Static Localization Sensor Experiment 2005

Static Localization Sensor Experiment 2005 Experimental Comparison of Navigational Sensor Units in Static Conditions

I. Vincent and D. Erickson DRDC Suffield

Technical Memorandum

DRDC Suffield TM 2005-213

December 2005

Defence Research and Recherche et développement Development Canada pour la défense Canada

Static Localization Sensor Experiment 2005 Experimental Comparison of Navigational Sensor Units in Static Conditions

I. Vincent and D. Erickson DRDC Suffield

Defence R&D Canada – Suffield Technical Memorandum DRDC Suffield TM 2005-213 December 2005

© Her Majesty the Queen as represented by the Minister of National Defence, 2005

© Sa majesté la reine, représentée par le ministre de la Défense nationale, 2005

DRDC Suffield TM 2005-213 i

Abstract

This document presents the background, objectives, experimental procedure and the results of the experiments held in April 2005 on the GOPHER platform for the following navigational sensor units : Lear Astronics, Crossbow Dynamic Measurement Unit DMU-FOG, Crossbow Rate Gyro Accelerometer RGA300CA and Microstrain 3DM-G. These sensors were tested concurrently in static and dynamic situations, with the presence and absence of the vehicle and its influences. This report presents the static experiment results. These trials are a unique opportunity to collect identical condition data, discover systematic/non-systematic error sources in aggregate across sensor types, observe individual sensor performance and compare the capability of these sensors under identical conditions.

Résumé

Ce document présente le contexte, les objectifs, la procédure expérimentale et les résultats d'essais menés en avril 2005 sur la plate-forme GOPHER pour diverses unités de mesure de navigation : le Lear Astronics, le Crossbow DMU-FOG, le Crossbow RGA300CA et le Microstrain 3DM-G. Ceux-ci sont testés simultanément, en situation statique et dynamique, ainsi que statique en présence de vibrations. Ce rapport présente les expériences statiques. Ces expériences sont une opportunité unique de recueillir des données dans des conditions identiques, de découvrir les sources d'erreurs systématiques et non systématiques, d'observer les performances individuelles des capteurs, ainsi que de comparer leurs capacités.

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Executive summary

Background

The TIS identifies Autonomous Intelligent Systems (AIS) as an important area of R&D investment for future military capabilities. AIS, specifically unmanned ground vehicles (UGV), unmanned aerial vehicles (UAV), unmanned sea vehicle (USV), etc., require considerable on-board sensing to be able to accomplish military missions. Localization is a key need for any autonomous vehicle and is needed before any other task can be completed. This experiment improves knowledge of the localization sensors used for navigation in the Autonomous Intelligent Systems Section, and improves the accuracy and consistency of autonomous vehicles to find their location. Improvements in localization lead to more reliable navigation and more complex tasks that can be achieved by military UGVs.

This document covers the background, objectives, procedures and findings of the experiments held during 19 - 21 April 2005 for various inertial, radio navigation, and odometric transducers on the GOPHER vehicle. This experiment was a unique opportunity to collect identical condition data, observe individual sensor performance in static and dynamic conditions and compare the capability of these sensors.

The experiment tested the sensor performance in static conditions to determine the influence of the vehicle electromagnetic fields and the engine/vehicle vibrations on the sensor data. The navigational sensor units compared were the Lear Astronics, Crossbow DMU-FOG, the Crossbow RGA300CA, and the Microstrain 3DM-G.

Principle Results

The Lear, Microstrain, DMU-FOG and RGA300 drifted linearly with and without the influence of the vehicle electromagnetic fields and vibration. In general, the sensors demonstrated Normal distributions. With the addition of electromagnetic and vibratory disturbances, these distributions changed in some cases to bi-modal Normal distributions, and in some others to non-normal behaviours. Furthermore, the impact of the electromagnetic fields and vehicle vibration was more severe on the inclinometers and the accelerometers than the rate gyros. Vibration had the largest impact on the accelerometers.

Significance of Results

Compared to itself, the Lear Astronics exhibited the least precision for angular velocity data over the course of the three experiments (no influence, electromagnetic influence, vibration influence). However, due to its internal system model, Kalman filter, and Course Acquisition (C/A) GPS, the Lear was the most precise sensor when compared to the other units. The Lear offers the smallest variances and the best tolerance to electromagnetic interference and vehicle vibration. In general, the smaller less expensive NSUs have not yet surpassed the precision of the Lear Astronics.

DRDC Suffield TM 2005-213 iii

Future Work

Further experiments should record additional electromagnetic data, voltage, and current levels to better separate the impacts of electromagnetic influence and vehicle vibration on the sensors. Analysis should employ a rotating table to examine the accuracy of the sensors as well as the precision of the measurements. Experiments in the future should also involve larger data sets taken at various times of the day to negate the effects such as the diurnal cycle on the temperature of the NSUs. The experiments helped to compare and identify the more appropriate navigational sensor units to use on the military unmanned ground vehicles developed by the Autonomous Intelligent Systems Section.

I. Vincent, D. Erickson. 2005. Static Localization Sensor Experiment 2005: Experimental Comparison of Navigational Sensor Units in Static Conditions. DRDC Suffield TM 2005-213. Defence R&D Canada – Suffield.

