5 9 10} and {6 8}. The size of each segment evaluated by number of nodes

is d1 = 1, d2 = 1, d3 = 7 and d4 = 2, respectively. So, the ratio among them is simply

d1 : d2 : d3 : d4 = 1 : 1 : 7 : 2.

A

Node Sequences: ( 4 A 1 C 2 7 11 3 5 9 10 B 6 8 )

d1 : d2 : d3 : d4 = 1 : 1 : 7 : 2

θ = (- π/2, π/3)

θC

B

A

C

B

θ

l1

l2

l3

l'1

l'2

l'3

S1

S3

S'1

S'3

(a) Scan angle with high probability

S1 : S2 : S3 : S4 ~ 2 : 1 : 8 : 2

(b) Scan angle with low probability

S'1 : S'2 : S'3 : S'4 ~ 1 : 5 : 4 : 4

S2

S4

S'2

S'4

Possible Scan 1 Possible Scan 2Scan Angle: π/6 Scan Angle: - π/6

Figure 3.49: Comparison Between Two Possible Scan Angles

With Algorithm 3, the scan angle is estimated to be within the range of θ = (−π/2, π/3),

for example. Now let’s look at two possible scan events with angle π/6 and −π/6 respec-

tively, as depicted in Fig. 3.49(a) and Fig. 3.49(b). Both of them are possible angles, because

they are within the range of θ. In Fig. 3.49(a), three dashed lines (l1, l2 and l3), which are

parallel with the possible scan line, split the map into four areas with size S1, S2, S3 and

S4, respectively. When normal nodes are uniformly distributed with a considerable density,

the number of nodes located in an area is supposed to be approximately proportional with

the size of area. Therefore, if the straight-line scan is conducted with a scan angle as that

in Fig. 3.49(a) (i.e., π/6), four segments in the node sequence should have a size ratio close

to S1 : S2 : S3 : S4, which is about 2 : 1 : 8 : 2 for this example in the figure. Similarly,

if the scan event has an angle close to the one in Fig. 3.49(b) (i.e., −π/6), the size ratio

among segments should be close to S′1 : S′

2 : S′3 : S′

4, which is approximately 1 : 5 : 4 : 4.

Comparing these two possible scans in Fig. 3.49(a) and Fig. 3.49(b), S1 : S2 : S3 : S4 is

much closer to d1 : d2 : d3 : d4 than that of S′1 : S′

2 : S′3 : S′

4. In other words, we can safely

claim that the hypothesized π/6 scan angle in Fig. 3.49(a) is more likely to be the real event

parameter. Extending this observation to general cases, the following relationship holds for

a node sequence with n anchors,

d1 : d2 : · · · : dn+1 ∼ S1 : S2 : · · · : Sn+1 (3.4)

Based on Eq. 4.13, a maximum likelihood estimation (MLE) can be applied to search

for a refined parameter range θ from θ with the highest probability. Algorithm 6 outlines

78

Algorithm 6: Event Generation Parameter MLE

input : A Node sequence NodeSeqEstimated event parameter θ

output: Maximum likelihood estimation θ

NodeRatio = GetNormalNodeRatio(NodeSeq) ;1

θ0 = LowBoundary(θ) ;2

repeat3

AreaRatioi = GetAreaRatio(θi) ;4

ρi = Likelihood(NodeRatio, AreaRatioi) ;5

θi = θi−1 + STEP ;6

until θi ≥ UpBoundary(θ) ;7

θ = SelectMaximum(ρ0, ρ1, · · · ) ;8

the computation structure. Line 1 gets segment ratio NodeRatio for NodeSeq, i.e., d1 :

d2 : · · · : dn+1 in Eq. 4.13. Line 2 to 7 compute the likelihood distribution within θ.

Specifically, starting from one boundary value θ0 at line 2, the area size ratio AreaRatioi

under parameter θi is computed at line 4, i.e., S1 : S2 : · · · : Sn+1 in Eq. 4.13. Then,

correlation coefficient ρi for θi is calculated between NodeRatio and AreaRatioi at line 5.

Line 6 prepares for the next loop by increasing θi with a predefined searching granularity

STEP . Finally, line 8 returns the refined range θ with maximum likelihood. Our evaluation

reported in Section 3.3.6 shows that Algorithm 6 can effectively improve the accuracy of

event generation parameter estimation while adding little extra cost.

3.3.3.2 Final Position MLE

Previous node sequences processing outputs a location area for each normal node. The last

step is to obtain a position point within the location area. One commonly used method-

ology is to apply the center of gravity of area as the final estimation. In our situation, if

abundant events are available, we can calculate the likelihood associated with each differen-

tiable position within the location area, and then select the one with maximum likelihood

as the final location estimation.

With a large number of randomly generated events, we may get identical node sequences

from multiple events. Identical node sequences can not contribute to localization in the basic

design. However, the appearance of duplicated node sequences embeds interesting statistical

information that can be used for inferring the position relationship among nodes.

Given one normal node, saying node 1, and two anchor nodes, saying anchor A and B,

the total number of permutations among them is P 33 = 6, and there exist three possible

structures for their ordering in a node sequence: (i) node 1 in the middle, e.g., node se-

quences look like (· · · , A, · · · , 1, · · · , B, · · · ) or (· · · , B, · · · , 1, · · · , A, · · · ); (ii) anchor

A in the middle; (iii) anchor B in the middle. Suppose that totally m node sequences are

79

obtained and among them the number of sequences following ordering structure (i), (ii) and

(iii) are M1,MA and MB , respectively, we have M1 + MA + MB = m.

1

A B

Node 1's location area

(a)

θ1 : θA : θB ~ M1 : MA : MB

1

θA

θ1

θB

A B

M1 : MA : MB = 11 : 10 : 12

Position with maximum likelihood

(b)

Center of Gravity

Figure 3.50: MLE for Final Position Selection

The key idea here is that location relationships among these three nodes determine

the ratio of M1 : MA : MB . Fig. 3.50 (a) shows an example for straight-line scan events.

According to the observation presented in section 3.3.2.1, if the scan angle is within θ1,

node 1 should be ranked between anchor A and B in the corresponding node sequence. The

scan angle has a range of (−π2 ,+π

2 ) , so the probability of obtaining a node sequence with

node 1 between anchor A and B is θ1

π , under the assumption of uncontrolled events with

uniform scan angle distribution. Similarly, the probabilities of getting a node sequence with

anchor A or anchor B in the middle are θA

π and θB

π , respectively. Therefore, with abundant

localization events, following equation holds statistically:

θ1 : θA : θB ∼ M1 : MA : MB (3.5)

Based on Eq. 4.14, likelihood computation can be done for every differentiable position

point in the location area of node 1. For example, as it is shown in Fig. 3.50(b), node 1 has

a location area depicted as a dashed rectangle. Suppose that there are three differentiable

position points, and from node sequences, we have M1 : MA : MB = 11 : 10 : 12, meaning

that θ1 : θA : θB should also be close to 11 : 10 : 12. For each position point, the likelihood

is calculated and illustrated by the darkness of the point, where a darker point owns higher

likelihood. From Fig. 3.50(b) we can see that the position point with maximum likelihood

is a better choice than the center of gravity for the final location estimation.

Eq. 4.14 gives location relationships between node 1 and a pair of anchors. In fact,

for each normal node, every pair of anchors in the node sequence can be used for such

maximum likelihood estimation. In general, if n anchors are available, there are C2n = n2−n

2

anchor pairs that can be utilized for likelihood computation. By accumulating likelihood

from all anchor pairs, the position point with maximum overall likelihood is chosen as the

final estimated position of the normal node.

Algorithm 7 gives the computation structure for final position MLE. Line 1 to 9 makes

80

Algorithm 7: Final Position Estimation MLE

input : All node sequences NodeSeqsThe location area of a normal node Area

output: Estimated position of this normal node Position

repeat1

AnchorPair = GetUnusedAnchorPair() ;2

StrucRatio = StrucRatio(NodeSeqs, AnchorPair) ;3

repeat4

P = GetUnprossedPositionPoint(Area) ;5

ρ = Likelihood(StrucRatio, AnchorPair) ;6

Accumulate(P , ρ) ;7

until all positions in the location area are processed ;8

until all anchor pairs are used ;9

Position = SelectMaximum(Area) ;10

use of each anchor pair and accumulates likelihood at every differentiable position point.

Specifically, line 3 calculates the ordering structure ratio StrucRatio (M1 : MA : MB in

Eq. 4.14) among the anchor pair obtained at line 2 and current normal node. Line 4 to 8

compute and accumulate the likelihood for each position point P within the location area

Area. Finally, line 9 selects the position with maximum likelihood in Area as the estimated

position of the node. Simulation results in later sections demonstrate that if sufficient

number of events are gathered, localization accuracy can be improved greatly with final

position MLE.

3.3.4 Overhead and Complexity Analysis

This section analyzes the overhead and computation complexity of the design. We empha-

size that our approach with uncontrolled events has two nice features:

• Localization with uncontrolled events eliminates sophisticated devices previously re-

quired for precise control over event generation and distribution.

• The system adopts an asymmetric architecture where resource constrained sensor

nodes only need to simply detect and report events.

On the other hand, timestamps for event detections have a compact footprint, and

can be efficiently piggybacked on normal traffic in the network to reach the sink where

localization is conducted only about node sequences processing. We discuss computation

complexity on sequence processing in the following.

In Algorithm 3, the complexity for event parameter estimation with a node sequence

containing n anchor nodes is O(n) (loop for O(n) effective estimation units). The cost for

one segment’s localization area searching with Algorithm 4 is O(S), where S is the size of

81

grid map. As a result, Algorithm 5 for the basic design has a complexity of O(m · (O(n) +

O(n) · (O(S) + i · O(S))) + i · O(S)), or equivalently,

O(m · n · i · S) (3.6)

where m is the number of localization events, n is the number of anchor nodes, i is the

number of normal nodes, and S is the map size.

In terms of the advanced design, Algorithm 6 has a complexity of

O(c · n) (3.7)

where O(n) comes from line 5 in Algorithm 6 for likelihood computation, and c =⌈

θSTEP

⌉

is determined by the search granularity STEP and the range of θ from the basic design.

Note that c is also an integer and c ≥ 1.

The complexity of final position MLE for one normal node using Algorithm 7 is O(n2−n2 ·

(m+O(S))+O(S)), where line 3 in Algorithm 7 contributes the factor m for scanning all m

sequences, while the cost for correlation coefficient computation at line 6 is considered O(1)

since it is not related to anchors, events and map size. One remark here is that the possible

localization area of a normal node mostly is significantly smaller than the map size S, so

the above expression is really an overestimation. In short, Algorithm 7 has a complexity as

(or less than)

O(n2 · (m + S)) (3.8)

When both improvements are implemented on top of the basic design, the overall com-

plexity can be obtained by embedding expression (3.7) and (3.8) in (3.6) as

O(m · (n + O(c · n)) · i · S) + O(i · n2 · (m + S)) (3.9)

or equivalently,

O(m · c · n · i · S + i · n2 · (m + S)) (3.10)

In practical systems, normally we have m >> n (much more normal nodes than anchors),

and S >> n (the pixels in the grid map is far more than in-field anchors). As a result, the

cost in (7) essentially can be rewritten as

O(m · c · n · i · S) (3.11)

Proof. If m ≥ S, we have i · n2 · (m + S) ≤ i · n2 · 2m, and expression (7) can be rewritten

as O(m · c · n · i · S + i · n2 · m), namely, O(m · c · n · i · S) for S >> n.

82

Similarly, if m ≤ S, we have i · n2 · (m + S) ≤ i · n2 · 2S, and expression (7) can be

rewritten as O(m · c · n · i · S + i · n2 · S), namely, O(m · c · n · i · S) for m >> n.

From above two cases, O(m · c · n · i · S) indicates the overall complexity. �

We can observe that the computation complexity has a liner relationship with each

individual factor in the system, and considering that the calculation is done asymmetrically

out of resource constrained sensor nodes, the computation cost for the proposed design is

far from prohibitive.

3.3.5 Discussion on Wave Propagation Events

So far, localization with uncontrolled events is described solely in the context of straight-line

scan event. In fact, algorithms proposed in previous sections are conceptually independent

of specific type of events, as long as node sequences can be obtained. This section gives a

brief explanation for wave propagation based events (e.g., ultrasound propagation, air blast

shockwave events, etc.), which are polar coordinate equivalences of straight-line scans in

the Cartesian coordinate system. Without losing generality, we have made the following

assumptions:

• Wave propagates uniformly in all directions and thus it has a circle frontier surface.

A certain distortion in wave propagation is tolerable since node sequence processing

does not rely on a rigid time-spatial relationship. If any directional wave is used, the

propagation frontier surface can be modified accordingly.

• Under the situation of line-of-sight, we allow obstacles to reflect or deflect the wave.

Reflection and deflection are not problems because each node reacts only to the first

detected event. The only thing a system needs to maintain is a safe interval between

two successive localization events.

• We assume that background noise exists, and thus band-pass filter can be used to

listen to a particular signal frequency. This reduces the chances of false detection.

The event generation parameter here is the source location of the event, because the

distance between each node and the event source determines the rank of the node in cor-

responding node sequence. In the following, we explain aforementioned algorithms for

wave-based events.

3.3.5.1 Basic Design with Wave-based Events

Fig. 3.51(a) gives an example for event generation parameter estimation using Algorithm 3

in the context of wave propagation. As shown in the figure, anchor pair ordering (A C) tells

that wave propagation reached anchor A earlier than anchor C. Under the assumption of

uniform propagation speed in all directions, anchor A should have shorter distance to the

83

event source than that of anchor C. In other words, the event source for this node sequence

should locate to right of dashed line l1 that perpendicularly bisects the doted line between

anchor A and C. Similarly, ordered pair (C B) indicates that the event source located to

the left of dashed line l2 that perpendicularly bisects the doted line between C and B. By

extracting the joint area, we can obtain a location area for the event source, shown as a

shaded region in the figure. Based on geometry, for △ACB, three bisect lines joint at one

point. Thus, anchor pair (A B) can hardly further contribute to parameter estimation. In

fact, for wave based events, only two consecutive anchors in anchor subsequence forms an

effective estimation unit.

Node Sequences: 3 A 1 6 4 8 C 2 B 7 5

Anchor Ordering: A C B

Estimated Source Location Area of the Event

1 A

2

3

B

C

4

6

75

8

l1

l2

l3

(a) Estimate Event Source

Node Sequences: 3 A 1 6 4 8 C 2 B 7 5

Testing P1 and P2

P1 is a possible location for node 3

P2 is not a possible position for node 3

1 A

2

3

B

C

4

6

75

8

P1P2

l4l5

(b) Find Segment Area

Figure 3.51: Basic LUE Design with Wave Propagation Events

Fig. 3.51(b) shows a simple example for segment location area finding using Algorithm 4.

For node 3 in the first segment of node sequence, its distance to the event source must be

shorter than that from anchor A. Investigating position point P1 for instance, the event

source needs to be located to the left of dashed line l4 to satisfy the above requirement. P1

is a possible position point for node 3 since the hypothetic location area for event source

has overlapping part with the estimated area (the shaded region). While for position point

P2, the event source needs to be located to the right of dashed line l5, where there is no

overlapping with the shaded region, therefore P2 is not possible for node 3.

3.3.5.2 Advanced Design with Wave-based Events

Fig. 3.52 depicts likelihood evaluation for position point P3 with Algorithm 6 (i.e., event

generation parameter MLE). If the event source located at P3, the size of location areas

for segment {3}, {1 6 4 8}, {2} and {7 5} shall be S1, S2, S3 and S4, respectively, as shown

in the figure (dash-dot curve shows the frontier of the wave). The ratio of normal nodes

among all segments in the node sequence is d1 : d2 : d3 : d4 = 1 : 4 : 1 : 2, inconsistent with

S1 : S2 : S3 : S4 ≈ 6 : 1 : 10 : 4. Therefore, the event source is unlikely to be located at P3.

Fig. 3.53 depicts the idea of final position MLE with wave propagation events. Position

point P4 is evaluated for node 1. Anchor A, B and P4 form a triangle whose perpendicular

84

Node Sequences: 3 A 1 6 4 8 C 2 B 7 5

d1 : d2 : d3 : d4 = 1 : 4 : 1 : 2

S1 : S2 : S3 : S4 ≈ 6 : 1 : 10 : 4

P3 is unlikely to be the

event source location

1A

2

3

B

C

4

6

75

8

P3

S1

S2

S3S4

Figure 3.52: Event Generation Parameter MLE with Wave Propagation Events

A B

P4

S(A 1 B)

S(A B 1) S(B A 1)

S(B 1 A)

S(1 A B) S(1 B A)

Node 1's Location Area

S(1 A B) : S(A 1 B) : S(A B 1) : S(B A 1) : S(B 1 A) : S(1 B A)

Figure 3.53: Final Location MLE with Wave Propagation Events

bisect lines divide the map into 6 parts: S(1AB), S(A1B), S(AB1), S(BA1), S(B1A) and S(1BA).

Each part corresponds to one of the possible ordering structures of three nodes. For example,

if the event source located in S(1AB), the node sequence should follow the structure as

(· · · 1 · · ·A · · ·B · · · ). When a large number of events are accumulated, the percentage ratio

among ordering structures should be proportional to the sizes of different parts. Thus,

Algorithm 7 can be applied to find out the final position with maximum likelihood.

3.3.6 Simulation Evaluation

We evaluated the design with both simulation and testbed implementation. In the simula-

tion, anchors and normal nodes are deployed randomly with uniform density. Straight-line

scan events are generated with random scan angles and directions. The statistics interested

include (i) the accuracy of event generation parameter estimation (i.e., the range of θ );

(ii) the accuracy of normal node localization, where the localization error is defined as the

offset between estimated position and the ground truth position. All statistics reported

were collected from 50 runs for high confidence. Table 4.4 lists the default simulation setup.

Table 3.2: Default Simulation Configurations for LUE

Parameter Description

Field Area S 100×100 (in grid unit)

Event Type Straight-line Scan

Number of Anchor Nodes 3 (Default)

Number of Events 6 (Default)

Number of Normal Nodes 100 (Default)

Random-Seed Loop 50 runs

85

3.3.6.1 Simulation for the Basic LUE Design

Simulation evaluation starts with the basic design. Firstly, we investigated the impacts of

number of anchor nodes n and number of localization events m to event generation param-

eter estimation and the localization accuracy. After that, two advanced designs applying

MLE are compared with the basic design.

2 4 6 8 10 12 14 16 18 20 220

20

40

60

80

100

120

140

Scan Angle Estimation VS Number of Anchors

Number of Anchors

E

sti

ma

ted

An

gle

Ra

ng

e(i

n d

eg

ree

s)

Averaged Max Angle Range

Averaged Mean Angle Range

(a) Angle Range vs. Number of Anchors

2 4 6 8 10 12 14 16 18 20 220

10

20

30

40

50

60

Localization Error VS Number of Anchors

Number of Anchors

L

oc

ali

za

tio

n E

rro

r(in

un

its

)

Averaged Max Error

Averaged Mean Error

(b) Error vs. Number of Anchors

Figure 3.54: Impact of the Number of Anchors for Basic LUE Design

2 4 6 8 10 12 14 16 18 20 220

20

40

60

80

100

120

140

Scan Angle Estimation VS Number of Events

Number of Events

E

sti

ma

tio

n E

rro

r(in

de

gre

es

)

Averaged Max Error (3 anchors)

Averaged Mean Error (3 anchors)

Averaged Max Error (6 anchors)

Averaged Mean Error (6 anchors)

(a) Angle Range vs. Number of Events

2 4 6 8 10 12 14 16 18 20 220

10

20

30

40

50

60

Localization Error VS Number of Events

Number of Events

L

oc

ali

za

tio

n E

rro

r(in

un

its

)

Averaged Max Error (3 anchors)

Averaged Mean Error (3 anchors)

Averaged Max Error (6 anchors)

Averaged Mean Error (6 anchors)

(b) Error vs. Number of Events

Figure 3.55: Impact of the Number of Events for Basic LUE Design

Impact of the Number of Anchors

In this experiment, we evaluate the scan angle estimation and localization error under

different number of anchors from 3 to 21 in steps of 2. The number of events was 6 by default.

In the basic design, anchor nodes contribute to event parameter estimation. Thus, we can

expect that better parameter estimation can be achieved with more anchors. Fig. 3.54(a)

confirms our expectation and shows that as the number of anchors increases, estimated

angle range shrinks quickly. Besides, more anchor nodes help to divide the whole area into

86

more small parts, further enhancing localization accuracy. Fig. 3.54(b) verifies that with

more anchor nodes, localization error gets reduced greatly.

Impact of the Number of Events

In this experiments, we investigated the impact of number of events. The simulation

is setup up with 3 anchors and 6 anchors respectively. Since event generation parameter

estimation is determined by anchor nodes alone, Fig. 3.55(a) shows that estimation accuracy

keeps stable under different number of events. However, with more events, each normal

node has more combination of location areas, thus smaller location area is possible to be

obtained. Fig. 3.55(b) confirms this analysis and shows that with increasing number of

randomly generated events, the system error also gets reduced. We can conclude from

this figure that either using more anchors or accumulating localization events can improve

localization accuracy.

3.3.6.2 Event Generation Parameter MLE

In this experiment, event generation parameter MLE (Algorithm 6) is investigated. Fig. 3.56(a)

illustrates a comparison of localization errors between the basic design and the design with

event generation parameter MLE. From this figure, we can see that (i) for the basic design,

the number of normal nodes does not affect the mean error (circle curve); (ii) for improved

algorithm using MLE, with increasing number of normal nodes, the mean error follows a

trend of being reduced (star curve), e.g., the mean error got reduced by more than 30%

from that of the basic design for 1000 normal nodes; (iii) although both maximum errors

increase with more normal nodes, design applying MLE reduced the averaged maximum

error from that of the basic design by more than 25%.

101

102

103

0

10

20

30

40

50

60

Localization Error VS Number of Normal Nodes

Number of Normal Nodes

L

oc

ali

za

tio

n E

rro

r(in

un

its

)

Averaged Max Error without MLE

Averaged Max Error with MLE

Averaged Mean Error without MLE

Averaged Mean Error with MLE

(a) Error vs. Number of Normal Nodes

101

102

103

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Unlocalized Ratio VS Number of Normal Nodes

Number of Normal Nodes

U

nlo

calized

No

de R

ati

o

Unlocalized Node Ratio with MLE

(b) Unlocalized Normal Nodes

Figure 3.56: Effectiveness of Event Generation Parameter MLE

87

Algorithm 6 tries to reduce the estimation uncertainty opportunistically. However some-

times the output from MLE is not sufficiently accurate and the shrunk range θ might fail to

cover the real event generation parameter. This will bring in a side-effect that some normal

nodes can not be localized (be erased from the map). Fig. 3.56(b) shows the percentage of

unlocalized normal nodes in the simulation. Although the curve has some fluctuation due

to random node deployment for each simulation loop, we can clearly see that with increas-

ing number of normal nodes, the percentage of unlocalized nodes gets reduced significantly,

e.g., from 18% to as low as 2%. The credit here goes to the “power of large numbers” that

makes the parameter estimation more accurate in a statistic sense.

The above simulation confirms that event generation parameter MLE (Algorithm 6)

enhances system performance, especially with high node density.

3.3.6.3 Final Position MLE

In this experiment, final position MLE (Algorithm 7) is investigated. Event generation

parameter MLE (Algorithm 6) is turned off to better understand the effectiveness of final

position MLE.

Fig. 3.57 shows the impact of number of events to both the basic design and the design

with final position MLE. For the basic design, with increasing number of events, localization

error gets reduced statistically as shown by the left part of the square curve in the figure.

However, after certain number of events (close to but not reach 102), the system accuracy

can hardly be further improved by simply accumulating more events (the square curve

becomes flat after 102). This is because all possible combinations of orderings among a

normal node and anchors in node sequences have been exhausted, and repeated events

fail to bring in additional information. While for the design applying final position MLE,

at the beginning, system error can be worse than that of the basic design as shown by

the diamond curve in the figure. This is because final position MLE needs a considerable

101

102

103

104

105

0

5

10

15

20

25

30

35

Localization Error VS Number of Events

Number of Events

L

oc

ali

za

tio

n E

rro

r(in

un

its

)

Averaged Mean Error without MLE

Averaged Mean Error with MLE

Figure 3.57: Effectiveness of Final Position MLE

88

number of events to do a good estimation; otherwise, the estimation is highly possible to

be biased. But with increasing number of events, final location MLE effectively improved

the localization performance continuously, as shown in the figure.

One remark here is that unlike event generation parameter MLE (Algorithm 6), final

position MLE (Algorithm 7) does not have the side-effect of erasing normal nodes from the

map. This is because Algorithm 7 essentially selects the most likely position for a normal

node from its location area obtained from the basic design, but without affecting location

area computation.

From above simulation results, we can see that final position MLE (Algorithm 7) allows

better localization performance by accumulating events (node sequences). In reality, this

feature provides us a nice potential option of localizing randomly deployed sensor nodes

gradually by accumulating long-term ambient events.

3.3.6.4 Simulation Summary

Simulation results demonstrate that: (i) sensor node localization can be accomplished with

uncontrolled events; (ii) increasing number of anchor nodes and localization events both

improve system performance; (iii) advanced designs including event generation parame-

ter MLE and final position MLE provide better localization accuracy under situations of

relatively high nodes density and abundant events, respectively.

3.3.7 Test-bed Evaluation

This section reports system evaluation results of the proposed LUE design on Mirage in

Fig. 3.26. An introduction about the testbed can be found in Section 3.2.8.

In our evaluation, 41 MICAz motes were mounted on the testbed, and we implemented

Java code for generating straight-line light beam scan events with random scan angles,

directions and line speeds. We also implemented TinyOS-based code at the mote side

with functions including light event detection, time synchronization (FTSP [117]), wireless

reporting to a sink node, etc.

3.3.7.1 Localization Results

In the experiment, 6 nodes were selected as anchor nodes with known position coordinates

in the testbed, while the remaining 35 nodes work as normal nodes to be localized. Syn-

chronization timestampes were flooded within the network from a sink node attached to the

event generator with a period of 60 seconds to realize approximately millisecond level time

accuracy. A total number of 10 light beam scan events of on-board line-speed of either 4.3

or 8.6 feet/s were generated with randomly angles and scan directions. And thus 10 node

sequences were collected and processed at the sink.

89

0 50 100 150 2000

10

20

30

40

50

60

70

80

Mean Error: 0.84 feet

Max Error: 3.91 feet

X axis (in 0.1 feet)

Y

axis

(in

0.1

feet)

Testbed Layout

Anchor Node

True Position

Estimated Location

Figure 3.58: Testbed LUE Result Illustration

0 5 10 15

0

1

2

3

4

5

6

7

8

Distance along event propagation (in feet)

Tim

e G

ap

(in

s)

scan at 4.3 feet/s

scan at 8.6 feet/s

Figure 3.59: Time Gap vs. Distance

0 0.5 1 1.5 2 2.5 30

1

2

3 (b) Scan at 8.6 feet/s

Distance along event propagation (in inch)

Flip

s

0 0.5 1 1.5 2 2.5 30

1

2

3 (a) Scan at 4.3 feet/s

Distance along event propagation (in inch)

Flip

s

Figure 3.60: Node Pair Flip vs. Distance

Fig. 3.58 shows the results obtained from the basic design. The whole area is modeled

as a 240 × 80 grid map since the testbed has a size of 24 feet by 8 feet. In the figure,

squares stand for anchor nodes, and circles depict normal nodes. An arrow origins from the

true position of each normal node and points to its estimated location marked with a cross.

In our experiment, 33 out of 35 nodes get localized with average and maximum error of

0.84 feet and 3.91 feet, respectively. Fig. 3.58 tells that the proposed localization algorithm

successfully accomplished sensor node positioning with only uncontrolled scan events.

3.3.7.2 Discussion on Node Pair Flip

The propagation speed of localization events has an important impact on system cost, since

the faster of events, the higher accuracy of time synchronization is required for a node

sequence with mostly correct orderings. Especially, when the distance between a pair of

nodes is short (along the direction of event distribution), incorrect ordering occurs, i.e.,

node pair flip that is explained and addressed for MSP in Section 3.2.6. Node flip can ruin

the localization algorithm by eliminating nodes from the map. This explains why 2 nodes

were missing in Fig. 3.58.

90

To better understand this problem, we analyzed event detection timestamps from pre-

vious scan events. Fig. 3.59 shows time gaps from all node pairs and corresponding true

distances (a node pair contributes multiple dots to this pattern, because they have different

projected distances under different scan directions). This linear pattern tells that orderings

in our node sequences should be mostly correct for either 4.3 or 8.6 feet/s scans, which

explains the reasonable localization results in Fig. 3.58. Fig. 3.60 gives a histogram for

node flips happened respect to various distance values. From this figure, we can see that

faster scans brought in not only increasing number of flips, but also longer-distance flips.

Two approaches might be used to alleviate the node flip problem: (i) better time syn-

chronization (for example, for sound wave propagation based events); and (ii) conservative

location area estimation that achieves node localization by sacrificing overall accuracy. We

consider this issue as an important part of our future work.

3.3.7.3 Discussion on Localization Performance

In this section, we give a simple comparison among three event-driven localization methods:

(i) Spotlight [192] with accurately controlled events, (ii) MSP in Section 3.2 with semi-

controlled events, and (ii) LUE with uncontrolled events, as listed in Table 3.3.

Table 3.3: Comparison of Event-driven Localization Methods

Method Description No. Event No. Anchor Accuracy Unlocalized

Spotlight precise control 2 (costly ) none 0.26 (0.30) feet NA

MSP semi-controlled 8 (fair) 6 0.37 (1.32) feet 1 out of 40

LUE uncontrolled 10 (easy) 6 0.84 (3.91) feet 2 out of 35

The data in Table 3.3 are based on line scan events. Specific values came from either

original publication or our evaluation with Mirage testbed. Specifically, Spotlight used 2

events with 17.5 cm event size [192]. MSP used 8 events (8.6 feet/s) and LUE employed 10

events. Both MSP and LUE applied 6 anchors. For the accuracy field, first values are mean

errors, and parenthesized values are max errors. From this table, we can see that three

methods shall be applied for different situations. For high accuracy, precisely controlled

events are needed; while for applications emphasizing on system flexibility and convenience,

the proposed design with uncontrolled events is a better choice.

3.3.8 Summary and Remarks on LUE

We demonstrate that sensor nodes can be localized using uncontrolled events (LUE) with

two steps: (i) estimate the event generation parameter from the ordering of in-field anchor

nodes; and then (ii) compute the location area for each normal node according to its rank

in the node sequences. Two maximum likelihood estimation (MLE) based improvements

are proposed for situations of high node density and abundant events, respectively. The

design is verified and evaluated through analysis, extensive simulation as well as testbed

91

experimentation. Evaluation results reported that with only uncontrolled events, node

localization is achievable with great flexibility and ultra low cost.

Sensor node localization using uncontrolled events provides us a potential option of using

ambient natural events for positioning purpose. As ongoing and future work, we plan to

further evaluate our design with different event modalities, such as sound wave propagation

in outdoor environments with noise. We would also like to investigate design methodologies

of the network, for instance, optimal anchor placement, so as to further enhance the system.

92

Chapter 4

Localization and Tracking with

Signature Distance

4.1 Chapter Introduction

Another major branch of range-free localization is to make use of wireless connectiv-

ity [178, 179, 166, 183]. Those methods have demonstrated great convenience for network

deployment, flexible and scalable system configuration, as well as the nice support for ultra-

low-cost sensor nodes. Nevertheless, most of the connectivity based localization approaches

can not provide high accuracy performance. This is because the sub-hop proximity in-

formation can hardly be caught and described with hop-count distance. Interestingly, our

empirical study found that localization depending only on connectivity may actually under-

utilize the proximity information embedded in neighborhood sensing, leading to degraded

localization accuracy.

In response to this limitation, in this chapter we present the idea of signature distance

(SD) and its revised version named regulated signature distance, or RSD for short, as met-

rics for describing the proximity information among 1-hop neighboring nodes. The design

of signature distance, for the first time, enables quantifying distance relationships among

neighboring nodes with sub-hop resolution in a range-free manner. It is demonstrated that

the RSD can be conveniently embedded in connectivity-based localization algorithms to

help improve localization performance with little additional overhead (LBC in Section 4.2).

We then extend the concept of localization with node sequence processing in Chapter 3

and the new idea of signature distance in Section 4.2 to mobile tracking applications, by

proposing a sequence based tracking (SBT) framework in Section 4.3. By converting the

tracking problem from traditional sequential localization to a maximum likelihood shortest

path searching in a graph, SBT demonstrates robust range-free tracking without movement

modeling. In addition, it provides a useful layer of abstraction that enables sensing modality

integration and a generic and flexible system design.

93

4.2 LBC: Range-free Localization Beyond Connectivity

Our work of LBC (localization beyond connectivity) is motivated by the observation that

localization by means of mere connectivity [166, 177] may underutilize the proximity in-

formation available from neighborhood sensing. Although radio signal strength (RSS) is

considered irregular in many situations due to the unknown radio propagation loss, multi-

path effects, hardware discrepancy, antenna issues and so forth [216, 217, 218, 221], our

empirical study shows that in the outdoor open-air scenario, radio signal strength weakens

approximately monotonically with the physical distance, especially from the viewpoint of a

single node, where RSS might provide some useful distance-related information about which

neighboring node is closer and which is further.

Following this finding, we propose the idea of regulated signature distance, or RSD

for short, a metric of proximity among 1-hop neighboring nodes. RSD brings in a novel

range-free approach to extracting relative distance information from neighborhood order-

ings that can be obtained easily from simple sensing and serve as unique high-dimensional

location signatures for sensor nodes in the network. With little extra overhead, RSD can

be conveniently embedded in many connectivity-based localization algorithms to greatly

improve accuracy. We augmented three such localization algorithms, i.e., MDS-MAP [166],

DV-Hop [177], RPA [179], with RSD, and evaluated in two outdoor test-bed systems: an

850-foot-long linear network with 54 MICAz motes, and a regular 2-dimensional network

covering an area of 10000 square feet with 49 motes. System evaluation showed noticeable

performance gains including eliminating estimation ambiguity and reducing localization er-

rors by as much as 35%. In addition, extensive simulation demonstrated the effectiveness

of our design for large-scale networks and revealed an interesting feature of robustness to

the spatially unevenly distributed radio path loss.

In the following, Section 4.2.1 explains the motivation with empirical data. Section 4.2.2

gives the main design. Section 4.2.3 briefs three range-free protocols on which we evaluated

our work. Section 4.2.4 analyzes the cost of applying the proposed design. Section 4.2.5 re-

ports outdoor test-bed experiments. Section 4.2.6 discusses results from simulation. Finally,

Section 4.2.7 summarizes and remarks on the LBC design.

4.2.1 Empirical Data as Motivation

The work of LBC is motivated by our experimental data showing that in the outdoor

environments,

• Network-wide monotonic relationship between radio signal strength and physical dis-

tance does not hold, but

• Per-node monotonic RSS-Distance relationship holds well, i.e., any single node’s RSS

sensing results for its neighboring nodes can be used as an indicator for the relative

94

“near-far” relationship among neighbors.

In the following, we first explain results from a preliminary test, and then provide data

obtained from large-scale outdoor experiments for verification.

4.2.1.1 Preliminary Experiments

Fig. 4.1 shows RSS sensing results from MICAz nodes in several outdoor experiments con-

ducted in two types of environment: grass land and parking lot. In the test, we placed 9

sender nodes at different distances from a receiver node. Each sender node broadcast 100

packets with 0dBm sending power, and the receiver node recorded the RSS upon receiv-

ing the packet. In the grass-land scenario, we performed the test twice with two different

receiver nodes placed at the same location and without moving or switching sender nodes

(Grass Land Test1 and Grass Land Test 2, respectively). In the parking lot scenario, identi-

cal sets of nodes were tested during day-time (Parking Lot Test 1) and at night (Parking Lot

Test 2). Tests were conducted multiple times, and results did not show significant changes

in the overall shapes of the curves shown in Fig. 4.1.

0 10 20 30 40 50 60 70 80−90

−85

−80

−75

−70

−65

−60

−55

Distance (in feet)

RS

S (

in d

Bm

)

Grass Land Test 1

Grass Land Test 2

Parking Lot Test 1

Parking Lot Test 2

Figure 4.1: Experimental Results: RSS vs. Distance

Fig. 4.1 tells that at the system level, using absolute values of RSS for distance estimation

is not reasonable since identical RSS values may correspond to different distances. However,

for each individual curve (i.e., from the viewpoint of a single node), RSS values mostly

decreased monotonically with increasing distance, conveying information about relative

“near-far” relationships among 1-hop neighbors.