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Sommaire

Contexte

La stratégie d'investissement technologique identifie les systèmes autonomes intelligents comme étant une importante aire d'investissement en recherche et developpement afin d'augmenter les capacités militaires futures. Les systèmes autonomes intelligents, tels les véhicules terrestres non-pilotés, les véhicules aériens non-pilotés et les véhicule marins non-pilotés, requièrent une quantité considérable de capteurs à bord pour être en mesure d'accomplir des missions militaires.

La localisation est un élément clé pour la navigation de tout véhicule autonome. L'expérience présentée dans ce document améliore la connaissance des capteurs de localization utilisés pour la navigation dans la Section des Systèmes Intelligents Autonomes, et améliore la précision et la consistence des véhicules autonomes à déterminer leur position. Cela conduit à une navigation plus fiable et à l'accomplissement de taches plus complexes par les véhicules terrestres militaries non-pilotés.

Ce document présente le contexte, les objectifs, les procédures expérimentales et les résultats des essais tenus du 19 au 21 avril 2005. L'expérience est conduite sur le véhicule appelé GOPHER et teste divers capteurs inertiels, odométriques et de radio navigation. C'est une opportunité unique de recueillir des données dans des conditions identiques, d'observer les performances individuelles des capteurs en condition statique et dynamique, ainsi que de comparer leurs capacités.

L'expérience teste les performances des capteurs en situation statique afin de déterminer l'impact des champs électromagnétiques du véhicule, ainsi que des vibrations du moteur/véhicule sur les lectures des capteurs. Les unités de navigation comparées sont : le Lear Astronics, les Crossbow DMU-FOG et RGA300, ainsi que le Microstrain 3DM-G. Des données GPS et odométriques du GOPHER sont également recueillies.

Résultats

Le Lear, le Microstrain, le DMU-FOG et le RGA300 dérivent linéairement en présence ou en l'absence de l'influence des champs électromagnétiques et des vibrations du véhicule. En général, les capteurs démontrent des distribution gaussiennes. Avec l'addition de perturbations électromagnétiques et vibratoires, ces distributions deviennent soit bimodales gaussiennes soit non-gaussiennes. De plus, l'impact des champs électromagnétiques et de la vibration du véhicule est plus importante sur les inclinomètres et les accéléromètres que sur les gyroscopes. La vibration a l'impact le plus important sur les accéléromètres.

Portée des résultats

Par rapport à lui-même, c'est au niveau de la vitesse angulaire que le Lear est le moins précis. Cependant, vu le modèle de son système interne, son filtre de Kalman et son “Course Acquisition (C/A) GPS”, le Lear Astronics semble être le meilleur choix de capteur puisqu'il offre les plus faibles variances et la meilleure tolérance aux champs magnétiques et aux vibrations. En général, les unités de navigation plus petites et moins dispendieuses n'ont pas encore surpassé la précision du Lear Astronics.

Travaux futurs

Des travaux futurs devraient adresser le besoin de recueillir des données électromagnétiques additionnelles, ainsi que les niveaux de tension et de courrant, afin de mieux séparer les impacts de l'influence électromagnétique et de la vibration du véhicule sur les capteurs. L'analyse devrait employer une table rotative pour examiner l'exactitude des capteurs et la précision des mesures. Les expériences futures devraient également recueillir de plus grands ensembles de données à divers moments de la journée pour cerner des effets, tel le cycle diurne sur la température interne des unités de navigation. Les expériences présentée ici aident à comparer et identifier les unités de mesure de navigation les plus appropriées pour utiliser sur les véhicule terrestres militaires non-pilotés dévelopés par la Section des Systèmes Intelligents Autonomes.

I. Vincent, D. Erickson. 2005. Static Localization Sensor Experiment 2005: Experimental Comparison of Navigational Sensor Units in Static Conditions. DRDC Suffield TM 2005-213. R & D pour la défense Canada – Suffield.

DRDC Suffield TM 2005-213 v

vi DRDC Suffield TM 2005-213

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Table of contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Résumé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Executive Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Sommaire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Table of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

List of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

1. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2. Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3. Experimental Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3.1 GOPHER Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3.2 Data Collection Computer . . . . . . . . . . . . . . . . . . . . . . . . . 2

3.3 ANCAEUS Control Station . . . . . . . . . . . . . . . . . . . . . . . . 3

3.4 Inertial Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3.5 Radio Navigation Transducers (GPS /DGPS) . . . . . . . . . . . . . . . 4

3.6 Encoders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.7 Sensor Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

4. Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4.1 Building 15 Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4.2 Weather . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

5. Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

5.1 Experiment # 1: Error characteristics of NSUs caused by vehicleelectromagnetic field and vehicle vibration . . . . . . . . . . . . . . . . 5

5.2 Experiment #1-1: Sensors detached from vehicle . . . . . . . . . . . . . 6

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5.3 Experiment #1-2: Sensors attached to vehicle, engine off . . . . . . . . 6

5.4 Experiment #1-3: Sensors attached to vehicle, engine on . . . . . . . . . 7

5.5 Experiment #1-4: Apparent Drift due to Earth’s Rotation . . . . . . . . 7

6. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

6.1 Data Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

6.2 Statistical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

6.2.1 Statistical results for experiment #1-1: sensors detached fromvehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

6.2.2 Statistical results for experiment #1-2: sensors attached tovehicle, engine off . . . . . . . . . . . . . . . . . . . . . . . . 12

6.2.3 Statistical results for experiment #1-3: sensors attached tovehicle, engine on . . . . . . . . . . . . . . . . . . . . . . . . . 14