4.2.1.2 Large-scale Experiments

We then conducted large-scale outdoor experiments with two types of networks to verify

the phenomena found in the preliminary test. The first experiment was a linear network

containing 54 MICAz nodes with a 16-foot intermediate distance between adjacent nodes

covering a 850-foot length along a road. In the second experiment, we constructed a regular

2D network with a 7 × 7 grid-shaped layout including 49 nodes occupying an open-air

95

0 16 32 48 64 80 96 112 128 144−100

−80

−60

−90dBm

↓

RSS vs. Physical Distance in Linear Network

Distance Between Node Pairs (in feet)

R

SS

(in

dB

m)

(a)

0 16 32 48 64 80 96 112−100

−80

−60

−90dBm

↓

RSS vs. Physical Distance in Regular 2D Network

Distance Between Node Pairs (in feet)

R

SS

(in

dB

m)

(b)

Figure 4.2: Empirical Date for System Level RSS vs. Physical Distance

parking lot area of 10000 square feet. The setup of the large-scale experiments will be

further detailed in Section 4.2.5.

Fig. 4.2 and Fig. 4.3 report the empirical data obtained from the two test-beds. Fig. 4.2(a)

and Fig. 4.2(b) plot the sensed RSS values for each pair of nodes against the distance be-

tween them in the linear network and the regular 2D network, respectively. These two

figures verify that monotonic RSS-distance relationship does not hold for the whole net-

work. In both the linear network and the regular 2D network, on one hand, RSS may

vary dramatically for identical distance. For example, as shown in Fig. 4.2(b), RSS ranges

from -60 dBm to -90 dBm for a 16-foot distance in the 2D network. On the other hand, a

single RSS value may correspond to a wide range of distances. For instance, as shown in

Fig. 4.2(a), -90 dBm could range from 32 feet to 112 feet in the linear network; even worse,

-90 dBm RSS covers almost all of the distance spectrum, i.e., from 16 feet to 112 feet, in

the 2D network showing in Fig. 4.2(b).

However, examining the data from the viewpoint of a single node tells a different story.

For any node, say ui, we can obtain an ordered node list, say A, by listing ui’s 1-hop

neighbors according to their RSS values sensed at ui in decreasing order; and another node

list, say B, by ordering ui’s 1-hop neighbors with increasing physical distance. Ideally, if the

sensed RSS decreases monotonically with increasing distance, A and B should be identical.

We define the similarity between two lists A and B as the percentage of accordant node

pairs between them. For example, let A = (u1, u2, u3) and B = (u1, u3, u2), then {u1, u2}is an accordant node pair between A and B since node u1 is ordered ahead of u2 in both

A and B; while {u2, u3} is not since their ordering gets reversed from A to B. We can see

that if A and B are consistent with their similarity close to 1, the monotonic feature holds.

Fig. 4.3 shows the similarity results for all nodes in two test-beds. We can see from

Fig. 4.3(a) that in the linear network, most of the nodes have a similarity close to 1 (the

minimum, mean and maximum similarities are 0.86, 0.96 and 1, respectively). It means

96

0 5 10 15 20 25 30 35 40 45 50 550

0.5

1

RSS Ordering vs. Distance Ordering in Linear Network

node ID

S

imil

ari

ty

(a)

0 5 10 15 20 25 30 35 40 45 500

0.5

1

RSS Ordering vs. Distance Ordering in Regular 2D Network

node ID

S

imil

ari

ty

(b)

Figure 4.3: Empirical Date for the Monotonicity from Each Node’s Point of View

that in the linear network, from single node’s point of view, RSS values for 1-hop neighbors

are approximately monotonic with the distance. This finding still holds for the 2D regular

network as shown in Fig. 4.3(b), where the minimum, mean and maximum similarities are

0.81, 0.88 and 0.96, respectively.

Above experiments confirm that the monotonic RSS-distance relationship does not hold

at the system level, but approximately holds from the viewpoint of a single node.

4.2.1.3 Analysis and Discussion

In addition to the physical distance between two nodes, there are many factors that affect

RSS sensing results. Table 4.1 lists some major aspects. We marked an aspect with a “√

”

if pre-deployment engineering efforts could possibly be applied to reduce its impact, or a

“×” if it would be hard or costly to address.

Table 4.1: Major Factors Affecting RSS Sensing

Types of Factors P

RF Transmit Parameters: Sending Power, Carrier Frequency, Modulation . . .√

Antenna Issues: TX/RX Gain, Radiation Pattern, Orientation, Height . . .√

Random Noise: Interference, Mobile Effects, Electronic Pulse . . .√

Propagation Path Loss: Terrain, Vegetation, Obstacle, Magnetic Field . . . ×Node-level Sensing Discrepancy: LNA, ADC Ref. Voltage, Ground Noise . . . ×

At the sender side, besides the sending power, the carrier frequency, modulation, baud

rate and etc. determine the band-width, center frequency and spectrum shape [221], which

all affect the RSS at the receiver side. Most of those parameters can be configured with

small offset errors and maintained relatively stable during the runtime. Antenna issues such

as isotropic gain, orientation and etc. can also be carefully engineered in the design phase.

For transient random noise, traditional filtering methods are able to help reduce its impact.

97

All of the above are considered addressable without significant in-field calibration.

On the contrary, unpredictable environmental factors are much harder to handle. For

example, radio path loss is unknown and costly to profile in most cases since it is temporally

dynamic and spatially unevenly distributed. Another difficult issue is the sensing hardware

discrepancy among different nodes. For example, a tiny bias of the ADC reference voltage

or small variance of LNA (low noise amplifier) gain caused by different ground noise levels,

may lead to different RSS values at two nodes, even when their received signal strengths are

equivalent. Runtime sensing discrepancy among nodes is caused by many dynamic reasons

and per-node in-field calibration could be very costly.

The above two “×” factors are hard to address in a deployed system, however, from the

viewpoint of a single node, their impacts could be less severe. Firstly, a 1-hop neighborhood

area is much smaller than the whole region covered by the network, so one node’s local

sensing alleviates the problem of spatially unevenly distributed path loss. In addition, RSS

from a single node’s sensing avoids the issue of node-level receiver side hardware discrepancy.

Therefore, as confirmed by our empirical data, the monotonic RSS-distance relationship

holds much better in the case of one node.

Unfortunately, this heuristic correlation is not utilized by previous localization methods

based on mere connectivity, where only a binary “1” or “0” is evaluated for either connected

or not, resulting in a degraded system accuracy.

4.2.2 Design: a Relative Distance

In this section, starting from defining neighborhood ordering as a unique position-dependent

high-dimensional signature for each node in the network, we present the design of a range-

free relative distance for extracting the proximity information among 1-hop neighboring

nodes from each node’s individual sensing results.

4.2.2.1 Neighborhood Ordering as a Signature

Given the RSS sensing results for neighboring nodes, a node can obtain a neighborhood

ordering with two steps:

• Sorting its 1-hop neighbors according to their signal strength by decreasing order, and

• Adding itself as the first element in the sorted node list.

A simple example is shown in Fig. 4.4. In this figure, graph G on the left illustrates the

connectivity of the network. On the right, each node generates a node list starting with

itself and containing all its 1-hop neighbors which are ordered by decreasing signal strength,

i.e., by increasing distance in an ideal case.

98

1

2

6

3

4

5

Connectivity Graph G Example �eighborhood Ordering

Node 1 S1 : 1 6 2 4 5 3

Node 2 S2 : 2 1 6 3

Node 3 S3 : 3 2 1

Node 4 S4 : 4 5 1 6

Node 5 S5 : 5 4 6 1

Node 6 S6 : 6 1 5 2 4

Figure 4.4: Neighborhood Ordering

For any node ui, we consider its neighborhood ordering Si as a high-dimensional signa-

ture of the node in the network. Si has a vector format and contains all 1-hop neighbors of

node ui with three important features:

• Si is unique for each node ui.

• Si is position-dependent. Si embeds location-related information on both connectivity

and proximity.

• Si is obtained without ranging.

For the sake of clarity, in the following design part, we first use ideal neighborhood

orderings for conveying ideas. Namely, Si is consistent with the ordering according to

physical distance. Later sections will verify the effectiveness and robustness of our design

in practical noisy scenarios through both test-bed and simulation experimentation.

4.2.2.2 SD: Signature Distance

The high-dimensional signatures of sensor nodes can be obtained easily via local signal

strength sensing. In this section, we explain the concept and rationale of signature distance

(SD) which quantifies the difference between two high-dimensional signatures. SD is the first

step toward a relative distance that effectively reflects the physical distance relationships

among neighboring nodes in the network.

Formation, Definition and Calculation of SD

Say that a pair of nodes um and un get flipped between two signatures Si and Sj, if the

ordering of um and un in Si gets reversed in Sj. For example, as shown in Fig. 4.5, the

ordered node pair {1, 6} in S2 = (2, 1, 6, 3) gets reversed to {6, 1} in S5 = (5, 4, 6, 1).

S2 : 2 1 6 3 S2 S5

S5 : 5 4 6 1 1 6 6 1

Figure 4.5: 1 Explicit Node-Pair Flip

99

There are three types of potential node-pair flips between two signatures Si and Sj : (i)

explicit flip, (ii) implicit flip, and (iii) possible flip. If node um and un appear in both Si

and Sj, then we can easily tell whether this node pair gets flipped or not, as the example

shows for node pair {1, 6} in Fig. 4.5. This type of flip is called explicit flip. Implicit flips

and possible flips are somewhat tricky, as explained in the following with examples.

S’2

S’5

S’2 S’5 S’2 S’5 S2

S5

Figure 4.6: 10 Implicit Node-Pair Flips

As shown in the left part of Fig. 4.6, S2 and S5 have different sets of node elements. For

example, S2 = (2, 1, 6, 3) contains node 2 while S5 = (5, 4, 6, 1) does not. In this case, many

node pairs in S2 do not have corresponding counterparts in S5. For instance, {2, 1}, {2, 6}in S2 have no related node pairs in S5 since node 2 is absent in S5. We solve this problem

by attaching “wildcards” to S2 and S5, as depicted by gray squares � in Fig. 4.6. Formally,

for Si and Sj, a number of |Si ∪ Sj − Si| wildcards are attached to Si to make S′i. In S′

i,

each wildcard can stand for any node u ∈ Sj but /∈ Si, namely ∀u ∈ (Si ∪ Sj − Si). For

example, in Fig. 4.6, each gray square in S′2 can stand for either 5 or 4, and a gray square

in S′5 can be substituted with either 2 or 3. Since “wildcard nodes” attached to Si are

naturally regarded as further away than neighbors of ui in Si, S′i maintains the features as

a location-dependent signature without violating proximity relationships embedded in the

original Si. Fig. 4.6 lists all implicit node pair flips from S′2 to S′

5. We call them implicit

flips since they are not as obvious as the explicit flips. For example, node pair {2, 1} in

S′2 can only have a counterpart node pair {1,�} in S′

5, where � stands for 2 in this case.

{2, 1} and {1,�} is a flip from S′2 to S′

5 because an order reversion occurs no matter which

� in S′5 stands for 2.

S’2 S’5

S’2 : 2 1 6 3

S’5 : 5 4 6 1

2 3 23

5 454

Figure 4.7: 2 Possible Node-Pair Flips

Fig. 4.7 gives examples of the possible node-pair flip. Formally, if a node pair {um, un}appears in Si but neither um nor un is in Sj , we consider it possible that {um, un} gets

reversed in Sj . For example, as shown in Fig. 4.7, {2, 3} from S′2 can only have a counterpart

{�,�} in S′5. With no additional information, this node pair gives a possible node-pair flip

with 50% probability. Based on the above explanations, we now define the signature distance

100

between Si and Sj as follows.

Definition 1: the signature distance SD(Si, Sj) is equal to the summation of the number

of explicit flips Fe(Si, Sj), implicit flips Fi(Si, Sj), and possible flips Fp(Si, Sj) times 0.5

(50% probability of flip for possible node pairs), namely,

SD(Si, Sj) = Fe(Si, Sj) + Fi(Si, Sj) + Fp(Si, Sj) × 0.5 (4.1)

Taking S2 and S5 in Fig. 4.5 as an example, Fe(S2, S5) = 1 as shown in Fig. 4.5,

Fi(S2, S5) = 10 as listed in Fig. 4.6, and Fp(S2, S5) = 2 as depicted in Fig. 4.7. According

to definition 1, we have SD(S2, S5) = 1 + 10 + 2 × 0.5 = 12.

In fact, each node-pair flip from S(i) to S(j) corresponds to one and only one node-pair

flip from S(j) to S(i), so the definition of SD guarantees SD(Si, Sj) ≡ SD(Sj, Si).

Algorithm 8: Calculation of the Signature Distance

input : Si and Sj

output: SD(Si, Sj)

Si = sort(Si); % O(Klog(K)) ;1

Sj = sort(Sj); % O(Klog(K)) ;2

S′i = wildCard(Si, Si, Sj); % O(K) ;3

S′j = wildCard(Sj , Sj, Si); % O(K) ;4

Fe+i = HeapSort(S′i, S

′j); % O(Klog(K)) ;5

Fp = (K−|Si|)(K−|Si|−1)2 +

(K−|Sj|)(K−|Sj |−1)2 ; % O(1) ;6

SD(Si, Sj) = Fe+i + Fp × 0.5; % O(1) ;7

Algorithm 8 illustrates a method for computing the signature distance. First of all, Si

and Sj get sorted at line 1 and 2 with complexity O(Klog(K)), where K = |Si ∪ Sj| is

the total number of neighbors of two nodes ui and uj. The function wildCard() at Line 3

attaches (K−|Si|) wildcards to Si and fills these wildcards with elements (Si∪Sj −Si) that

are ordered the same as they are in Sj. Line 4 performs similarly to Sj to obtain S′j. Line 3

and 4 have a cost of O(K) with sorted input Si and Sj. Line 5 computes the total number

of explicit and implicit node-pair flips using a variant of heap-sort algorithm [204] with

complexity O(Klog(K)). Line 6 calculates the number of possible flips. Line 7 gives the

result of SD(Si, Sj) based on Eq. 4.1. The time complexity of Algorithm 8 is O(Klog(K)).

Normally K ≪ n, where n is the total number of nodes in the network.

Insights into the Signature Distance

In a signature Si, each ordered node pair contains a proximity relationship. For example,

as shown in Fig. 4.8(a), S2 = (2, 1, 6, 3), the ordered node pair {1, 3} in S2 means that from

node 2’s point of view, node 1 is closer than node 3. In other words, if we divide the plane

with B(1, 3) (depicted as a dashed line), which is the perpendicular bisector of the line

101

segment L(1, 3) connecting node 1 and 3, the ordering of {1, 3} in S2 indicates that node 2

is located on the left side of B(1, 3).

Based on the above example, we can see that a node-pair flip between two signatures

corresponds to passing a bisector line. For example, as shown in Fig. 4.8(a), S2 contains

node pair {1, 3} which gets reversed to {3, 1} in S3, meaning that node 2 and node 3 are on

different sides of B(1, 3). So going from node 2 to node 3 along the straight line segment

L(2, 3) needs to pass B(1, 3), as shown in the figure. Fig. 4.8(b) illustrates an opposite case,

in which signature S2 and S3 have an accordant node pair {2, 1}, indicating that node 2 and

3 are located at the same side of B(1, 2) and L(2, 3) does not intersect B(1, 2). Fig. 4.8(c)

shows an example of the implicit flip. In S′2, node pair {6, 3} has a counterpart {3,�} in

S′3, where � is a wildcard standing for node 6 in this case. This implicit flip corresponds

to an intersection of L(2, 3) and B(3, 6), as shown in the figure.

1

2

6

3

4

5

S2 : 2 1 6 3

S3 : 3 2 1

B(1, 3)

(a) Explicit Flip

S2 : {1,3} S3 : {3,1} Passing B(1, 3)

1

2

6

3

4

5

B(3, 6)

S’2 : 2 1 6 3

S’3 : 3 2 1

(c) Implicit Flip

S2 : {6,3} S3 : {3,6} Passing B(3, 6)

6

1

2

6

3

4

5

B(1, 2)

S2 : 2 1 6 3

S3 : 3 2 1

(b) Non-Flip

S2 : {2,1} S3 : {2,1} Without Passing B(2, 1)

L(1, 3)

L(2, 3) L(2, 3) L(2, 3)

Figure 4.8: The Physical Meaning of Node-Pair Flips

In general, we have the following observation:

Observation 1: a node-pair flip {um, un} ⇒ {un, um} from Si to Sj indicates that the line

segment L(ui, uj) passes the perpendicular bisector line B(um, un).

One remark about the above observation is that there is only one intersection between

L(ui, uj) and B(um, un) when node-pair flip happens. This is because two straight lines

(segments) have at most one crossing point.

On the other hand, based on the definition of signature distance, SD(Si, Sj) evaluates

the difference between two signatures Si and Sj by counting the total number of node-pair

flips. Thus, we can conclude from Observation 1 that

Observation 2: SD(Si, Sj) is equivalent to the number of bisector lines we need to pass

if going from neighboring node ui to uj along the line segment L(ui, uj).

Another key observation concerning the physical distance between two neighboring

nodes is that

Observation 3: under roughly uniform bisector line density, for neighboring nodes ui

102

and uj, the number of bisector lines passed by line segment L(ui, uj) is approximately

proportional to the physical distance between ui and uj, i.e., the length of L(ui, uj), denoted

as PD(ui, uj).

The insight offered by Observation 3 is that longer physical distances provide a higher

probability of passing more bisector lines. Here bisector line density is defined as the number

of lines exist between two positions with unit distance. Fig. 4.9 shows an example for this

observation. Fig. 4.9(a) draws the layout of perpendicular bisector lines (denoted as dashed

lines) for all node pairs, and line segments connecting node 1 with its 1-hop neighbors (de-

noted as solid lines). Fig. 4.9(b) lists line segments, corresponding number of bisector lines

they passing, and signature distances between their terminal nodes, respectively. We can

see that the number of bisector lines passed by a line segment is approximately proportional

to the length of the line segment, i.e., the physical distance between two nodes.

(a)

1

2

6

4

5

3

(b)

Line

Segments

Bisectors

Passing

3

421

61

41 6

51 8

31 8

SD

3

4.5

6.5

8.5

8.5

Figure 4.9: Physical Distance vs. Bisector Lines Passing

Combining the above three observations, we have a heuristic rule as follows: for two

neighboring nodes ui and uj , their signature distance is approximately proportional to the

physical distance between them, namely

SD(Si, Sj) ∝ PD(ui, uj) (4.2)

An important remark is that Eq. 4.14 is not valid for non-neighboring node pairs most

of the time. This is because SD(ui, uj) only counts the number of passed bisector lines

generated by node pairs from the set Si∪Sj. Fig. 4.10 shows an example for explaining this

ui

uj

uk

Network Area

Neighborhood of ui

Neighborhood of uj

Neighborhood of uk

Figure 4.10: Far-away Node Pairs

103

remark. In this figure, ui, uj and uk are located far from each other, and their neighboring

areas, which are denoted with dashed circles, do not overlap at all. As a result, SD(Si, Sj)

and SD(Si, Sk) both are determined only by possible flips that depend on the number

of nodes in Si, Sj and Sk. Under similar 1-hop radio range, SD(Si, Sj) and SD(Si, Sk)

could have similar values calculated from Algorithm 8, despite that the physical distances

of these two node pairs may be dramatically different. In a word, the heuristic relationship

of Eq. 4.14 is meaningful only for 1-hop neighboring nodes.

Based on Eq. 4.14, signature distance can be utilized as a relative distance for localiza-

tion purposes because it approximately reflects the “near-far” relationships among 1-hop

neighbors. However, in some cases, SD can be biased due to spatially non-uniform bisector

line density throughout the network area, a violation of the condition in Observation 3. In

the next section, we propose a more robust relative distance, i.e., Regulated SD, to address

this problem.

4.2.2.3 RSD: Regulated Signature Distance

This section introduces the regulated signature distance, or RSD for short, as a refined

version of SD. We first give an intuitive explanation about the motivation for SD refinement.

After that, we derive the formation of RSD.

The Rationale behind SD Refinement

Spatially non-uniform bisector line density could affect the effectiveness of SD as a

relative distance. This problem comes from two aspects: (i) local node placement; and (ii)

network wide neighborhood size, both of which are explained in the following with examples.

Figure 4.11: Motivation for SD Regulation

As shown in Fig. 4.11(a), L(2, 3) passes 4 bisector lines and L(6, 1) intersects 3. However,

L(2, 3) is more than twice as long as L(1, 6). This inconsistency is caused by spatially

unbalanced bisector line density within the local area. For example, the area close to node

1 has a higher bisector line density, while boundary areas close to node 2 and 3 have a low

density. This micro-level observation indicates that SD needs to be refined considering the

104

local bisector line density.

At the macro level, for the same physical distance, the value of signature distance could

be different, depending on the neighborhood size. For example, as shown in Fig. 4.11(b),

two nodes ui and uj has a constant physical distance W . When they have a large 1-hop

radio range illustrated by two big circles, both of them have node v and c as neighbors

included in their signatures. In this case, SD(ui, uj) counts the passing of B(v, c) which is

the bisector for node pair {v, c}. However, if ui and uj have a smaller 1-hop radio range

(e.g., due to strong ambient noise) denoted by gray-filled circles. Node v, u are absent

from signatures of ui and uj , so SD(ui, uj) does not count B(v, c), resulting a smaller value

of SD(ui, uj) comparing to the previous case. In fact, under random node deployment

with uniform density, the signature distance for node ui and uj should be regarded as a

relative value in terms of the dimension of their neighborhood area that affects the number

of available bisector lines counted for passing in the map.

Based on the above analysis, we propose the Regulated Signature Distance, or RSD for

short, defined as follows:

RSD(ui, uj) = SD(Si, Sj) ·√

K

K(K − 1)/2(4.3)

Eq. 4.3 refines SD(Si, Sj) with a factor√

KK(K−1)/2 , where K = |Si ∪ Sj| is the total number

of nodes in the neighborhood of node ui and uj combined. In this equation, K(K − 1)/2

calculates the number of local bisector lines, used to normalize SD(Si, Sj) with the local

bisector density;√

K estimates the diameter of this neighborhood, which puts the factor of

neighborhood size into consideration. We formally derive and explain this equation in the

next section.

Regulation Factor Derivation

For neighboring nodes ui and uj , let |Si∪Sj| = K. There are a total of nB = K(K−1)/2

bisector lines generated by node pairs in Si ∪ Sj. According to the Pie-Cutting Theo-

rem [200], nB bisector lines divide the local area into nR small regions, where

nR = O((n2B + nB + 2)/2) = O(n2

B) (4.4)

Let S be the size of the local area occupied by the neighborhoods of ui and uj . The expected

size and diameter of each small region, denoted as E[sR] and E[dR] respectively, are

E[sR] =S

nR=

S

O(n2B)

, E[dR] = α ·√

E[sR] =α√

S

O(nB)(4.5)

where α is a constant factor determined by the shape modeling of the small region.

Suppose that line segment L(ui, uj) intersects NB(ui, uj) bisector lines, then L(ui, uj)

105

ui uj...

Passing �B(ui,uj) BisectorsL(ui,uj)

(�B(ui,uj) − 1) Small Regions

Bisector Line

Residual

Residual

Figure 4.12: Bisector Lines and Small Regions

passes (NB(ui, uj)− 1) small regions as shown in Fig. 4.12. Adding residuals at both ends

(each counted as a half region), we get an approximation

PD(ui, uj) ≈ NB(ui, uj) · E[dR] (4.6)

meaning that the distance between ui and uj approximately equals the number of small

regions times expected diameter.

SD(ui, uj) estimates the number of bisector lines that L(ui, uj) passes, i.e., SD(ui, uj) ≈NB(ui, uj). So we have

PD(ui, uj) ≈ SD(Si, Sj) · E[dR] = SD(Si, Sj) ·α√

S

O(nB)(4.7)

For uniform random node deployment, the expected number of nodes in an area is

proportional to the area size, namely E[K] = φ · S where φ is the node density. Since

nB = K(K − 1)/2, we can rewrite Eq. 4.7 as

PD(ui, uj) ≈ SD(Si, Sj) ·ϕ√

K

K(K − 1)/2, where ϕ =

α√φ

(4.8)

ϕ is a constant scaling factor that can be eliminated without violating near-far relationship

among different neighboring nodes. Thus, we obtain the proposed relative distance RSD:

RSD(ui, uj) = SD(Si, Sj) ·√

K

K(K − 1)/2(4.9)

where the above Eq. 4.9 is identical to Eq. 4.3.

RSD Versus SD

Fig.4.13 compares SD and RSD obtained from a simulated network of 150 randomly

deployed nodes with 100-foot radio covering a 500 × 500 square feet area. For each node

pair, both SD and RSD are plotted against their physical distance in Fig.4.13(a) and 4.13(b)

respectively. Fig.4.13 conveys two messages: (i) within 1-hop radio range, RSD offers a

much better linear correlation with physical distance than SD; (ii) beyond 1-hop radio

range, signature distance (i.e., SD or RSD) no longer correlates with the physical distance.

106

0 100 200 300 400 500 600 7000

200

400

600

800 ← 1−Hop Radio Range

Physical Distance (in feet)

S

D

(a) SD vs. Physical Distance

0 100 200 300 400 500 600 7000

1

2

3

4

5

6

← 1−Hop Radio Range

Physical Distance (in feet)

R

SD

(b) RSD vs. Physical Distance

Figure 4.13: Correlation with Physical Distance − SD vs. RSD

RSD for Multi-hop Nodes

Fig.4.13 shows that RSD is also not effective for multi-hop nodes. To address this, we

propose a general definition of RSD considering multi-hop nodes as follows,

• For 1-hop neighboring nodes ui and uj, RSD(ui, uj) is directly computed with Eq.4.9;

• For non-neighboring nodes ui and uj , RSD(ui, uj) is calculated as the smallest accu-

mulated RSD from all paths between ui and uj.

Here the accumulated RSD is computed as the summation of the RSD values of all 1-hop

node pairs along a path. Fig.4.14 depicts a simple example, where RSD(a, d) is accumulated

along the path from node a to d .

a

b

c

d

RSD(a,b)

RSD(b,c)

RSD(c,d)

RSD(a,d) = RSD(a,b) + RSD(b,c) + RSD(c,d)

Figure 4.14: RSD for Non-neighboring Nodes

4.2.3 Design as a Supporting Layer

RSD can be conveniently applied as a transparent supporting layer for connectivity-based

localization algorithms to achieve better system accuracy with little overhead. As shown

in Fig. 4.15, we simply use the smallest accumulated RSD instead of the shortest-path

hop count as the distance metric among nodes. In the following, we briefly describe three

connectivity-based localization schemes studied in our evaluation.

4.2.3.1 Connectivity-Based Schemes

The key idea in connectivity-based localization is to use the number of communication hops

between two nodes to evaluate the physical distance between them. The following three

schemes are typical examples:

107

• MDS-MAP [166] by Y. Shang, W. Ruml, et al.

• DV-Hop [178] by D. Niculescu and B. Nath.

• RPA [179] by C. Savarese, J. M. Rabaey, et al.

MDS-MAP [166] starts with a distance matrix A in which the value at the ith row and the

jth column is the shortest hop-based distance between node ui and uj . The algorithm first

computes a “relative map” of the network with the MDS (multi-dimensional scaling) [166]

technique using matrix A as input. Then, an “absolute map” can be obtained by scaling

and rotating the “relative map” according to the absolute coordinates constructed by at

least three anchors in the map.

DV-Hop [178] uses a mechanism that is similar to classical distance vector routing. After

beacon flooding from more than three anchors in the network. The algorithm estimates the

expected physical distance for 1-hop with

HopSize =

∑i6=j Distance(vi, vj)∑

i6=j Hops(vi, vj)(4.10)

where vi and vj are anchor nodes. Distance(vi, vj) and Hops(vi, vj) are the physical distance

and the least number of hops between vi and vj , respectively. For normal node ui, it

estimates its distance to anchor vi with HopSize × Hops(ui, vi). Finally, ui’s location is

computed using least-square multilateration with all anchors.

RPA [179] uses a similar mechanism of hop-based distance called Hop-TERRAIN for its

first step. Besides, it introduces an iterative refinement step for position adjustment based

on local sensing results. Basically, at iteration k, the position of node ui is recomputed

based on the estimated positions of its neighbors obtained from iteration k − 1. More

sophisticated approaches such as confidence based filtering are also proposed in RPA.

Localization Algorithm

Physical Layer: Neighborhood Sensing

Distance between two nodes

=Least number of hops

Hop-Based RSD

Distance between two nodes

=Smallest accumulated RSD

Relative Distance Estimation Layer

Figure 4.15: RSD Design Embedding

108

4.2.3.2 Design Embedding

With local RSS sensing results, RSD can be calculated at each node or in a localization

server. For range-free connectivity based localization algorithms such as MDS-MAP, DV-

Hop, and RPS, applying RSD is convenient and incurs little overhead. Without modifying

the major design of the original algorithm, the RSD value can be used instead of “1” (indicat-

ing connection) for neighboring nodes. Specifically, in MDS-MAP, for example, everything

remains the same except that the distance matrix now holds the smallest accumulated RSD

values instead of least number of hops. For DV-Hop, similarly, the relative distance turns

to the smallest accumulated RSD instead of shortest-path hops. And the expected physical

distance for 1 unit of RSD is given by

RSDunitSize =

∑i6=j Distance(vi, vj)∑

i6=j RSD(vi, vj)(4.11)

For RPA, besides embedding RSD in the Hop-TERRAIN step, the refinement step also

benefits from applying RSD for local iterative position adjustment.

Note that as a supporting layer under specific localization algorithm, our design actually

can be similarly embedded in more sophisticated designs [184, 187, 190], that consider

anisotropic network topology due to obstacles, radio irregularity, complex shapes [186, 188,

189], etc, to provide enhanced localization performance.

4.2.4 Complexity of RSD Embedding

Involving RSD in localization introduces little additional cost. Algorithm 8 costs O(Klog(K))

for SD calculation, where K is the maximum length of a signature in the network, and nor-

mally K ≪ n where n is the total number of nodes. Even in a centralized localization

system, additional overhead of RSD calculation is O(n · K2log(K)) (n nodes and each has

at most K − 1 neighbors), which is negligible comparing with the complexity from other

parts. For instance, MDS has a complexity of O(n3) for the matrix decomposition step

alone [86]. About communication, the only additional overhead is for signature exchange

among neighboring nodes. Signatures are very short and can be piggybacked economically

on messages during network initialization. Importantly, signature exchange only occurs

within 1-hop neighborhood without multi-hop flooding. Therefore, embedding RSD does

not affect the scalability of the localization system.

4.2.5 Test-bed Experimentation

The design of RSD is evaluated with both test-bed experimentation and extensive simula-

tion. In this section, we report two types of outdoor experiments with 54 and 49 MICAz

motes respectively. Section 4.2.6 will further investigate the performance gain of our design

in large scale systems under various configurations by simulation.

109

In-field View

�ode #1

�ode #54

Figure 4.16: Test-bed Experiments I: Linear Network

4.2.5.1 Experiment I: Linear Network

We start our test-bed evaluation from a linear network widely applied in transportation-

related road networks.

Experiment Setup

As shown in Fig. 4.16, 54 MICAz motes were deployed on the grass covered curb along

a road (with surrounding obstacles including trees, metal fence and parked vehicles). Each

node was left 8 inches above the ground and the distance between two immediate nodes

was about 16 feet. Every node broadcasts 100 packets with carrier-sensing and back-off

time intervals set from 200ms (millisecond) to 1690ms individually for collision avoidance.

The radio sending power was 0dBm at channel 26 (Fc = 2480MHz) to avoid possible WiFi

interference from the surroundings. Each packet contained the sender’s node ID and a

sequence number of the packet. When a node received a packet, it logged the sensed signal

strength, sender’s ID, and the sequence number of the packet into its flash memory.

Table 4.2: Statistics of the Linear Network

Scale Max. Hops Max. 1-Hop RF Range Neighborhood Size

≈ 848(feet) 15 ≈144(feet) 6.7 (nodes)

Table 4.2 lists some of the collected information about the linear network. The whole

length of the network was about 848 feet with 15 hops between two terminal nodes (node#1

and node#54). The maximum 1-hop radio communication range in this experiment was

about 144 feet and the average 1-hop neighborhood size was 6.7 (nodes).

Distance Correlations

For either the traditional hop-based distance or the newly proposed RSD, their effec-

tiveness as a relative distance in localization is determined by the correlation between their

values and the physical distance.

Fig. 4.17 illustrates the correlations between hop-based distance, RSD, and the physical

distance. Fig. 4.17(a) and 4.17(b) plot all the node pairs within 1-hop communication

110

0 20 40 60 80 100 1200

0.5

1

1.5

2

ρ = 0

Physical Distance (in feet)

H

op

Dis

tan

ce (

in h

op

s)

Hops vs. Distance (within 1−Hop)

(a)

0 20 40 60 80 100 1200

0.5

1

1.5

2

2.5

3

ρ = 0.89

Physical Distance (in feet)

R

SD

RSD vs. Distance (within 1−Hop)

(b)

0 200 400 600 800 10000

5

10

15

Physical Distance (in feet)

H

op

Dis

tan

ce (

in h

op

s)

ρ = 0.98

Hops vs. Distance (Multi−Hop)

(c)

0 200 400 600 800 10000

5

10

15

20

25

30

ρ = 0.99

Physical Distance (in feet) R

SD

RSD vs. Distance (Multi−Hop)

(d)

Figure 4.17: Distance Correlation Comparison: RSD vs. Hop (Linear Network)

range in the linear network. In both figures, the X-axis is the physical distance between

two nodes, and the Y -axis is the hop-based distance and RSD, respectively. Fig. 4.17(a)

reveals that all 1-hop node pairs have an identical hop distance of 1, thus the correlation

coefficient is ρ = 0 within 1-hop range. On the contrary, as shown in Fig. 4.17(b), most of

the node pairs with different distances can be differentiated from each other according to

their RSD value. The empirical data shown in Fig. 4.17(b) have a correlation coefficient

ρ = 0.89. Comparing Fig. 4.17(a) and 4.17(b), we can conclude that RSD owns a sub-hop

resolution that is not available from the traditional hop-based distances.

Fig. 4.17(c) plots all the node pairs (both 1-hop and multi-hop node pairs) according to

their hop distance and physical distance. Similarly, Fig. 4.17(d) plots RSD (accumulated

RSD for multi-hop nodes) against physical distance for all node pairs. Comparing these

two figures, although the correlation coefficients are close (ρ = 0.98 for hop distance and

ρ = 0.99 for RSD), RSD provides better resolution. In Fig. 4.17(c), a physical distance can

only be mapped to an integer hop distance in a discrete manner, while in Fig. 4.17(d), the

mapping is continuous.

Localization results in next section show that RSD’s sub-hop resolution can nicely solve

the ambiguity problem, i.e., mapping closely located nodes to identical positions.

Localization Performance

111

We use the terminology “MDS-Hop”, “DV-Hop” and “RPA-Hop” for the original hop-

based approaches and “MDS-RSD”, “DV-RSD” and “RPA-RSD” for corresponding meth-

ods embedded with RSD.

0 100 200 300 400 500 600 700 800 900

−50

0

50

100

150

DV−Hop Localization Results

X Axis (in feet)

Y

Ax

is(i

n f

ee

t)

Deployed Positions

↓

Estimated Positions↑

(a)

0 100 200 300 400 500 600 700 800 900

−50

0

50

100

150

DV−RSD Localization Results

X Axis (in feet)

Y

Ax

is(i

n f

ee

t)

Deployed Positions

↓

Estimated Positions↑

(b)

Figure 4.18: Localization in Linear Networks: DV-Hop vs. DV-RSD

0 100 200 300 400 500 600 700 800 900−50

0

50

100

150

RPA−Hop Localization Results

X Axis (in feet)

Y

Ax

is(i

n f

ee

t)

(a)

0 100 200 300 400 500 600 700 800 900−50

0

50

100

150

RPA−RSD Localization Results

X Axis (in feet)

Y

Ax

is(i

n f

ee

t)

(b)

Figure 4.19: Localization in Linear Networks: RPA-Hop vs. RPA-RSD

Let us first look at DV-Hop (Fig. 4.18(a)) and DV-RSD (Fig. 4.18(b)). Fig. 4.18 shows

the localization results from both algorithms with two terminal nodes of the linear network

as anchors. In the figure, black line segments are plotted starting from nodes’ deployed

positions (depicted as blue dots) and pointing to corresponding estimated locations, for clear

observation. In Fig. 4.18(a) for DV-Hop, many nodes are mapped to identical estimated

locations, i.e., the ambiguity problem; while DV-RSD does not encounter this issue as

shown in Fig. 4.18(b). This result confirms that RSD offers a unique sub-hop resolution

112

0 100 200 300 400 500 600 700 800 900−50

0

50

100

150

MDS−Hop Localization Results

X Axis (in feet)

Y

Ax

is(i

n f

ee

t)

(a)

0 100 200 300 400 500 600 700 800 900−50

0

50

100

150

MDS−RSD Localization Results

X Axis (in feet)

Y

Ax

is(i

n f

ee

t)

(b)

Figure 4.20: Localization in Linear Networks: MDS-Hop vs. MDS-RSD

while hop-based distance does not.