6.3 Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

6.4 Apparent Drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

7. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

7.0.1 Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

7.0.2 Gyro rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

7.0.3 Accelerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

7.0.4 Comparison Graphs . . . . . . . . . . . . . . . . . . . . . . . . 20

8. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Annexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

A Procedure for Experiment # 1: Error characteristics of NSUs caused by vehicleelectromagnetic field and vehicle vibration . . . . . . . . . . . . . . . . . . . . 27

A.1 Experiment #1-1: Sensors detached from vehicle . . . . . . . . . . . . . 27

A.2 Experiment #1-2: Sensors attached to vehicle, engine off . . . . . . . . 27

A.3 Experiment #1-3: Sensors attached to vehicle, engine on . . . . . . . . . 27

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A.4 Experiment #1-4: Apparent Drift due to Earth’s Rotation . . . . . . . . 28

B Data Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

B.1 Experiment #1-1: Error Characteristics for static NSU away from thevehicle influence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

B.2 Exp 1-2: Error Characteristics for static NSU, sensors on the vehicle . . 52

B.3 Exp 1-3: Error Characteristics for static NSU, vehicle engine on . . . . 75

C Initialisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

D Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

E Equipment Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

DRDC Suffield TM 2005-213 ix

List of figures

Figure 1. GOPHER vehicle denoting {R} the local robot-fixed coordinate frame ofreference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Figure 2. Mounting Board for Sensor Platform showing {R} . . . . . . . . . . . . . . . 5

Figure 3. Comparison of NSU roll angle variance . . . . . . . . . . . . . . . . . . . . . 21

Figure 4. Comparison of NSU gyro rates about the z-axis . . . . . . . . . . . . . . . . . 22

Figure 5. a) Comparison of NSU acceleration variance along the z-axis in experience#1-1. b) As all curves are superimposed, this second graph is generated bymultiplying the variance by 10,000 to distinguish the distribution separation order. . 23

Figure B.1. Exp 1-1: DMU-FOG graph of the roll angle vs time . . . . . . . . . . . . . 29

Figure B.2. Exp 1-1: DMU-FOG graph of the pitch angle vs time . . . . . . . . . . . . . 30

Figure B.3. Exp 1-1: DMU-FOG graph of the gyro rate about X vs time . . . . . . . . . 30

Figure B.4. Exp 1-1: DMU-FOG graph of the gyro rate about Y vs time . . . . . . . . . 31

Figure B.5. Exp 1-1: DMU-FOG graph of the gyro rate about Z vs time . . . . . . . . . 31

Figure B.6. Exp 1-1: DMU-FOG graph of the acceleration along X vs time . . . . . . . 32

Figure B.7. Exp 1-1: DMU-FOG graph of the acceleration along Y vs time . . . . . . . 32

Figure B.8. Exp 1-1: DMU-FOG graph of the acceleration along Z vs time . . . . . . . . 33

Figure B.9. Exp 1-1: Crossbow DMU-FOG histograms a) roll b) pitch c) yaw d) gyrorate about X e) gyro rate about Y f) gyro rate about Z g) acceleration along X h)acceleration along Y i) acceleration along Z . . . . . . . . . . . . . . . . . . . . . . 34

Figure B.10. Exp 1-1: Lear Astronics graph of the roll angle vs time . . . . . . . . . . . 35

Figure B.11. Exp 1-1: Lear Astronics graph of the pitch angle vs time . . . . . . . . . . 35

Figure B.12. Exp 1-1: Lear Astronics graph of the yaw angle vs time . . . . . . . . . . . 36

Figure B.13. Exp 1-1: Lear Astronics graph of the gyro rate about X vs time . . . . . . . 36

Figure B.14. Exp 1-1: Lear Astronics graph of the gyro rate about Y vs time . . . . . . . 37

Figure B.15. Exp 1-1: Lear Astronics graph of the gyro rate about Z vs time . . . . . . . 37

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Figure B.16. Exp 1-1: Lear Astronics graph of the acceleration along X vs time . . . . . 38

Figure B.17. Exp 1-1: Lear Astronics graph of the acceleration along Y vs time . . . . . 38

Figure B.18. Exp 1-1: Lear Astronics graph of the acceleration along Z vs time . . . . . 39

Figure B.19. Exp 1-1: Lear Astronics histograms a) roll b) pitch c) yaw d) gyro rateabout X e) gyro rate about Y f) gyro rate about Z g) acceleration along X h)acceleration along Y i) acceleration along Z . . . . . . . . . . . . . . . . . . . . . . 40

Figure B.20. Exp 1-1: Microstrain graph of the roll angle vs time . . . . . . . . . . . . . 41

Figure B.21. Exp 1-1: Microstrain graph of the pitch angle vs time . . . . . . . . . . . . 41

Figure B.22. Exp 1-1: Microstrain graph of the yaw angle vs time . . . . . . . . . . . . 42

Figure B.23. Exp 1-1: Microstrain graph of the gyro rate about X vs time . . . . . . . . 42

Figure B.24. Exp 1-1: Microstrain graph of the gyro rate about Y vs time . . . . . . . . 43

Figure B.25. Exp 1-1: Microstrain graph of the gyro rate about Z vs time . . . . . . . . . 43

Figure B.26. Exp 1-1: Microstrain graph of the acceleration along X vs time . . . . . . . 44

Figure B.27. Exp 1-1: Microstrain graph of the acceleration along Y vs time . . . . . . . 44