Fig. 4.19 illustrates the results of RPA-Hop (Fig. 4.19(a)) and RPA-RSD (Fig. 4.19(b)),

both with two iterative refinement steps. Both RPA-Hop and RPA-RSD achieved unique

position estimation for each node. For RPA-Hop, this is credited to the refinement step

that smooths the estimated position of each node over its neighbors, naturally solving the

problem of clustered mapping. From Comparing results in Fig. 4.19(a) and Fig. 4.19(b),

we can observe that RPA-RSD achieves better localization accuracy than RPA-Hop.

Fig. 4.20 shows the localization results from MDS-Hop (Fig. 4.20(a)) and MDS-RSD

(Fig. 4.20(b)). We found that 2-dimensional MDS is not stable for linear or close-to-linear

networks because of singularity issues in matrix decomposition. Here, 1-dimensional MDS

is applied first, and then two terminal nodes are used as anchor nodes for map scaling and

rotation to obtain the 2-dimensional absolute map. Fig. 4.20 tells that MDS algorithm itself

is not able to solve the ambiguity problem as shown in Fig. 4.20(a); while MDS-RSD in

Fig. 4.20(b) shows better performance without clustered mapping.

MDS−Hop MDS−RSD DV−Hop DV−RSD RPA−Hop RPA−RSD0

5

10

15

20

25

30

Methods

E

rro

rs (

in f

ee

t)

Max Error

Mean Error

Figure 4.21: Comparison: RSD vs. Hop Distance

In our evaluation, the localization error is defined as the distance from the true position

of a node to its estimated location, namely, the length of the line segments in Fig. 4.18,

113

Fig. 4.19, and Fig. 4.20. We can roughly see from those figures that RSD-applied methods

result in better localization accuracy than their counterparts with hop-based distances for

shorter line segments. Fig. 4.21 compares the maximum and mean localization errors from

results in Fig. 4.18, Fig. 4.19, and Fig. 4.20 for all six methods. We can clearly observe

that all the RSD-embedded methods (“*-RSD”) have smaller errors than their original “*-

Hop” versions. Specifically, the maximum and mean errors of “MDS-Hop”, “DV-Hop” and

“RPA-Hop” get reduced by 27%, 22%, 35%, 23%, 29% and 24%, respectively.

4.2.5.2 Experiment II: Regular 2D Network

The second test-bed evaluation aims at a 2-dimensional (2D) grid-shaped network with

considerations about futuer investigation about the impact of irregular network topology

to the localization performance, where a grid can be easily transformed to irregular shapes

by simply removing “pixels” from the grid.

Experiment Setup

Fig. 4.22 shows the experiment scenario of a large open-air parking lot at night. We

placed 49 MICAz sensor nodes in a 7 × 7 grid shape, as shown in the left of Fig. 4.23.

The network covered an area of about 100 × 100 square feet. Rows and columns were

approximately 16 feet apart. Similarly to Experiment I, each node was left 8 inches above

Figure 4.22: Test-bed Experiments II: Regular 2D Network

0 50 100−20

0

20

40

60

80

100

120

Network Layout

X Axis (in feet)

Y

Ax

is (

in f

ee

t)

1234567

1 2 3 4 5 6 70

10

20

30

40

Neighborhood Size

X Axis (in column) Y Axis (in row)

Figure 4.23: Network Layout and Neighborhood Size

114

the ground with antennas pointing to the sky.

Table 4.3: Statistics of the 2D Network

Statistics 1-Hop 2-Hop 3-Hop

Number of Node Pairs 575 519 82

Minimum Distance (in feet) 16 22.63 80

Median Distance (in feet) 35.78 71.55 97.32

Maximum Distance (in feet) 97.32 124.96 135.76

Table 4.3 lists some key statistics regarding the experiment. This 49-node system is a

3-hop network. 1-hop radio range varies from about 20 feet to 100 feet among different node

pairs along diverse directions. The right subfigure in Fig. 4.23 shows the neighborhood size

of each node. The X-axis and Y-axis in this figure depict the index of rows and columns in

the network. The height of each bar indicates the 1-hop neighborhood size of the node at

that position. This figure verifies that nodes in the center of the network have more 1-hop

neighbors while the boundary nodes have smaller neighborhood size.

0 20 40 60 80 1000

0.5

1

1.5

2

ρ = 0

Physical Distance (in feet)

H

op

Dis

tan

ce (

in h

op

s)

Hops vs. Distance (within 1−Hop)

(a)

0 20 40 60 80 1000

1

2

3

4

5

ρ = 0.78

Physical Distance (in feet)

R

SD

RSD vs. Distance (within 1−Hop)

(b)

0 50 100 150 2000

0.5

1

1.5

2

2.5

3

3.5

4

Physical Distance (in feet)

H

op

Dis

tan

ce (

in h

op

s)

ρ = 0.75

Hops vs. Distance (Multi−Hop)

(c)

0 50 100 150 2000

2

4

6

8

10

ρ = 0.86

Physical Distance (in feet)

R

SD

RSD vs. Distance (Multi−Hop)

(d)

Figure 4.24: Distance Correlation Comparison: RSD vs. Hop (Regular 2D Network)

Distance Correlations

Fig. 4.24 shows the correlations between hop-based distance, RSD, and physical dis-

tance in this grid-shaped 2D network. Fig. 4.24(a) and 4.24(b) confirms that RSD provides

a better sub-hop resolution than hop-based distance. Furthermore, Fig. 4.24(b) also ver-

ifies that for MICAz motes using monopole whip antenna with radiation pattern close to

115

−20 0 20 40 60 80 100 120−20

0

20

40

60

80

100

120

X Axis (in feet)

Y

Ax

is (

in f

ee

t)

(a) Localization by MDS-Hop

−20 0 20 40 60 80 100 120−20

0

20

40

60

80

100

120

X Axis (in feet)

Y

Ax

is (

in f

ee

t)

(b) Localization by MDS-RSD

4 5 6 7 8 9 100

10

20

30

40

50

60

Number of Anchors

Err

or

(in

fe

et)

MDS−Hop: Max Error

MDS−RSD: Max Error

MDS−Hop: Median Error

MDS−RSD: Median Error

(c) Statistical Comparison

Figure 4.25: Localization Results of MDS-RSD and MDS-Hop

isotropic [224], neighborhood ordering based on RSS can be a good heuristic indicator for

physical distance. For multi-hop distance, Fig. 4.24(c) and Fig. 4.24(d) show that RSD

provides a higher correlation coefficient than hop-based distance, verifying that RSD is

superior to hop-based distance as a relative distance for proximity expression.

Localization Performance

Since the network has only 3 hops that is not suitable for DV-Hop and RPS, to be

fair, we only applied MDS-based algorithms in this evaluation. Performance comparisons

for DV-Hop and RPS in non-linear-shape networks will be investigated in Section 4.2.6 via

large-scale simulation.

Fig. 4.25(a) and 4.25(b) depict localization results from MDS-Hop and MDS-RSD with

4 randomly selected anchors in the system, respectively. In both figures, the blue dots

are the true positions of nodes and a line segment originating from each dot point to

its estimated position. We can see from these two figures that MDS-RSD gives better

116

localization accuracy than MDS-Hop in this case.

In order to eliminate possible bias caused by anchor selection, we randomly picked

different numbers of anchors, from 4 to 10 in step of 1, and tried each for 1000 runs.

Fig. 4.25(c) plots the averaged maximum and median errors for both methods, from which

we can conclude that (i) MDS-RSD offers a significantly better performance over MDS-

Hop across all numbers of anchors, and (ii) more anchor gives slight gain in localization

accuracy. By embedding RSD, both the maximum and median errors are reduced greatly.

For example, for 4 anchor nodes, RSD reduces the maximum and median errors by about

27% and 30%, respectively.

4.2.5.3 Test-bed Evaluation Summary

Radio is notorious for it irregularity, however, we are able to achieve better localization

accuracy than considering connectivity alone. Test-bed experiments show that RSD pro-

vides sub-hop resolution and correlates more with physical distance than the traditional

hop distance. Embedding RSD in connectivity-based methods is convenient, low cost, and

can effectively enhance localization accuracy.

4.2.6 Simulation Evaluation

In this section, we report simulation results about the performance gain from the RSD design

for large-scale networks under different system settings. First of all, the correlation between

RSD and physical distance as well as the effectiveness of RSD for improving localization

accuracy are examined. Then, we introduce an interesting feature of robustness about RSD

concerning spatially uneven radio path loss.

4.2.6.1 The Noise Model

In the simulation, we applied the widely used logarithmic attenuation model [85, 86, 221,

225] for RSS sensing as follows.

Pi,j(t) = P0 − 10β · log(

PD(ui, uj)

d0

)+ Xi(t) (4.12)

where Pi,j(t) stands for the sensing result at node ui for node uj at time instance t. P0

is the received power at a short reference distance d0. PD(ui, uj) is the physical distance

between ui and uj . β is the path loss factor (also called fading factor in some literatures)

and Xi(t) is a random noise at time t for node ui following Xi(t) ∼ N(0, σ2X). We set a

reference 1-hop radio range of R = 100 feet. The corresponding signal strength was set as

the receiver sensitivity threshold.

We modeled the area of interest as a square map without holes where radio can not

reach. More complicated maps can be used with works [184, 186, 187, 188, 190]. Unless

117

Table 4.4: Default Simulation Configurations for LBC

Parameter Default Values and Description

Field Area 500 (in feet)×500 (in feet)

Noise Model β = 4, σX = 6 for the whole map

Sensor Nodes 200, randomly deployed with uniform distribution

Anchor Nodes 8, randomly deployed

otherwise mentioned, Table 4.4 lists the default simulation configurations in simulation and

all statistics reported were averaged over 50 runs for high confidence.

4.2.6.2 RSD as a Metric of Proximity

As a metric of proximity, the correlation between RSD and the physical distance is a key

parameter. Starting from the RSD vs. Distance pattern, we evaluated the impacts of

random noise (σx), path loss factor (β), and node density to the correlation coefficient ρ.

0 50 100 1500

1

2

3

4

5

Distance (in feet)

R

SD

(a) RSD vs. Distance (1-Hop)

2 4 6 8 10

0.65

0.7

0.75

0.8

0.85

0.9

0.95

σx

ρMean of ρMin of ρ

(b) Impact of σx

2 3 4 5 6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

β

ρ

Mean of ρMin of ρ

(c) Impact of β

100 150 200 250 3000.72

0.74

0.76

0.78

0.8

0.82

0.84

Number of Nodes

ρ

Mean of ρMin of ρ

(d) Impact of Node Density

Figure 4.26: The Correlation Coefficient between RSD and Physical Distance

Fig.4.26(a) shows a typical plot of RSD against physical distance for 1-hop node pairs.

This figure tells two features: (i) RSD is approximately proportional with physical distance,

and (ii) the black dashed lines indicate that the pattern gets spread with increasing distance.

This is because the longer distance between two neighboring nodes, the fewer common node

118

elements are shared in their signatures. Then, the signature distance is determined primarily

by the estimated possible node-pair flips, resulting in a loss of accuracy.

Impact of Random Noise

In this experiment, we compared the correlation between RSD and physical distance for

1-hop node pairs under different noise levels from σX = 2 to 10 in steps of 2. Two curves

shown in Fig.4.26(b) represent the mean and minimum values of ρ for 50 runs. Both curves

indicate that the correlation gets weaker with increasing noise. This result is expected since

large noise brings in severer radio irregularity.

Impact of Path Loss Factor

Fig.4.26(c) shows the impact of path loss factor β to the correlation coefficient. From

this figure, we can see that ρ becomes larger as β increases. This is because bigger β enhance

the “weight” of physical distance PD(ui, uj) in the radio model in Eq.4.21, meaning that

RSS is determined by distance more than random noise. Thus, a higher correlation appears.

Impact of Node Density

We compared the correlation coefficient under different node densities. Without modi-

fying the size of the map, we increased the number of sensor nodes from 100 to 300 in steps

of 50. Fig.4.26(d) shows that higher node density results in larger ρ , meaning that RSD

is better qualified to be a distance metric. As explained in Section 4.2.2.3, a neighborhood

of K nodes creates O(K2) bisectors that divide the map into O(K4) small regions. With

increasing node density, “the power of large numbers” makes the expected diameter of a

small region more accurate, contributing to the accuracy of RSD.

4.2.6.3 The Effectiveness of RSD

This section evaluates the effectiveness of RSD by comparing localization errors between

connectivity-based methods (MDS-Hop, DV-Hop, and RPA-Hop) with corresponding RSD-

embedded versions (MDS-RSD, DV-RSD, and RPA-RSD) under various system configura-

tions. We normalized localization errors respect to the radio range R = 100 (feet) for

consistency with the evaluations in previous works [166, 168].

Impact of Random Noise In this experiment, the random noise level is set from σx = 0

to 12 in steps of 2. Fig.4.27 illustrates the median errors given by six methods. We can

see from the figure that (i) all the broken lines are lower than their corresponding solid

lines, meaning that RSD-applied methods achieved better localization accuracy than their

original versions. (ii) with the increasing noise, the error of all methods increased. And the

performance gain from RSD embedding gets reduced. This is because larger noise makes

RSD itself less correlated with the physical distance.

119

0 2 4 6 8 10 12

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

σx

Me

dia

n E

rro

rs (

in R

)

DV−Hop

RPA−Hop

MDS−Hop

DV−RSD

RPA−RSD

MDS−RSD

Figure 4.27: Impact of Different σx

2.5 3 3.5 4 4.5 5 5.50.2

0.4

0.6

0.8

1

1.2

β

Me

dia

n E

rro

rs (

in R

)

DV−Hop

RPA−Hop

MDS−Hop

DV−RSD

RPA−RSD

MDS−RSD

Figure 4.28: Impact of Different β

Impact of Path Loss Factor In this experiment, the path loss factor is set from β = 2.5

to 5.5 in a step of 0.5. Fig.4.28 indicates the median errors given by six methods. We can

see from the figure that (i) RSD-applied methods achieved better localization accuracy than

their original versions; (ii) with the increasing β, the error of all methods gets reduced since

bigger β makes the distance a more dominant factor over the random nose. And the the

performance gain from RSD embedding ascends.

Impact of Anchor Density

In this experiment, we increased the number of anchor nodes in the network from 4 to 16

in steps of 2. As expected, Fig.4.29 shows that more anchors help improve the localization

accuracy for all methods. More notable is that RSD embedding is more effective than

adding several anchors, especially after 8 anchors when curves become flat. By embedding

RSD, localization error gets reduced constantly by around 30% for DV-Hop and RPA-Hop,

and by about 10% for MDS-Hop.

120

4 6 8 10 12 14 160.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Number of Anchors

Me

dia

n E

rro

rs (

in R

)

DV−Hop

RPA−Hop

MDS−Hop

DV−RSD

RPA−RSD

MDS−RSD

Figure 4.29: Impact of Different Numbers of Anchors

100 150 200 250 300 350 400

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of Nodes

Me

dia

n E

rro

rs (

in R

)

DV−Hop

RPA−Hop

MDS−Hop

DV−RSD

RPA−RSD

MDS−RSD

Figure 4.30: Impact of Different Node Densities

Impact of Node Density

In this experiment, we increased the number of nodes in the map from 100 to 400 in

steps of 50. Fig.4.30 shows that: (i) RSD-applied methods always showed better perfor-

mance (e.g., about 30% and 10% performance gain from DV-Hop/RPA-Hop and MDS-Hop,

respectively); (ii) for DV-Hop and RPA-Hop, increasing the nodes from 100 to 200 did not

affect the system accuracy too much. This is because at this stage, higher node density helps

estimate the hop-based distance. While after 200 nodes, the hop distance can hardly be

improved but more nodes are mapped to identical estimated positions, bringing up the error

statistically; (iii) for MDS-Hop and MDS-RSD, higher node density mostly gives smaller lo-

calization error. This is because the system becomes more robust to a single node’s sensing

errors with more 1-hop connectivity among nodes.

Impact of System Scale

In this experiment, we enlarged the dimension of the map from 150 feet (length and

121

200 300 400 500 600 700 800 900 1000

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Scale of the Map (Length and Width)

Me

dia

n E

rro

rs (

in R

)

DV−Hop

RPA−Hop

MDS−Hop

DV−RSD

RPA−RSD

MDS−RSD

Figure 4.31: Different System Scales

width) to 1050 feet in steps of 150 feet. The number of nodes in the network was increased

proportionally to maintain the same node density. The number of anchors was kept con-

stant. Fig.4.31 shows that (i) RSD-applied methods always achieve better performance than

their original hop-based versions; (ii) localization performance gets worse in larger systems

because anchors were not increased proportionally; and (iii) MDS-based methods are more

robust than DV-based approaches in terms of system scales. This is because MDS-based

methods utilize both local proximity and estimated distance to remote nodes, while DV

and RPA depend more on the later one, the error of which accumulates easily in larger

networks.

4.2.6.4 The Robustness of RSD

In previous evaluations, the path loss factor β was kept uniform throughout the map. While

in real systems, β is more than unknown but temporally dynamic and spatially unevenly

distributed in the map [221][225]. In this experiment, we generate a β distribution model for

a 1000 feet × 1000 feet map based one previous empirical studies [221][225]for evaluating the

robustness of localization algorithms in the case of spatially unevenly distributed radio path

loss. As shown in Fig.4.32(a), β was around 4 but varied gradually across the map, with a

“hill” located close to X = 800, Y = 500 and a “valley” located around X = 200, Y = 500.

Basically, a hill indicates bigger β and a valley depicts smaller β.

Fig.4.32(b) shows the placement of 300 randomly deployed sensor nodes, where similar

node colors indicate proximity. Fig.4.32(c) illustrates 1-hop links of the network with line

segments (edges). The path loss factor β of each link is assigned based on the patches of

the spatial model it traverses. A link exists only when the signal strength at both terminal

nodes are higher than the default RF sensitivity threshold. We can see from Fig.4.32(c)

that the link density is higher in the left part of the map, especially near X = 200, Y = 500,

where β “valley” exists in Fig.4.32(a). On the contrary, links are sparse in the right part,

122

(a) Spatial Modelof β

(b) Node Deployment

0 200 400 600 800 1000

0

200

400

600

800

1000

X Axis (in feet)

Y

Ax

is (

in f

ee

t)

(c) Connectivity Graph

Figure 4.32: Example Spatial Distribution of the Radio Path Loss β

especially close to X = 800, Y = 500, where β “hill” locates. This result is expected since

a larger β creates a shorter communication range, thus nodes close to the “hill” are less

connected.