Figure B.28. Exp 1-1: Microstrain graph of the acceleration along Z vs time . . . . . . . 45

Figure B.29. Exp 1-1: Microstrain histograms a) roll b) pitch c) yaw d) gyro rate aboutX e) gyro rate about Y f) gyro rate about Z g) acceleration along X h) accelerationalong Y i) acceleration along Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Figure B.30. Exp 1-1: Crossbow RGA300 graph of the roll angle vs time . . . . . . . . . 47

Figure B.31. Exp 1-1: Crossbow RGA300 graph of the pitch angle vs time . . . . . . . . 48

Figure B.32. Exp 1-1: Crossbow RGA300 graph of the gyro rate about Z vs time . . . . 48

Figure B.33. Exp 1-1: Crossbow RGA300 graph of the acceleration along X vs time . . . 49

Figure B.34. Exp 1-1: Crossbow RGA300 graph of the acceleration along Y vs time . . . 49

Figure B.35. Exp 1-1: Crossbow RGA300 graph of the acceleration along Z vs time . . . 50

Figure B.36. Exp 1-1: Crossbow RGA300 histograms a) roll b) pitch c) yaw d) gyro rateabout X e) gyro rate about Y f) gyro rate about Z g) acceleration along X h)acceleration along Y i) acceleration along Z . . . . . . . . . . . . . . . . . . . . . . 51

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Figure B.37. Exp 1-2: DMU-DOG graph of the roll angle vs time . . . . . . . . . . . . . 52

Figure B.38. Exp 1-2: DMU-DOG graph of the pitch angle vs time . . . . . . . . . . . . 53

Figure B.39. Exp 1-2: DMU-DOG graph of the gyro rate in X vs time . . . . . . . . . . 53

Figure B.40. Exp 1-2: DMU-DOG graph of the gyro rate in Y vs time . . . . . . . . . . 54

Figure B.41. Exp 1-2: DMU-DOG graph of the gyro rate in Z vs time . . . . . . . . . . 54

Figure B.42. Exp 1-2: DMU-DOG graph of the acceleration in X vs time . . . . . . . . . 55

Figure B.43. Exp 1-2: DMU-DOG graph of the acceleration in Y vs time . . . . . . . . . 55

Figure B.44. Exp 1-2: DMU-DOG graph of the acceleration in Z vs time . . . . . . . . . 56





Figure B.49. Exp 1-2: Lear Astronics graph of the gyro rate in X vs time . . . . . . . . . 59

Figure B.50. Exp 1-2: Lear Astronics graph of the gyro rate in Y vs time . . . . . . . . . 60

Figure B.51. Exp 1-2: Lear Astronics graph of the gyro rate about Z vs time . . . . . . . 60

Figure B.52. Exp 1-2: Lear Astronics graph of the acceleration in X vs time . . . . . . . 61

Figure B.53. Exp 1-2: Lear Astronics graph of the acceleration in Y vs time . . . . . . . 61

Figure B.54. Exp 1-2: Lear Astronics graph of the acceleration along Z vs time . . . . . 62





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Figure B.59. Exp 1-2: Microstrain graph of the gyro rate in X vs time . . . . . . . . . . 65

Figure B.60. Exp 1-2: Microstrain graph of the gyro rate in Y vs time . . . . . . . . . . 66

Figure B.61. Exp 1-2: Microstrain graph of the gyro rate in Z vs time . . . . . . . . . . . 66

Figure B.62. Exp 1-2: Microstrain graph of the acceleration in X vs time . . . . . . . . . 67

Figure B.63. Exp 1-2: Microstrain graph of the acceleration in Y vs time . . . . . . . . . 67

Figure B.64. Exp 1-2: Microstrain graph of the acceleration in Z vs time . . . . . . . . . 68


Figure B.66. Exp 1-2: Crossbow RGA300 graph of the roll angle vs time . . . . . . . . . 70

Figure B.67. Exp 1-2: Crossbow RGA300 graph of the pitch angle vs time . . . . . . . . 71

Figure B.68. Exp 1-2: Crossbow RGA300 graph of the gyro rate in Z vs time . . . . . . 71

Figure B.69. Exp 1-2: Crossbow RGA300 graph of the acceleration in X vs time . . . . . 72

Figure B.70. Exp 1-2: Crossbow RGA300 graph of the acceleration in Y vs time . . . . . 72

Figure B.71. Exp 1-2: Crossbow RGA300 graph of the acceleration in Z vs time . . . . . 73

Figure B.72. Exp 1-2: Crossbow RGA300 histograms a) roll b) pitch c) yaw d) gyro rateabout X e) gyro rate about Y f) gyro rate about Z g) acceleration along X h)acceleration along Y i) acceleration along Z . . . . . . . . . . . . . . . . . . . . . . 74

Figure B.73. Exp 1-3: DMU-FOG graph of the roll angle vs time . . . . . . . . . . . . . 75

Figure B.74. Exp 1-3: DMU-FOG graph of the pitch angle vs time . . . . . . . . . . . . 76

Figure B.75. Exp 1-3: DMU-FOG graph of the gyro rate in X vs time . . . . . . . . . . 76

Figure B.76. Exp 1-3: DMU-FOG graph of the gyro rate in Y vs time . . . . . . . . . . 77

Figure B.77. Exp 1-3: DMU-FOG graph of the gyro rate in Z vs time . . . . . . . . . . . 77

Figure B.78. Exp 1-3: DMU-FOG graph of the acceleration in X vs time . . . . . . . . . 78

Figure B.79. Exp 1-3: DMU-FOG graph of the acceleration in Y vs time . . . . . . . . . 78

Figure B.80. Exp 1-3: DMU-FOG graph of the acceleration in Z vs time . . . . . . . . . 79

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Figure B.85. Exp 1-3: Lear Astronics graph of the gyro rate in X vs time . . . . . . . . . 83

Figure B.86. Exp 1-3: Lear Astronics graph of the gyro rate in Y vs time . . . . . . . . . 83

Figure B.87. Exp 1-3: Lear Astronics graph of the gyro rate in Z vs time . . . . . . . . . 84

Figure B.88. Exp 1-3: Lear Astronics graph of the acceleration in X vs time . . . . . . . 84

Figure B.89. Exp 1-3: Lear Astronics graph of the acceleration in Y vs time . . . . . . . 85

Figure B.90. Exp 1-3: Lear Astronics graph of the acceleration in Z vs time . . . . . . . 85





Figure B.95. Exp 1-3: Microstrain graph of the gyro rate in X vs time . . . . . . . . . . 88

Figure B.96. Exp 1-3: Microstrain graph of the gyro rate in Y vs time . . . . . . . . . . 89

Figure B.97. Exp 1-3: Microstrain graph of the gyro rate in Z vs time . . . . . . . . . . . 89

Figure B.98. Exp 1-3: Microstrain graph of the acceleration in X vs time . . . . . . . . . 90

Figure B.99. Exp 1-3: Microstrain graph of the acceleration in Y vs time . . . . . . . . . 90

Figure B.100. Exp 1-3: Microstrain graph of the acceleration in Z vs time . . . . . . . . 91


xiv DRDC Suffield TM 2005-213

Figure B.102. Exp 1-3: Crossbow RGA300 graph of the roll angle vs time . . . . . . . . 93

Figure B.103. Exp 1-3: Crossbow RGA300 graph of the pitch angle vs time . . . . . . . 94

Figure B.104. Exp 1-3: Crossbow RGA300 graph of the gyro rate in Z vs time . . . . . . 94

Figure B.105. Exp 1-3: Crossbow RGA300 graph of the acceleration in X vs time . . . . 95

Figure B.106. Exp 1-3: Crossbow RGA300 graph of the acceleration in Y vs time . . . . 95

Figure B.107. Exp 1-3: Crossbow RGA300 graph of the acceleration in Z vs time . . . . 96

Figure B.108. Exp 1-3: Crossbow RGA300 histograms a) roll b) pitch c) yaw d) gyrorate about X e) gyro rate about Y f) gyro rate about Z g) acceleration along X h)acceleration along Y i) acceleration along Z . . . . . . . . . . . . . . . . . . . . . . 97

List of tables

Table 1. GOPHER Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Table 2. Sensor drift rates for the static experiments. (Exp #1-1: sensors detached fromvehicle, Exp #1-2: sensors attached to vehicle, engine off and Exp #1-3: sensorsattached to vehicle, engine on) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Table 3. Exp 1-1 (sensors detached from vehicle): Mean, variance and standarddeviation for angle measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Table 4. Exp 1-1 (sensors detached from vehicle): Mean, variance and standarddeviation for gyro rate measurements . . . . . . . . . . . . . . . . . . . . . . . . . 11

Table 5. Exp 1-1 (sensors detached from vehicle): Mean, variance and standarddeviation for acceleration measurements . . . . . . . . . . . . . . . . . . . . . . . 12

Table 6. Exp 1-2 (sensors attached to vehicle, engine off): Mean, variance and standarddeviation for angle measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Table 7. Exp 1-2 (sensors attached to vehicle, engine off): Mean, variance and standarddeviation for gyro rate measurements . . . . . . . . . . . . . . . . . . . . . . . . . 13

Table 8. Exp 1-2 (sensors attached to vehicle, engine off): Mean, variance and standarddeviation for acceleration measurements . . . . . . . . . . . . . . . . . . . . . . . 14

Table 9. Exp 1-3 (sensors attached to vehicle, engine on): Mean, variance and standarddeviation for angle measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

DRDC Suffield TM 2005-213 xv

Table 10. Exp 1-3 (sensors attached to vehicle, engine on): Mean, variance and standarddeviation for gyro rate measurements . . . . . . . . . . . . . . . . . . . . . . . . . 16

Table 11. Exp 1-3 (sensors attached to vehicle, engine on): Mean, variance and standarddeviation for acceleration measurements . . . . . . . . . . . . . . . . . . . . . . . 16

Table 12. Comparison of angle standard deviations (s) between the three staticexperiments. The s ratio is obtained by dividing the standard deviation of thecurrent experiment by the standard deviation from Exp #1-1. (Exp #1-1: sensorsdetached from vehicle, Exp #1-2: sensors attached to vehicle, engine off and Exp#1-3: sensors attached to vehicle, engine on) . . . . . . . . . . . . . . . . . . . . . 19

Table 13. Comparison of gyro rate standard deviations between the three staticexperiments for every sensor. (Exp #1-1: sensors detached from vehicle, Exp #1-2:sensors attached to vehicle, engine off and Exp #1-3: sensors attached to vehicle,engine on) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Table 14. Comparison of acceleration standard deviations between the three staticexperiments for every sensor. (Exp #1-1: sensors detached from vehicle, Exp #1-2:sensors attached to vehicle, engine off and Exp #1-3: sensors attached to vehicle,engine on) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Table E.1. GOPHER Shock Mount Specifications for 6188K412, Steel Cup VibrationDamping Mount Neoprene, 1/4"-20 Thread, 24 Lbs Max Load . . . . . . . . . . . . 101

xvi DRDC Suffield TM 2005-213

1. Background

This document covers the background, objectives, experimental procedure, and findingsof the experiments conducted in April 2005 for various inertial, radio navigation, andodometric transducers conducted on the GOPHER platform. This trial was a uniqueopportunity to collect identical condition data, discover systematic/non-systematicerror sources, observe individual sensor performance and compare the capability ofthese sensors. The background to similar experiments can be found in [1] and [2].