Figures 4.33(a), 4.33(c), and 4.33(e) show the localization results from MDS-Hop, DV-

Hop and RPA-Hop, respectively. We can see that the overall shape of the network gets

distorted. Many nodes are clustered toward the position X = 200, Y = 500, while others

are sparsely spread out from the point X = 800, Y = 500. This interesting phenomenon

is consistent with the connectivity graph in Fig.4.32(c). Basically, lower β value allows a

larger 1-hop radio range, which shrinks the number of hops among nodes and thus creates

an illusion of shorter physical distances; while bigger β have the opposite effects. RSD does

not fluctuate with the radio range due to the regulation step in the design. This nice feature

gets confirmed from localization results shown in Figures 4.33(b), 4.33(d) and 4.33(f) where

the overall shape of the network is correct for all RSD-applied methods. Therefore, RSD

provides an important feature of robustness for uneven path loss factors across the area.

123

(a) MDS-Hop (b) MDS-RSD

(c) DV-Hop (d) DV-RSD

(e) RPA-Hop (f) RPA-RSD

Figure 4.33: Robustness of RSD for Spatially Unbalanced Radio Path Loss β

4.2.6.5 Simulation Summary

Systematic simulations presented in this section investigate the quality and characteristics

of RSD used as a relative distance for localization in various scenarios. Simulation results

124

tell that (i) embedding RSD helps improve the system accuracy of connectivity-based lo-

calization algorithms; and (ii) RSD embedded designs offer a nice feature of robustness to

the spatially unevenly distributed radio path loss in the map.

4.2.7 Summary and Remarks on LBC

We propose a proximity metric named signature distance for achieving range-free localiza-

tion beyond connectivity. Starting from introducing neighborhood ordering as a location-

dependent signature for each node in the network, we presented the designs of SD as well

as its revised version RSD, which quantify the difference between signatures to capture dis-

tance relationships among neighboring nodes with sub-hop resolution. With little overhead,

RSD can be conveniently embedded in many connectivity-based localization algorithms to

improve system accuracy. Test-bed evaluations demonstrate that applying RSD helps solve

the ambiguity problem and considerably enhance localization accuracy. In addition, ex-

tensive simulation reveals that RSD is effective under different network configurations and

offers a nice feature of robustness for spatially unevenly distributed radio path loss.

4.3 SBT: Sequence-based Tracking Under Unreliable Sensing

In this section, we extend the concept of localization with node sequence processing in

Chapter 3, and the new idea of signature distance in Section 4.2 to mobile target tracking

applications.

Tracking mobile targets using sensor networks have been considered as a promising but

challenging task [2, 8, 20], because of the impacts of in-the-filed factors such as environ-

ment noise, sensing irregularity and etc. We investigate a new approach called sequence

based tracking (SBT). Without assumptions of target movement models and without accu-

rate range-based localization, mobile tracking is accomplished by processing node sequences

that serve as location-dependent node signatures and can be easily obtained by ordering

related sensor nodes according to their sensing results of the mobile target. As a range-free

approach, tracking by processing node sequences (signatures) provides a useful layer of ab-

straction: as long as the node sequences obtained reflect the relative distance relationships

among the target and the sensor nodes with known positions, specific format of the phys-

ical sensing modality (e.g., heat/RF radiation, acoustic/sematic wave) is irrelevant to the

tracking algorithm. Thus, the design is very generic, flexible, and compatible with different

sensing modalities.

The major difficulty in the SBT system is that node sequences are unreliable due to

combined factors such as irregular signal patterns emitted from the target, environment

noise, sensing irregularity [219] and so on. By applying the space and time domain constrains

that are universally appropriate for any moving object, we demonstrate that our design

owns better tracking accuracy than a base-line method using sequential-based localization,

125

especially in the scenarios where considerable noise exists. In short, the design in this

section owns the following features.

• To the best of our knowledge, SBT is among the first on mobile tracking with unreli-

able node sequence processing.

• No assumptions about the target movement model, costly per-node hardware and no

environment profiling and in-situ calibration.

• Tracking by processing node sequences provides a useful layer of abstraction, making

the design framework more generic and compatible with different sensing modalities.

The rest of this section is organized as follows. Section 4.3.1 gives an overview about

the design. Section 4.3.2 and 4.3.3 detail the SBT design. Section 4.3.4 discusses several

issues concerning practical system deployment. Section 4.3.5 and 4.3.6 evaluate the design

with extensive simulation and a real system implementation. Section 4.3.8 briefly discusses

related work on tracking and summarizes the design of SBT.

4.3.1 System Overview

The purpose of the design described in this section is to track mobile events or targets in an

open area in which wireless sensor networks are deployed. This section gives an overview

of the tracking system which is composed of three parts as shown in Fig. 4.34.

In Fig. 4.34(a), after the deployment of sensor nodes, the map of the area under surveil-

lance can be divided into lots of small regions, named faces, according to the positions of

the sensor nodes, which can be obtained during the network deployment and initialization

period with various techniques [57, 59, 62, 83, 85, 135, 145, 152, 178, 169, 195, 196, 197, 198].

Using the center of gravity of each face as vertices, a neighborhood graph can be built for

the purpose of preventing biased movement estimation caused by sensing noise. In practice,

both map dividing and neighborhood graph building can be pre-computed as soon as the

network has been deployed.

When a mobile target enters the monitored area, sensor nodes detect certain forms of

physical signals emitted from the target. Due to different geographic distances between

each sensor node and the target, the sensing results at each sensor node vary, e.g., different

signal strength, time-of-arrival. This naturally gives an ordering of the sensor nodes called

a detection node sequence, or for short, a detection sequence. Along the moving trace of

the target, periodic sensing results from related sensor nodes produce a series of detection

sequences, as shown in Fig. 4.34(b), which embed relative position relationships among the

sensor nodes and mobile target. Then, with pre-computed map division and neighborhood

graph, the trace of the mobile target can be estimated by processing a series of detection

sequences, as shown in Fig. 4.34(c).

126

1

2

3

4

5

(a) Map Dividing and Neighborhood Graph Building

(b) Detection Node Sequences Obtained for the Mobile Target

1 2 3 4 5...

1 3 2 4 5

...2 3 4 5 1

5 4 3 1 2

...

1 2 3 4 5

...

1 3 2 4 5

...

2 3 4 5 1

5 4 3 1 2

...

2

1

4

3

5

1

2

3

4

5

1

2

3

4

5

(c) Tracking with Unreliable Node Sequence Processing

Target moving traceEstimated trace

Target moving trace

Center of gravity point Edge between neighbor faces

1 Senor Node 1

2

1

4

3

5

A detection

node sequence

A series of

detection sequences

Figure 4.34: SBT System Overview

In the following, we concentrate on the abstract layer of node sequence processing rather

than a certain type of sensing. For the sake of clarity, we first present the design without

considering some practical issues such as system scalability, multiple objects and etc, all of

which are addressed later in Section 4.3.4.

4.3.2 Main Design

This section presents the basic ideas and algorithm for tracking with node sequence pro-

cessing. After the deployment of wireless sensor networks, pre-tracking preparation builds

the neighborhood graph at the sink node with the location information of all sensor nodes,

for limiting a continuous estimated trajectory of the target so as to filter out errors brought

about by unreliable sensing results. Neighborhood graph building is based on the map

division that is introduced firstly in the following.

127

4.3.2.1 Division of the Map

The division of the map is based on the fact that, ideally, the geographic distance between a

sensor node and the target has a monotonic impact on the sensing readings, such as signal

strength, signal time-of-fly, and etc. For example, radio, acoustic, and heat radiation signals

attenuate monotonically with increasing distance in free space [221, 225, 226], and so does

the time of fly for signal propagation.

(a)

1

2

Div(1, 2)

(b)

2

1

3

f3 (2, 3, 1)

f4 (3, 2, 1)

f5 (3, 1, 2)

f6 (1, 3, 2)

f1 (1, 2, 3)

f2 (2, 1, 3)

Div(1, 2)

Div(2, 3)

Div(1, 3)

f1 : Sf1 = (1, 2)

f2 : Sf2 = (2, 1)

Center of gravity point 1 Sensor �ode 1

Figure 4.35: Examples for Map Division after WSN Deployment

As shown in Fig. 4.35(a), given node 1 and 2 with known positions, the whole area can

be divided into two parts by the perpendicular bisector Div(1, 2) for the dotted segment

connecting two nodes. By geometry, every position point in the gray area under Div(1, 2)

is closer to node 1 than to node 2. So if node 1 and node 2 are ordered by increasing

distance at each position point, all the position points in the gray area have a common

node sequence: (1, 2). We call such an area composed of position points with identical node

sequences as a face f , and the corresponding node sequence as the signature node sequence

of face f , or for short, signature sequence Sf . For example, in Fig. 4.35(a), there are two

faces: f1 and f2 with signature sequences Sf1= (1, 2) and Sf2

= (2, 1), respectively.

With n sensor nodes, there are C2n = n(n−1)

2 perpendicular bisector lines, which divide

the whole map into O(n4) faces, according to geometry study [227]. So statistically, with

an increasing number of sensor nodes, the whole map will be divided into more faces with

smaller sizes. Fig. 4.35(b) shows an example with three sensor nodes. The whole map is

divided into six faces with distinct signature sequences. One fact about map division is that

each face has a unique signature sequence.

Proof: Going from any fi to fj (i 6= j) along a straight line, we need to across the

boundary of fi to reach fj. The boundary is a perpendicular bisector for a pair of nodes

in the map, say node u and node v. Since we follow a straight line, we can only cross this

perpendicular bisector once. Therefore, when we arrive at fj, the order of node u and v

must get flipped in Sfjfrom Sfi

, namely Sfj6= Sfi

.

In ideal case, the geographic distance between a sensor node and the target has a

monotonic impact on the sensing readings. If the target locates in f , the signature sequence

128

Sf of face f reflects the perspective ranking of in-the-field sensor nodes according to their

sensing results. Therefore, with map division results, a simple localization system works as

follows: given a detection sequence Sd, target can be localized by matching Sd with each

Sfi. The face making the best match shows the estimated position area of the target.

4.3.2.2 Unreliable Detection Node Sequence

In ideal case, a detection sequences Sd should be identical with one of the face signatures.

However, in a real system, sensing at each sensor node could be irregular and affected by

many factors including environment noise, obstacles and etc. As a result, Sd is unreliable,

which could be either a full detection sequence including all the related sensor nodes, or a

partial detection sequence, in which some of the nodes supposed to appear are missing. In

addition, nodes in Sd could get flipped due to noisy sensing.

A node sequence with k sensor node elements has P (k, k) = k! possible permutations. In

addition, Sd could be a partial sequence, so the total number of possible unreliable detection

sequences in a system with n sensor nodes is:

n∑

k=1

P (n, k) =

n∑

k=1

n!

(n − k)!(4.13)

On the other hand, for n sensor nodes, there are a number of O(n4) faces with distinct

signature sequences. This is a much smaller space than that of the detection sequences

in Eq. 4.13. Therefore, as depicted in Fig. 4.36, given a detection sequence Sd, most of

the time there is no direct face matching; instead, we need to search for a face with the

maximum likelihood.

. . .

. . .

. . .

. . . . . .

Detection Sequence

DomainFace Signature

Sequence Domain

∑= −

n

k kn

n

1 )!(

!)( 4nO

Detection sequenceFace signature sequenceMaximum likelihood matching

. . .

Figure 4.36: Detection Sequences v.s. Signature Sequences

Before going further, there are two questions that need to answer: (i) how to evaluate

the likelihood between a detection sequence Sd and a signature sequence Sfi? (ii) is there

a monotonic relationship between the likelihood and the geographical distance? Next sub-

section addresses both questions by defining a metric, explaining the insight, and proposing

the computing algorithms.

129

4.3.2.3 The Sequence Distance

Given two signature sequences S1 and S2, their sequence distance, denoted with SeqD(S1, S2),

is defined as the number of flipped node pairs between S1 and S2.

2

1

3

f2 (2, 1, 3)

SeqD(Sf1, Sf2) = 1

SeqD(Sf1, Sf3) = 2

Sf1 = (1, 2, 3), Sf2 = (2, 1, 3)

Sf1 = (1, 2, 3), Sf3 = (2, 3, 1)Div(1, 2)

f1 (1, 2, 3)

f3 (2, 3, 1) f4

(3, 2, 1)

f5 (3, 1, 2)

f6 (1, 3, 2)

(1, 2) (2, 1)

(1, 2) (2, 1)

(1, 3) (3, 1)

Figure 4.37: Examples for the Sequence Distance

Fig. 4.37 shows an example, for f1 and f2, Sf1= (1, 2, 3) and Sf2

= (2, 1, 3). Only

one pair of nodes gets flipped from Sf1to Sf2

, namely (1, 2) =⇒ (2, 1). So the sequence

distance SeqD(Sf1, Sf2

) = 1. Similarly, two pairs of nodes get flipped from Sf1to Sf3

, so

SeqD(Sf1, Sf3

) = 2.

The Insight into the Sequence Distance

The rational behind node pair flips is crossing the bisector lines in the map. For example,

in Fig. 4.37, if we go from f1 to f2 along a straight line, we need to cross the perpendic-

ular bisector Div(1, 2), which causes the distance relationships for node 1 and node 2 get

reversed. Similarly, going from f1 to f3 needs to cross two bisector lines, shown with the

dashed arrow, so two node pairs get flipped.

For two faces fi and fj (i 6= j), now there are two types of distance: (i) the geographical

distance GeoD(fi, fj) between the center points of fi and fj, and (ii) the sequence distance

SeqD(Sfi, Sfj

). For these two distances, we have the following Observation I :

SeqD(Sfi, Sfj

) ∝ GeoD(fi, fj) (4.14)

Eq. 4.14 indicates that the sequence distance between two faces is approximately pro-

portional with their geographical distance. This is because longer geographical distance

creates chances for crossing more bisectors, resulting in more flipped node pairs. Fig. 4.38

2

1

3

4

Seq. Distance = 1

Seq. Distance = 2

Seq. Distance = 3

Seq. Distance = 4

Seq. Distance = 5

Seq. Distance = 6f1

Figure 4.38: Sequence Distance vs. Geographic Distance

130

depicts a simple example for this observation: faces with identical sequence distances to f1

are filled with the same pattern. We can see that: (i) faces with smaller sequence distance

to face f1 locate geographically closer to it, and (ii) faces with identical sequence distance

form roughly a layer of faces surrounding face f1. This example illustrates that sequence

distance has a positive correlation coefficient with the geographic distance.

The Sequence Distance Algorithm

The total number of discordant node pairs on ordering between two sequences is called

the Kendall Tau Distance [228], or KTD for short. Traditional KTD addresses only the situ-

ation that two sequences have identical length and digit sets. As analyzed in Section 4.3.2.2,

the detection sequence in our system could be partial, therefore, the traditional KTD can

not be applied directly.

In our system, nodes from any detection sequence is always a subset of the node set

of signature sequences. This is because a signature sequence includes all nodes that can

possibly detect the targets. So, given a detection sequence, it can only be (i) a full sequence

with the same length as any signature sequence, or (ii) a shorter sequence composed of

a subset of the nodes in the map. To accommodate both issues, we apply the signature

distance mechanism proposed in previous Section 4.2 to calculate the sequence distance

(i.e., SeqD). For the sake of clarity, we provide the definition of sequence distance and a

simple example for its calculation in the following.

Definition: The sequence distance (SeqD) between a detection sequence Sd and a signature

sequence Sfiequals the total number of flipped node pairs, considering those missing nodes

in Sd.

The basic idea for calculating the SeqD is to use wildcard characters, shown in Fig. 4.39.

In Fig. 4.39(a), if the detection sequence Sd is shorter than the signature sequence Sfi, add

∗ at the end of the Sd to make S′d with the same length as Sfi

. Then, for every node pair

in Sfi, search in S′

d to check if the ordering of this pair gets flipped. There are three cases:

(i) if two nodes u and v, appear in both S′d and Sfi

, simply compare their ordering; (ii) if

one node, saying u, is missing from S′d, call it a flip if the order is (u, v) in Sfi

, otherwise,

it is a match; (iii) if both u and v are missing in S′d, consider no flip.

...

... ...

Sd

Sfi

...

... ...

1 2

1 3 2

Match Flip

SeqD(Sd , Sfi) = 1

1 2

1 3 2

Match

1 2

1 3 2

1 2

1 3 2

(a) (b)

...Sd’

Sfi

Sd

Sfi

Figure 4.39: Examples for SeqD Calculation with Wildcard Matching

131

Fig. 4.39(b) shows a simple example. There are three ordered node pairs in Sfi: (1, 3),

(1, 2), and (3, 2). Correspondingly, three ordered node pairs in S′d: (1, ∗), (1, 2), and (2, ∗).

It is clear that we can match the first two ordered pairs from two sequences, and we can

find a flip between (3, 2) and (2, ∗). Counting the number of flips, we can conclude that

their sequence distance SeqD(Sd, Sfi) = 1.

While the SeqD idea is straightforward, the rationale behind adding wildcards at the

end of a detection sequence deserves further explanation. If a node is missing in Sd, it is

likely to be further from the target than those nodes appearing in Sd, thus it is assumed

to be at the end of the sequence. Theoretically, adding two wildcards at the end of Sd is

sufficient for SeqD calculation. Here, we keep the design of making a full length sequence

to maintain concept elegance.

4.3.2.4 Neighborhood Graph

In this subsection, the neighborhood graph is introduced for filtering out errors brought

about by unreliable detection sequences.

Most of the mobile targets follow the following Observation II :

△Xmax = Vmax · △T (4.15)

meaning that the maximum moving offset of the target △Xmax within the time interval

△T between two sensing operations of a sensor node is bounded by its maximum speed

Vmax times △T . This is because that with limited maximum speed, a target moves from

one position to another following a continuous trace rather than performing a “hyper-space

fold operation”.

Target’s movement is one type of mechanical action, which is much slower when com-

paring with sensor’s sampling rate that is one type of electronic action. For example, it

is reasonable to assume that a vehicle moves with a maximum speed of 30 miles per hour

(i.e., 13.4 meters per second) in the wide area. While achieving 10 Hz sampling rate is

trivial even for the resource constrained senor nodes. During the time interval between two

samples, the target can only move at most 1.3 meters. Therefore, according to Eq. 4.15, we

can comfortably consider that if the target currently locates in one face in the map, at the

next sampling instance the target is either still in the current face or at most moves into a

neighbor face that is defined as follows.