Research in the area of mobile robot localization/guidance has been ongoing for manyyears. [2, 3, 4, ?, 5, 6, 7, 8, 9] provide some recent examples of work in this area;reference [7] provides a complete treatment of the field of localization. It is importantto collect odometry data to separate the sources of systematic errors (errors caused bythe mechanical properties of the vehicle design [9]) from non-systematic errors (errorsnot caused by the mechanical properties of the vehicle design [9]) associated with anindividual mobile robot platform was demonstrated by Borenstein and colleagues at theUniversity of Michigan. [6] demonstrated a 7-fold increase in performance when usingpolynomial correction equations for nonlinear scale error and temperature. This wasmore than a demonstrated two-fold increase in performance using Kalman filteringtechniques alone. All of the references support the application of calibration as a meanto reduce the error in position and orientation estimation. This experiment supportsALS project activities to automate UxV’s.

The unique contribution of this experiment was the concurrent data collection andstatistical analyses from multiple sensor suites, termed Navigational Sensor Units(NSU), in parallel under identical experimental conditions1 . These conditions were asclose to ideal as can be obtained. Two quadrature encoders were installed on the drivenwheels to get the wheel speed to compare the vehicle odometry with the integratedNSU data. Ground truth for position was obtained using GPS receivers with DGPScorrection so that measuring vehicle pose was a matter of dwelling in the sameconfiguration long enough to obtain a reasonable amount of accuracy. Error in positionestimation using this ground truth is smaller than measuring offset from a perceivedposition. Also, this gives us a set of global data points rather than local offsets from anarbitrary origin.

The individual transducers within the various sensor packages interpret differentphysical phenomena, such as the Sagnac effect, with different methods to infer currentestimated state. These sensors will be affected by the presence of electromagneticinterference and vehicle vibration interference. These experiments collect the data fromthe various components of the NSUs, such as inclinometers and accelerometers, in thepresence and absence of the vehicle’s electromagnetic and vibration influence.

1The one glaring exception to the concurrent identical data collection supposition is that each NSU cannotphysically occupy the same space on the vehicle while travelling the same course at the same instant in time. As theNSUs will be fitted as close to the vehicle’s x-y centre of gravity but not on the centre of gravity then there will be aresultant moment-arm affecting all NSUs. Therefore, the moment arm of each gyro will be different (although stepswere taken to limit the impact of the variation in moment arms) and the independent conditions will not be identical.

DRDC Suffield TM 2005-213 1

Figure 1: GOPHER vehicle denoting {R} the local robot-fixed coordinate frame of reference

2. Objectives

The objectives of this experiment were:

1. To collect data from co-located orthogonal and complementary sensors underidentical conditions and motion;

2. To determine bias drift and bias drift rate of each of the inertial sensors;

3. To determine apparent drift of inertial sensors at our global position on the Earth;

4. To determine the statistical mean and standard deviation of error for each sensor.

3. Experimental Equipment3.1 GOPHER Vehicle

The GOPHER is a six wheel, skid-steered, hydrostatic drive vehicle. It is operatedremotely with semiautomatic speed and steering control. The engine on the GOPHERoperates at a variable engine speed. The GOPHER uses two hydraulic motors coupledto chain drives to drive the left three and right three wheels independently. Thehydraulic pressure is regulated by swash-plates and the control law used wasproportional, integral, and derivative (PID). See Table 1 for the GOPHERspecifications. The vehicle origin {R} affixed to the GOPHER is the centre of thesensor board where the inertial sensors were located. It is sketched on figure 1.

3.2 Data Collection ComputerThe onboard computer is a Pentium 4 class computer with Windows 2000 as theonboard computer operating system. NSU, odometers, and DGPS were connected to

2 DRDC Suffield TM 2005-213

Specification Element ValueDimensions Height 0.78m

Width 1.55mLength 2.10m

Wheel diameter 0.57mWheelbase 1.205m

Bar length between the two GPS antennas 2.75mMass 1000kg

Height of DGPS Antenna above GOPHER 2.09m

Table 1: GOPHER Specifications

the data collection computer using RS-232C and USB ports. Data from the sensors waslogged to files and then analyzed offline.

3.3 ANCAEUS Control StationThe GOPHER is commanded by the onboard ANCAEUS vehicle controller linked to acontrol pendant. The remote control pendant permits velocity commands, enginecontrol, brakes, emergency stop, and other direct control of the vehicle. The vehiclewas controlled by pendant for the comparative motion experiment and to start and stopthe GOPHER during the static experiment. The ANCAEUS control system uses PIDcontrol loops to alter the velocities of the GOPHER locomotion system.

3.4 Inertial TransducersThe following IMU/DMU navigational sensor units are part of the experiment:

1. Crossbow RGA-300CA: provides roll, pitch, gyro about the Z-axis, accelerationalong the X, Y and Z axes. This unit has the following sensors: MicroElectro-Mechanical Sensors (MEMS) gyro rate sensors and capacitiveaccelerometers. According to [10], the MEMS angular rate gyros generate aCoriolis acceleration by the angular rotation of a vibrating silicon MEMS structure.A change in the direction around one axis of a driving transducer induces avibration in a detection transducer on another axis.

2. Crossbow DMU FOG: provides roll, pitch, gyro about X, Y and Z, accelerationalong the X, Y and Z axes. This unit uses three fibre-optic gyro transducers andthree MEMS accelerometers. The MEMS accelerometers are surfacemicro-machined silicon devices that use differential capacitance to senseacceleration. According to [10], the FOG rate sensors operate using a fibre-opticring and a solid-state laser to measure rotation rates using the Sagnac effect.

3. Microstrain 3DMG: provides roll, pitch, yaw, gyro about X, Y and Z, accelerationalong the X, Y and Z axes, magnetic field strength along X, Y and Z axes,


quaternion and rotation orientation matrix. It uses MEMS gyro rate sensors to trackdynamic orientation, and MEMS accelerometers and magnetoresistivemagnetometers to track static orientation. A built-in algorithm blends thesesensor’s outputs in real-time to prevent gyro drift, and eliminate the inertial effectson the accelerometers.

4. Lear Astronics NSU: provides roll, pitch, yaw, gyro about X, Y and Z,acceleration along the X, Y and Z axes, latitude, longitude, altitude, easting speed,northing speed, up speed. This is the most expensive and most extensive navigationsensor unit. It is an avionics grade unit that has its own internal system model,Kalman filter model, and Course Acquisition (C/A) GPS. While it is not reasonableto expect identical results from the other raw sensors above, the Lear Astronics hasbeen included for comparison. The NSU consists of a solid state three-axis inertialmeasurement unit (IMU) coupled with an integrated C/A Code Global PositioningSystem (GPS) receiver and a solid state magnetometer. The NSU consists of solidstate gyros and accelerometers. The digital compass module is built using solidstate magnetoresistive sensors to provide heading.

3.5 Radio Navigation Transducers (GPS /DGPS)

A DGPS base station is used during the outdoor experiments so that the errorcorrections may be applied to the data logged by the onboard computer. The GOPHERhas 2 Novatel RT2 DGPS receivers separated by 2.75m along traversal axis. Thesereceivers used a Pacific Coast DGPS receiver to accept error corrections from theDGPS base station.

3.6 Encoders

GOPHER is equipped with 2 shaft encoders measuring the rotation of a driven wheelon each side of the vehicle. The incremental optical encoders, model H25 of BEITechnologies Inc., have 325 cycles per revolution. Since they work in quadrature, eachcycle counts 4 ticks. The resolution of these encoders corresponds to 5.5mm forwardmotion.

3.7 Sensor Platform

The computer and infrastructure components are mounted atop a plywood board as perfigure 2 at the front of the GOPHER. The sensors that are not internal to the vehicle aremounted on a metal plate atop the wooden board. The origin of {R} is located at thecentre of this steel plate between the mounted sensors. This wooden mounting board isaffixed to the top of the GOPHER using 6 shock absorbing mounts as detailed in AnnexE.1. The NSUs are mounted above the x-y centre of gravity of the vehicle with anormal offset of approximately 0.3m above the z centre of gravity.


Figure 2: Mounting Board for Sensor Platform showing {R}

4. Experimental Setup4.1 Building 15 Area

The experiment was conducted outside the Building 15 area. Building 15 Area issurrounded by low-level hills consisting of grassland primarily. The site of experiments#1 (sensors detached from vehicle) and #2 (sensors attached to vehicle, engine off) wasthe parking lot and gravel roadway north of the building. The roadway consists of loosegravel and soil. The soil was dry and the surface of the roadway where the experimentswere undertaken had not been graded recently. There was wind on the day of exteriorexperimentation with wind gusts upwards of 10 km/h.

4.2 Weather

The weather for these experiments was partial cloud to clear skies with temperaturesranging from 12oC to 20oC . There was no precipitation during the experiments.

5. Experimental Procedure5.1 Experiment # 1: Error characteristics of NSUs caused by

vehicle electromagnetic field and vehicle vibration

This set of experiments will attempt to observe a difference in sensor behaviour over along duration without the vehicle, with the vehicle, and with the vehicle engine turnedon. This experiment examines the potential interference from two common mobilerobotics sources of error: the large electromagnetic fields (generated by the metalcontent of the vehicle and engine/alternator) and the vibration of the vehicle. It isimportant to characterize the statistics of the individual sensors under the dependentvariables of electromagnetic interference and vehicle vibration interference becauseNSUs must work in these conditions. The important findings will be if the vehicle’s


electromagnetic field or vibration in itself makes some of the sensors less certain andunder which precise conditions this is true. The implication is that statistics can beadjusted for the error characteristics when employing these transducers with or withoutthe specific interference. For example, perhaps data should be collected with the engineoff and a different, presumably smaller, noise coefficient can be used to improvelocalization accuracy.