Definition: If the geographic distance between the closest points of two faces are shorter

than △Xmax, these two faces are neighbor faces to each other.

As shown in Fig. 4.40(a), the gray area is f1. If a target is currently in f1, after △T ,

its location is bounded by the offset boundary depicted with a thick gray curve. Therefore,

the dashed faces illustrated in Fig. 4.40(b) are the neighbor faces of f1. Connect the center

132

2

1

4

3

5

Edge for neighbor faces

Neighborhood of f1

2

1

4

3

5

(a) (b)

Offset boundary of f1

f1 f1

Figure 4.40: Neighbor Faces and Neighborhood Graph Building

of gravity points of neighbor faces with that of f1, as shown in Fig. 4.40(b), indicating that

it is possible for the mobile target to move from f1 to those linked faces during △T , and

vice versa. Connecting all the faces with their neighbor faces builds a neighborhood graph

G, examples of which are shown in Fig. 4.41. The vertex set V (G) is composed of center

of gravity points of all faces, and the link set E(G) limits possible inter-face movements

within △T . In other words, sensing errors, which shows that the target moves out of the

neighborhood area, can be filtered out.

4.3.2.5 Tracking as Optimal Path Matching

Given a series of detection sequences Sd(k) where k = 0, 1 · · · ,M , instead of performing per-

sequence face matching, a path composed of faces f(k) with minimal accumulated sequence

distance to Sd(k) owns the maximal overall likelihood. Now, the tracking problem turns

into an optimal path matching issue as follows.

minimize

M∑

k=0

SeqD(Sd(k), Sf(k))

subject to f(k) ∈ V (G)

∀k, edge(f(k), f(k + 1)) ∈ E(G) (4.16)

Section 4.3.2.1 mentioned that with n sensor nodes, the map can be divided into O(n4)

faces, meaning that there are O(n4) central of gravity points that be used to plot the

estimated tracking trace. The tracking accuracy gets significantly enhanced with increasing

number of sensor nodes, verified by Fig. 4.41 showing example G with increasing n. However,

G becomes extremely complicated with larger n. Finding the optimal path becomes so

challenging that a naive algorithm would lead to exponential complexity growth with n.

Optimal Path Matching

This subsection presents a forward dynamic programming based method for solving the

optimization problem shown by Eq. 4.16 with polynomial complexity.

133

0 20 40 60 80 1000

10

20

30

40

50

60

70

80

90

100

Sample Neighborhood Graph (4 Sensor Nodes)

x−coordinate (by meters)

y−

co

ord

inate

(b

y m

ete

rs)

0 20 40 60 80 1000

10

20

30

40

50

60

70

80

90

100

Sample Neighborhood Graph (8 Sensor Nodes)

x−coordinate (by meters)

y−

co

ord

inate

(b

y m

ete

rs)

0 20 40 60 80 1000

10

20

30

40

50

60

70

80

90

100

Sample Neighborhood Graph (12 Sensor Nodes)

x−coordinate (by meters)

y−

co

ord

inate

(b

y m

ete

rs)

0 20 40 60 80 1000

10

20

30

40

50

60

70

80

90

100

Sample Neighborhood Graph (16 Sensor Nodes)

x−coordinate (by meters)

y−

co

ord

inate

(b

y m

ete

rs)

Figure 4.41: Neighborhood Graph for Randomly Deployed 4, 8, 12 and 16 Nodes

Fig. 4.42(a) shows a simple example for a neighborhood graph G. In the figure, each

vertex stands for a face, namely face f1, f2, f3, f4 and f5. For the sake of clarity, temporarily

assume that at time k = 0, the starting face s of the target is f1. Later, we will address the

issue of unknown starting face s.

Starting with s = f1 at k = 0 in G, at k = 1, the target can only either remain at f1

or move into f2 or f3. So, f1, f2, and f3 are candidate faces for time k = 1, listed under

k = 1 in Fig. 4.42(b). Connecting f1 under k = 0 with its candidate faces under k = 1 adds

edges to the graph in Fig. 4.42(b). Repeating this process, we can list candidate faces for

k = 2 and add corresponding edges wiring to vertices under k = 1. Given two detection

f1

s

k = 0

f1

f2

f3

k = 1

Sd (1)

f1

f2

f3

k = 2

Sd (2)

f4

f5

(b) Candidate Path Graph H

...

...

...

…

...

e

s

f3

f1

f4f2

f5

(a) G

s

(c) Shortest Path in H

......

k = 0 k = 1 k = M-1 k = M

Figure 4.42: Converting Optimal Path Matching to Shortest Path Searching

134

sequences Sd(1) and Sd(2) for time instance k = 1 and k = 2, compute the sequence distance

(SeqD) from the signature sequence of each face under k = 1 and k = 2 to Sd(1) and Sd(2),

respectively. We can obtain a candidate path graph H, in which each vertex in column k

is a possible face to reach at time k, and carries a weight of SeqD to Sd(k).

As shown in Fig. 4.42(c), finding an optimal path in G with overall maximum likelihood

to a series of detection sequences (Sd(1), Sd(2) · · ·Sd(M)) is equivalent to searching for a

path in H from k = 0 to k = M with minimum accumulated vertex weight. Defining the

accumulated vertex weight of a path in H as the length of the path, now the problem turns

into a shortest path problem in graph H, which can be solved with the forward dynamic

programming with polynomial complexity (or the Viterbi algorithms) [229]. The basic idea

is to keep only the best path to each vertex under each k in H. Then choose the vertex

under k = M with the minimum path length as the terminal vertex e, and recursively trace

back to build the whole shortest path.

In practice, without knowing s at k = 0, the matching algorithm starts from k = 1 by

choosing c faces, where 1 ≤ c ≪ O(n4), with the smallest sequence distance to Sd(1). Later

simulation reveals that a small number c (e.g., c = 3) is sufficient to get sound results.

4.3.2.6 Algorithm and Complexity Analysis

The grid-like structure of graph H conveniently supports both off-line tracking, which com-

putes an overall optimal path of the mobile target after collecting all detection sequences,

and on-line tracking, which processes a new detection sequence immediately by adding

another column in H and outputs an optimal path so far. Algorithm 9 illustrates the

computation structure applicable for both systems.

Algorithm 9: Optimal Path Matching

input : Detection sequences Sd(k), k = 1, · · · ,MNeighborhood graph G

output: Optimal path P

H(1).faces = Initialization (Sd(1), G) ;1

repeat2

H(k).faces = Neighbor (H(k − 1).faces,G) ;3

repeat4

f = Unprocessed (H(k).faces) ;5

f.dis = SeqD(Sf , Sd(k)) ;6

f.preface = Min (H(k − 1).faces.cost) ;7

f.cost= f.preface.cost + f.dis ;8

until all faces in H(k) are processed ;9

until k = M ;10

P = TraceBack (minimum{H(M).faces.cost}) ;11

135

Line 1 initializes the faces for H(k = 1) by selecting c faces in G with the shortest

sequence distance to Sd(1). The H graph is built between line 2 and 10. Line 3 prepares

the faces for H(k), each of which is processed between line 4 and 9 by computing sequence

distance (SeqD), finding its single optimal preface, and accumulating the path cost. Finally,

an overall optimal path P can be obtained by recursively tracing back from H(M) to H(1)

at line 11.

Each H(k) contains at most O(n4) faces for a system with n nodes. The SeqD calculation

costs a complexity of O(n log(n)) with a bubble-sort algorithm [204]. Preface searching at

line 7 costs O(1) since the optimal preface can be obtained at line 3 when listing all neighbor

faces. So, the time complexity for Algorithm 9 is O(M · n5 log(n)) for off-line systems and

O(n5 log(n)) for updating in on-line systems. The storage complexity for both systems

is O(M · n4). For the moment, the complexity seems high due to O(n4) faces. In later

section, we will explain how the complexity can be significantly reduced to a feasible level

for large-scale networks.

4.3.3 Multi-dimensional Smoothing

This section introduces multi-dimensional smoothing in the modality domain, time domain,

and space domain, working together to contribute to the accuracy and generality of the

whole system design.

4.3.3.1 Modality Domain Smoothing

If a sensor node is capable of sensing the environment with multiple modalities (e.g., acous-

tic, infrared and etc), it could be hard to merge those sensing results at the physical layer.

For example, comparing a 10 dB acoustic signal with a −60 dBm RF strength is meaning-

less. In our design shown in Fig. 4.43, by converting the sensing results from each modality

into node sequence at the sink, an abstract layer is provided for integrating sensing results

from diverse modalities.

Radio ...Infrared Acoustic Magnetic

Detection Node Sequence Layer

Tracking Algorithm

Temp.

Figure 4.43: SBT Allows Multi-modality Integration at the Sequence Layer

Given detection sequences from Q modalities for time k, denoted as Sid(k) (i = 1, 2 · · · , Q),

final SeqD to face f , Df (k), can be obtained by smoothing over individual SeqD values for

136

each modality i with different weight wi according to its precision and reliability.

Df (k) =

Q∑

i=1

(wi · SeqD(Si

d(k), Sf ))

(4.17)

For the tracking algorithms on top of the sequence layer, specific physical modalities

become invisible.

4.3.3.2 Time Domain Smoothing

Time domain smoothing over continuous detection results is commonly used for filtering

out random noise in many systems. Unlike most of the other systems conducting time

domain averaging at the physical modality layer, in our design, smoothing can be performed

conveniently at the node sequence layer. The basic idea is to average the weighted sequence

distance (SeqD) obtained from Eq. 4.17 to each face f along the timeline over a smoothing

window with odd length L:

Df (k) =

∑(L−1)/2i=−(L−1)/2 Df (k + i)

L(4.18)

The length of the averaging window can vary in specific applications. The sequence

distance to a face roughly reflects the geographic distance, so averaging sequence distances

has an effect similar to averaging sensing results directly.

4.3.3.3 Space Domain Smoothing

The design presented so far maps the position of the mobile target at each time instance

to the center of gravity point of a face in the map. This results in two phenomena: (i)

many positions in the true trace are projected to the same estimated position, and (ii)

estimated positions scatter at both sides of the true trace. It is not a good idea to plot

the estimated trace by simply connecting those estimated positions without space domain

smoothing, because it could give a curve oscillating around the true trace. A better trace

estimation can be obtained by smoothing over the estimated positions using a smoothing

window with odd length L′:

xk =

∑(L′−1)/2i=−(L′−1)/2 xk+i

L′ , yk =

∑(L′−1)/2i=−(L′−1)/2 yk+i

L′ (4.19)

where (xk, yk) are estimated position coordinates for time k before space domain smoothing,

which actually are the coordinates of the center of a face; (xk, yk) is the final estimated

position after space domain smoothing.

137

4.3.4 Issues in Practical Applications

This section discusses issues for real system implementation, including system scalability,

multiple targets tracking, time synchronization, and energy efficiency.

4.3.4.1 Issue on System Scalability

Although system computation and storage complexity are O(M · n5 log(n)) and O(M · n4)

respectively according to the analysis in Section 4.3.2.6, we show in this section that in

large-scale system deployment, where hundreds or thousands of sensor nodes exist in a

large area, the design can work well with tolerable complexity after implementation level

optimization.

An observation for large-scale systems is that only a small portion of sensor nodes close

to the mobile target are effective for target detection at any time instance.

Effective area IEffective area II

Sensor Node Mobile Target

Target ITarget II

R

R

Figure 4.44: Issues of System Scalability and Multiple Targets Tracking

As it is shown in Fig. 4.44, the gray area depicts the signal pattern emitted from the

target. So, the length of a detection sequence is much shorter than n which is total number

of sensor nodes deployed. Setting a range R for the effective area large enough to cover

perspective signal pattern with high confidence as shown in Fig. 4.44, map division can be

done locally with sensing range R instead of including all the sensors in the map. Now

face signature sequences have diverse length but not longer than m which is the maximum

number of sensor nodes in an effective area with radius R. The sequence distance can be

computed with complexity of O(m log(m)) rather than O(n log(n)), where m ≪ n.

When the target stays in the monitored area for a long time, the shortest-path-searching

graph H illustrated in Fig. 4.42 could be too big to store. This problem comes from our

intention to obtain an overall optimal path, however remembering all candidate optimal

pathes is neither necessary nor possible in large-scale systems.

Fig. 4.45 illustrates the basic idea for effectively truncating H. A processing window

with length M and height N is applied to the original graph H. Horizontally, when a

column moves out of the dashed window (e.g., k = T − M), the decision for the shortest

path until this column is made and stored. Then the system works as if there is a new

starting vertex in k = T − M for columns K = T − M + 1, · · · . Vertically, a limit N is set

for the maximum number of candidate faces under any K in the window. If the faces under

138

k = T-1 k = T

...

...... ...

k = T-M +1

...

k = T-M

...

k = 1

...

M

N

Figure 4.45: Demo of Reduced Candidate Path Graph H

k = T − 1 have more than N neighbor faces, only let faces with smaller accumulated path

costs post their neighbors (totally no more than N) as candidate faces under k = T .

Now, the computation complexity is not directly related to the total number of sensor

nodes n, but turns to O(T · (N log(N) + N ·m log(m))), where N log(N) is for sorting, and

storage complexity becomes O(M · N) for all the vertices within the dashed window.

4.3.4.2 Issue on Multiple Targets

Multi-target tracking (MTT) [211] is not an easy extension of single target tracking because

of inherent data association ambiguity, i.e., the uncertainty in mapping sensing measure-

ments with individual targets which might have the same or similar signal signatures. Such

ambiguity increases combinatorially with the number of targets. To disambiguate, MTT

should be able to uniquely identify the signature of each target, which is normally beyond

the capability of the sensor nodes we discussed in this thesis. In our design, if targets are

far apart from each other, the tracking system is able to differentiate them and achieve

simultaneous tracking.

Fig. 4.44 depicts a simple example of two mobile targets’ existing in the area. If a

distributed tracking system is available, the processing terminal close to effective area I

could handle target I, and simultaneously another processing terminal close to effective area

II could handle target II. If only a single sink is used for detection sequence processing, after

receiving a stream of node detections without in-network detection sequence assembling, the

sink is also able to differentiate detections for target I from those for target II since the set

of sensor nodes in area I is totally different and geographically distant from that in area II.

4.3.4.3 Issues on Time Synchronization and Energy Efficiency

Current time synchronization techniques can achieve microsecond level accuracy (e.g., FTSP

[117], TPSN [115], etc). The sampling rate of each sensor could be from several HZ to

hundreds of Hz. The time interval between two samples varies from microseconds to seconds.

So by timestamping each sensing results, the sink or the distributed tracking terminals can

correctly assemble the detection sequences for different time instance.

Energy efficiency is vital in sensor networks. Most of the time, sensor nodes keep a low

139

duty cycle until some event or target appears in the monitored area. Nodes near the target

increase their sampling rate and alert only nodes close to the projected moving trace [205],

keeping others remain in sleep. On the other hand, working nodes can dynamically adjust

sampling rate according to realtime tracking results. For instance, if the sensing results

vary slowly, meaning that the target slows down, sensor nodes can reduce the sampling

rate, vice versa. In addition, nodes adjusting their sampling rates may also notify related

nodes helping them prepare for the coming target.

4.3.5 Simulation Evaluation

We evaluated the system design with both simulation and testbed implementation. In this

section, we compare the tracking performance of the optimal path matching (PM) proposed

in this section with the sequential maximum likelihood estimation, or Direct MLE [94].

In the simulation, we model the monitored area as a grid map. A movement trace of the

mobile target is generated with the random way-point mobility model (RWP) [206, 207].

An estimation error at one point in the trace is defined as the geographic offset between the

estimated position and corresponding true position. The mean tracking error is defined as

averaged error of all the points in the trace. All the statistics are averaged over 50 runs for

high confidence. The following table illustrates the default simulation setup.

Table 4.5: Default Simulation Configurations for SBT

Parameter Description

Field Area 100 (meters)×100 (meters)

Noise Model Logarithmic (β = 4, σX = 6)

Number of Sensor Nodes 10, randomly deployed with uniform distribution

Sensing Sampling Rate 10Hz

Target Velocity Random between 1 ∼ 5 (meters/s)

Averaging Window 2.9s (Time Domain ), 99 points (Space Domain)

4.3.5.1 Noise Models

For signal detection, two noise models are used for simulation evaluation: (i) a linear delay

noise model for time-of-fly based detection, depicted in Eq. 4.20, and (ii) a logarithmic

attenuation noise model for signal-strength based detection [221, 226], described by Eq. 4.21.

Si(k) ∝ 1

(1 + α) · di(k), α ∼ N(0, σ2

α) (4.20)

Si(k) ∝ −10β log(di(k)

d0) + Xi(k) (4.21)

d0 = 1 and Xi(k) ∼ N(0, σ2X )

Si(k) stands for the sensing result of senor node i at time instance k. di(k) is the physical

distance between node i and the target at time k. In the linear model (Eq. 4.20), α is a

140

random variable for time delay following a normal distribution with 0 mean and variance

σ2α. In logarithmic model, β is the signal fading factor and Xi(k) is a random noise at time

k for node i following a normal distribution with 0 mean and variance σ2X .

4.3.5.2 An Example by Figures

This subsection gives an intuitive comparison between Direct MLE (D-MLE) and path

matching (PM).

Fig. 4.46(a) and Fig. 4.46(b) show the position points estimated by D-MLE and PM,

respectively. From these two figures, it is clear that position points given by PM are more

closely distributed around the true trace. Fig. 4.46(c) gives the smoothed traces from PM.

4.3.5.3 SBT Performance Evaluation

Impact of the Sensing Noise

In this experiment, we compare the tracking accuracy of the path matching algorithm

with direct MLE under different levels of sensing noise. Both linear and logarithmic noise

models are investigated.

Fig. 4.47(a) illustrates the performance of both methods under different σα for the linear

noise model (Eq. 4.20). Fig. 4.47(a) indicates: (i) noise introduces tracking error; (ii) path

matching-based tracking is very robust to noise (error increases slightly with larger noise),

while the Direct MLE degrades quickly. For example, when σα = 0.4, the D-MLE has

doubled the error rates of PM. (iii) when noise is 0 (σα = 0), the results of two methods

converge. This is because if noise is 0, identical faces are chosen by both methods.

Similarly, Fig. 4.47(b) shows the performance trend of both methods under different σx

for the logarithmic noise model (Eq. 4.21). The figure indicates that (i) greater sensing

noise brings in larger tracking error, and (ii) path matching-based tracking is more robust

to noise compared with the Direct MLE. Fig. 4.47(c) shows the performance trend as β

increases for the logarithmic noise model. We can see that bigger β reduces the tracking

error. This is because the distance owns more weight with increasing β, and noise has less

impact comparatively.

From the above three figures, we can conclude that the path matching based method is

superior to the Direct MLE based solution, especially when the noise is considerable.

Impact of the Sensor Node Density

We compare the path matching method with Direct MLE under a different number of

sensor nodes, ranging from 6 to 14 in steps of 1. Fig. 4.48 depicts that (i) with the increasing

number of deployed sensor nodes, the tracking error is reduced, and (ii) the path matching

system outperforms the system using Direct MLE.

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10

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Position Points by Direct MLE

x−coordinate (meter) y

−c

oo

rdin

ate

(m

ete

r)

Anchor Nodes

Enter Point

Exit Point

Ground Truth of Moving Trace

Estimated Positions

(a) Position Points by D-MLE

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10

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Position Points by Path Matching

x−coordinate (meter)

y−

co

ord

inate

(m

ete

r)

Sensor Nodes

Target Enter Point

Target Exit Point

Ground Truth of Moving Trace

Estimated Positions

(b) Position Points by PM

0 20 40 60 80 1000

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Smoothed Tracking Results by Path Matching

x−coordinate (meter)

y

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Sensor Nodes

Target Enter Point

Target Exit Point

Ground Truth of Moving Trace

Estimated Moving Trace

(c) Smoothed Result by PM

Figure 4.46: A Tracking Example from Simulation

Impact of the Number of Starting Faces

In order to achieve an optimal path, in theory, searching should start from every face in

the neighborhood graph. Simulation results shown in Fig. 4.49 indicate that (i) increasing

the number of starting faces from 1 to 2 enhances the system accuracy considerately, while

142

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

5

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Impact of Noise (Linear Noise Model)

σα

T

rac

kin

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rro

r (m

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Maximum Error of Direct MLE

Maximum Error of Path Matching

Mean Error of Direct MLE

Mean Error of Path Matching

(a) Linear Noise Model

4 5 6 7 8 9 10 11 120

10

20

30

40

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60

Impact of Noise (Logarithmic Noise Model β = 4)

σx

T

rackin

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Maximum Error of Direct MLE

Maximum Error of Path Matching

Mean Error of Direct MLE

Mean Error of Path Matching

(b) Logarithmic Noise Model: σx

2 2.5 3 3.5 4 4.5 5 5.5 60

10

20

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Impact of Noise (Logarithmic Noise Model σx = 6)

β

T

rac

kin

g E

rro

r (m

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Maximum Error of Direct MLE

Maximum Error of Path Matching

Mean Error of Direct MLE

Mean Error of Path Matching

(c) Logarithmic Noise Model: β

Figure 4.47: Impact of the Sensing Noise to Tracking Error

(ii) more than 3 starting faces gets little performance gain. So, we can safely use 5 starting

faces as the default system setup.

143

6 7 8 9 10 11 12 13 140

5

10

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50

Impact of the Number of Sensor Nodes

Number of Sensor Nodes T

rac

kin

g E

rro

r (m

ete

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Maximum Error of Direct MLE

Maximum Error of Path Matching

Mean Error of Direct MLE

Mean Error of Path Matching

Figure 4.48: Impact of the Number of Sensor Nodes

1 2 3 4 5 6 7 8 920.2

20.3

20.4

20.5

20.6

Impact of the Number of Starting Faces

Number of Starting Faces

M

ax E

rro

r (m

ete

r)

Maximum Error of Path Matching

1 2 3 4 5 6 7 8 95.083

5.084

5.085

5.086

5.087

Number of Starting Faces

M

ean

Err

or

(mete

r)

Mean Error of Path Matching

Figure 4.49: Impact of the Number of Starting Faces

4.3.5.4 Effectiveness of Smoothing

Fig. 4.50 illustrates the effectiveness of smoothing at each dimension individually and com-

bined together. For modality domain smoothing, we assume that a node has two sensors for

acoustic and radio signal strength detection, respectively. This figure shows that smoothing

at each individual dimension contributes to the accuracy of the tracking system. Further

more, they can work together to additively enhance the system.

4.3.5.5 Impact of the Node Placement

In this experiment, three different types of sensor node placement are simulated for com-

parison. All of them contain 9 sensor nodes.

Figure 4.51 and Figure 4.52 illustrate the neighborhood graphs of a matrix -shaped node

placement and a cross-shaped node placement, specifically. Black stars in the figures denote

the sensor nodes. Filled circles are the central of gravity points of the faces in the map.

We call the above two types of placements regular placements. The third type of node

144

Maximum Error Mean Error0

5

10

15

20

25

30

35

Impact of Smoothing

T

rac

kin

g E

rro

r (m

ete

r)

Without Smoothing

Only Modality−domain Smoothing

Only Time−domain Smoothing

Only Space−domain Smoothing

Multi−dimensional Smoothing

Figure 4.50: The Effectiveness of Smoothing

placement is random node deployment. The layout of the network for random placement

changes in each simulation run. Figure 4.53 shows an example.

The total number of faces for each type of placement is counted for 50 simulation trail-

runs, as shown in Figure 4.54. Regular placements have a constant number of computed

faces, i.e., 96 for the matrix style and 160 for the cross shape. (note that the computed

numbers of faces may not equal the numbers of faces in theory because of resolution con-

strains in the grid map modeling used in our simulation). For the random deployment,

the bottom sub-figure in Figure 4.54 shows a histogram of the number of faces occurred

in the simulation. Observing above Figure 4.51, 4.52, 4.53 and 4.54, we can see that (i)

considering about the number of faces, matrix < cross < random. This is because reg-

ular placements have many overlapping bisector lines; (ii) in terms of balanced face size

and balanced distribution of the central of gravity points, cross is better than both matrix

and random. The above relationships have an direct impact on the system error, which is

illustrated in Figure 4.55.

Figure 4.55 gives the boxplot of the mean errors and maximum errors for three place-

ments over 50 runs. The left boxplot in the figure depicts the mean error comparison. We

can see that cross has the smallest mean error, statistically. Cross has better performance

than random deployment because of its more balanced sensor node distribution. Matrix

has a higher mean error than cross mainly because it contains fewer faces and in addition

there are four holes in the graph as shown in Figure 4.51. The right boxplot in Figure 4.55

shows the maximum error comparison. Random placement has the biggest maximum error

because random placement owns a high probability of creating a small number of big faces

in the map. Cross has the best performance on maximum error due to the smaller size of

its big faces.

145

0 20 40 60 80 1000

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50

60

70

80

90

100

Regular Placement: Matrix (96 Computed Faces)

x−coordinate (meter)

y

−c

oo

rdin

ate

(m

ete

r)Figure 4.51: Regular Deployment: Matrix Shape

0 20 40 60 80 1000

10

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Regular Placement: Cross (160 Computed Faces)

x−coordinate (meter)

y

−c

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(m

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Figure 4.52: Regular Deployment: Cross Shape

0 20 40 60 80 1000

10

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Random Placement Example (346 Computed Faces)

x−coordinate (meter)

y

−c

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rdin

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(m

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Figure 4.53: An Example of Random Deployment

4.3.5.6 Simulation Summary

From the above simulation results, we can conclude that path matching method outper-

forms direct MLE under different noise levels, and diverse numbers of sensor nodes. Multi-

dimensional smoothing is effective, and a small number of starting faces for optimal path

146

100 150 200 250 300 350 4000

50

C

ou

nt

Number of Faces in Matrix Deployments

100 150 200 250 300 350 4000

50

C

ou

nt

Number of Faces in Cross Deployments

100 150 200 250 300 350 4000

5

10

Number of Faces in Random Deployments

C

ou

nt

Figure 4.54: Number of Faces in Different Placements

Matrix Cross Random

2

3

4

5

6

7

8

9

E

rro

r(m

ete

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Mean Error ComparisionMatrix Cross Random

10

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50

55

E

rro

r(m

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Max Error Comparision

Figure 4.55: Error Distributions for Different Placements

searching is sufficient to give good results. With the same number of sensor nodes, place-

ments generating more faces with balanced sizes helps achieve better performance.

4.3.6 Test-bed Experimentation

A system implementation of the design is conducted in the outdoor environment. A Pioneer

III robot is used as a mobile target. 10 MICAz motes are used and 9 of them are deployed

as a cross “+” shape in a lawn as shown in Fig.4.56. The robot, carrying a MICAz sensor

node continuously sending out radio packages in every 100 ms, is programmed to move

along a “⊓” shape trace in the field at a velocity of 10 cm/s. The robot moves with a

relatively slow speed since the grass land is not even and the robot itself is heavy. The

sensor nodes deployed in the lawn record the RF signal strength as well as the timestamps

of the packages received. The data is processed off-line and Fig.4.57 illustrates the results.

The true movement trace of the robot is a distorted “⊓” since the grass ground is

not flat. We can see from Fig.4.57 that (i) the system gives a good tracking result; (ii)

larger estimation error appears at two corners of “⊓”, when the robot was turning and the

147

Figure 4.56: Outdoor System Evaluation: Tracking A Mobile Robot

0 20 40 60 80 100 1200

20

40

60

80

100

120

Smoothed Tracking Results by Path Matching

x−coordinate (0.1 meter)

y−

co

ord

inate

(0.1

mete

r)

Sensor Nodes

Robot Moving Trace

Estimated Moving Trace

Figure 4.57: RF Signal Strength Based Tracking Results

antenna radiation pattern was changing; (iii) there is a small burr in the estimated trace

near x = 80, y = 80. We checked the data and found that there were 3 packages only

received by the node located at x = 60, y = 30 when the robot was close to x = 80, y = 80.

However, this strong noise is almost filtered out in the estimated trace. From the outdoor

system evaluation, we can see that the LUE design is robust to the strong noise and works

in a real system.

4.3.7 A Brief Discussion on Mobile Tracking

Target tracking in sensor networks has been an active research topic recently [208, 209, 210,

211]. One of the basic elements in tracking is the capability of localizing the target. For

sensor networks, both ranging-based localization [73, 76, 81, 83, 100, 212, 149] and ranging-

free localization [52, 158, 162, 166, 177, 192] are investigated. Ranging-based localization

methods perform point-to-point distance measurements between the target whose location

is to be determined, and sensor nodes with known location information, normally called

reference nodes, beacon nodes or anchor nodes. Then triangulation is applied for target

148

location calculation. Ranging-based methods either are costly in terms of adding special

ranging hardware or requiring system calibration and in-the-field environment profiling,

both of which are undesired in sensor networks. Ranging-free localization does not require

per-node distance measurements, instead, proximity [158, 162] or time-spatial relationship

embedded in controlled localization events [192, 196] are used for target positioning.

Another key element in tracking is movement modeling based filtering and estimation.

The most widely used techniques are Bayesian networks [213, 230], Particle filters [214,

231, 232, 233, 234], Kalman filter [49, 153, 215] and its extended versions [153] for nonlinear

system or object with sudden maneuvers. Most of the existing tracking algorithms in sensor

networks assume a certain movement and/or noise model, which might not be available

without in-situ noise profiling and sensor calibration. Although some recent systems let the

mobile target to maintain its location information and only estimate the velocity vectors

for updating [153]. They can not work with uncooperative targets which could be common

in real sensor networks. In contrast, our work is shown to be robust to different types of

noise models, and we impose maximum speed as the only constraint in the design.

The SBT design presented in this section is a new investigation about mobile target

tracking using sensor networks. It does not assume specific movement model for the mobile

target. Instead, only based on the fact that any moving target should have a reasonable

maximum speed. In addition, SBT does not relay on costly ranging-based localization.

Sensor nodes are only responsible for detection and reporting so that system overhead can

be lifted from resource constrained sensor node. Tracking computation can be done outside

of the network where resources are plentiful.

4.3.8 Summary and Remarks on SBT

In this section, we presented a work SBT for mobile target tracking using unreliable node

sequences in wireless sensor networks. Tracking is modeled as an optimal path matching

problem in a graph. In addition to the basic SBT design, multi-dimensional smoothing is

proposed for further enhancing system accuracy. Practical issues including system scalabil-

ity, multi-target tracking, time synchronization and energy efficiency also are discussed and

addressed accordingly. Evaluation results show that tracking with optimal path matching

outperforms per-position maximum likelihood estimation and demonstrate robustness to

the sensing noise. In addition, the design provides a general platform for different physical

modalities with an abstract layer of node sequence.

149

Chapter 5

Concluding Remarks

5.1 Summary of Contributions

The work presented in the preceding chapters has concentrated on investigating new ideas

and techniques for range-free localization in wireless sensor networks, particularly the issue

of event-driven localization and localization with only local sensing. The main contributions

of this work can be summarized as follows.

• Range-free localization with uncontrolled events.

Chapter 3 provides two designs (i.e., MSP in Section 3.2 and LUE in Section 3.3)

to release traditional event-driven localization from using precisely-controlled events

that could be both costly and inconvenient to generate in practical WSN applica-

tions. In the work of MSP, we propose the concept of node sequence processing to

localize low-cost sensor nodes without rigid control over event distributions. MSP

reveals an interesting fact that not only anchor nodes but also target sensor nodes can

contribute to the accuracy performance of localization. By making full use of the infor-

mation embedded in the one-dimension and easy-to-get node sequences, those location

undetermined target nodes are utilized as boundary landmarks to help shrink the pos-

sible localization areas of each other. Importantly, MSP introduces a useful trade-off

between physical costs (anchor nodes) and soft cost (localization events), while main-

taining the desired positioning accuracy. As another substantial step further, the

second work LUE, for the first time, demonstrates the possibility of accomplishing

range-free localization with uncontrolled events. The rational behind LUE is to ex-

plore and estimate event generation parameters according to the detection results

from anchor nodes with known position coordinates. From MSP to LUE, our work on

range-free localization with uncontrolled events successfully bridges the gap between

system cost/flexibility and localization accuracy, and enables a potential option of

achieving sensor node positioning via long-term natural ambient events.

150

• Range-free localization and tracking with signature distance.

Chapter 4 provides two designs (i.e., LBC in Section 4.2 and SBT in Section 4.3) to

promote the performance of range-free localization by means of only local sensing. In

the work of LBC, motivated by the empirical study showing that localization depend-

ing only on radio connectivity may actually underutilize the proximity information

embedded in neighborhood sensing, we invented and applied the idea of signature

distance (e.g., RSD), as a metric to quantify the proximity relationships among 1-hop

neighboring nodes and beyond in the network. RSD successfully provides a sub-hop

solution in a range-free manner. The framework of signature distance can be con-

veniently applied together with the node sequence concept proposed in Chapter 3

to collectively improve connectivity based range-free localization without significant

additional cost. The second work in this chapter, i.e., SBT, extends the discovery of

signature distance and the idea of sequence processing to the mobile target tracking

applications. SBT converts the tracking problem from traditional sequential localiza-

tion to a maximum likelihood shortest path searching in a graph, and demonstrates

robust tracking without complex movement modeling. More importantly, SBT veri-

fies that using the node sequence as a high-dimensional location-dependent signature

provides a useful layer of abstraction that enables sensing modality integration as well

as a quite generic and flexible localization or tracking system design.

5.2 Future Research Directions

This thesis addressed several important problems for range-free localization in wireless

sensor networks. As part of future research, we are interested in and would like to investigate

the following four aspects concerning localization and tracking in wireless sensor networks,

or more generically, in the future pervasive computing environments [235].

• Improving the designs in this thesis.

MSP and LUE in Chapter 3 have achieved range-free localization with uncontrolled

events (either artificially generated or naturally occur). Nevertheless, these systems

may suffer from the extreme situation of events with severely distorted propagation

frontiers, due to a combination of factors including in-field obstacles, uneven terrains,

directional propagation, etc. We could like to address this problem by introducing

carefully designed mechanisms for distortion detection. On the other hand, the signa-

ture distance in Chapter 4 (i.e., LBC and SBT) can be improved in multiple aspects

such as the adaption to unbalanced node density, the optimization of node (anchor)

placement, and proximity information extraction with enhanced resolution. We ex-

pect that by overcoming the difficulties mentioned above, the work in this thesis can

be further improved with better usability in a wide range of applications.

151

• Integrating range-based and range-free methods.

Range-based localization can provide high accuracy but at the cost of additional

ranging hardware, extensive environmental profiling, or careful system tuning and

calibration. Range-free methods could be more economic at the resource constrained

sensor node side, however, by scarifying localization performance as well as deployment

convenience and flexibility. We would like to investigate hybrid solutions so as to

leverage the advantages of both types. In fact, the signature distance proposed in

LBC has demonstrated an intermediate design by offering a relative distance metric

calculated from only range-free sensing results, which resembles the physical distance

measurements. We believe that there should be no clear cut-off line between range-

based and range-free methods. Instead, different applications may require different

combinations of localization techniques.

• Exploring the impact of sensing noise for range-free localization

It is well known that low-cost sensor nodes can output highly unreliable detection

results because of the environmental noise as well as their hardware limitations [219].

Researchers have reported that the impact of sensing noise can be mitigated in

the process of localization by applying various methods such as uncertainty-based

averaging (e.g., designs applying LS based triangulation or multilateral), data fu-

sion [236, 237, 238], error prorogation control [239, 240, 241], etc. However, most of

the prior designs target range-based localization with noisy distance or angle measure-

ments [76, 145]. Thus, we would like to study the effects of sensing noise specifically

for range-free positioning in WSN.

• Investigating elastic and probabilistic localization

We consider the fundamental question of whether a sensor network as a whole or each

sensor node in the network is localizable deserves more attention and efforts. Previous

research has applied the graph theory to prove the localizability for certain types of

network topology [242, 243, 244, 245, 246, 247, 248, 249, 250]. Their focuses are mostly

on the rigidity and uniqueness of the network graph based on deterministic sensing

detections and ranging measurements. On the contrary, we are quite interested in

searching for possible algorithms that can cooperate with different levels of sensing

uncertainty to provide elastic and probabilistic localization results with abundant

options for human recognition, when there is lack of sufficient information for definite

or semi-definite localization with high accuracy.

As we wrap up this work, we are excited to find wireless sensor networks facing the

dawn of wide-spread deployment for location-dependent applications that bring significant

convenience to our daily life. We hope that our work will facilitate the realization of this

vision and help to bring the wireless sensor network one step closer to real-world usage.

152

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