This experiment is not meant as a consumer comparison of the sensors because therehas been no effort to reduce sources of error that may tend to favour one device versusanother. For example, the centres of momentum for the individual sensors wereestimated but not properly measured to eliminate moment arm effects in the x-y axes.Analyses may reveal which NSUs are more suited for the role of vehicle NSU. Becausethere is no comparison to a ground truth for the measured value, these comparisons willassess the precision of the transducers under interference but not the general accuracy.

The prediction is the NSUs should behave uniformly with the lowest variance andstandard deviation in data while detached from the GOPHER. The NSUs should behavesimilarly with the vehicle underneath them in a static data collection mode fornon-magnetic transducers but magnetic transducers will experience an increase in thestandard deviation and variance of the data collected. There should be an additionalincrease in the variance of the electromagnetic transducers due to the steel GOPHERbody and natural polarization of the vehicle. When the GOPHER is turned on, theNSUs should change in sensor behaviour, presumably with a steady state change to theperformance of transducers, due to the electromagnetic field generated by the engineand the oscillatory motion of the drive system. Since the vehicle is not in motion(oscillatory motion notwithstanding) then the vehicle dynamics should play no part inthe experiment. The vehicle vibration should impact the mechanical transducers, thosethat use a movement of parts to infer motion like a gyroscope, during experiment #1-3The three experiments are now outlined.

5.2 Experiment #1-1: Sensors detached from vehicle

The first experiment requires that the NSUs are powered and left to collect data from astatic position for a significant period of time. The NSUs were mounted on the plywoodboard detached from the GOPHER. The board was placed outside on a concrete slabaway from the building so that the influence of the machines inside the building and theGOPHER were minimized. The NSUs were left for a period of over 40 minutes whiledata was logged to local hard drive. Refer to Annex A for full experimental procedure.

5.3 Experiment #1-2: Sensors attached to vehicle, engine off

The second experiment involved mounting the NSUs from Experiment #1-1 atop theGOPHER, powering them and leaving them static to collect data without the GOPHERturned on. The NSUs were powered again with a power cord so that data could be


collected for a long period without turning the engine on. The NSUs were left for aperiod of over 40 minutes. Refer to Annex A for full experimental procedure.

5.4 Experiment #1-3: Sensors attached to vehicle, engine on

The third experiment involved using the GOPHER to power the NSUs, with theinternal battery and power conversion circuits, and leaving them static to collect datawithout the GOPHER turned on. The NSUs were left for a period of over 40 minutes.Refer to Annex A for full experimental procedure.

5.5 Experiment #1-4: Apparent Drift due to Earth’s Rotation

Without the vehicle present, it is predicted that data collected should observe apparentdrift of the Earth, which is approx. 15 degrees per hour from East to West. Thistranslates to 0.00416666667 degrees /sec at the North Pole that should either becompensated for or will be apparent in the NSU data readings. For Medicine Hat ,which sits at a latitude of 50.021847 degrees, the apparent drift should be

15◦/hr ∗ (sin(50.021847)) = 11.494342255◦/hr = 0.003192783◦/sec(1)

along the NSUs when facing True North. All readings should be taken from theidentical pose so that readings can be compared. The prediction is that the IMUs withsufficient resolution will present this apparent drift as a constant bias. For those IMUswithout sufficient resolution, it may not register as an independent source of error. Theexperimental procedure is listed in Annex A.

6. Results

This section analyzes the results and compares the different sensors for the above staticexperiments. The analysis includes a comparison of drift rates, a qualitative assessmentof the type of distribution for each data measurement, and an evaluation of the mean,variance and standard deviation of the data. Furthermore, relative errors produced bythe influence of electromagnetic fields and vibrations on each sensor are discerned.

6.1 Data Graphs

Data graphs of the sensor readings are found in Annex B. Table 2 presents the sensormeasurement drift rates per experiment. As can be seen, the raw data signals are verynoisy and despite the internal filtering they exhibit drift. In general, the drift rateincreased slightly for most sensors from the baseline experiment #1-1 (sensorsdetached from vehicle) through to experiment #1-3 (sensors attached to vehicle, engineon). The direction, or sign, of the drift is not consistent throughout the experiments.


For example, The DMU-FOG drift is negative for Exp #1-1 and positive for Exp #1-2and Exp #1-3. This suggests that interference from the vehicle alters the natural drift ofthe sensors individually and not globally which supports the prediction that interferencefrom the vehicle will vary.

In general, the drift rates were on the order 10−4and smaller and for short termpurposes the drift rates for most of these sensors could be considered negligible. Itshould be noted that for systems working over long periods this drift would accumulatewithout resetting the measurements periodically. Some of these NSUs have calibrationroutines available for this operation. The Lear, Microstrain and the RGA300 all driftedin the same direction with and without the influence of the vehicle. The DMU-FOG,the only instrument using fibre-optic laser ring gyros, drifted without a directional bias.

The order of magnitude for the drift for all accelerometers was not considerable. Table2 shows gyro rate drift for all sensors as roughly a constant order of magnitude for allthree experiments for the DMU_FOG, Lear, Microstrain. The RGA300 gyro rate in thez-axis increases in order of magnitude from experiment #1-2 (sensors attached tovehicle, engine off) to #1-3 (sensors attached to vehicle, engine on). The accelerationdata suggested linear drift rates, except for the Microstrain’s acceleration in z-axiswhich fit a parabolic curve. The one exception is the Microstrain yaw drift with a driftrate on the order of 10−3 degrees that would drift significantly over long periods oftime.

Angle measurements drift on the order of 10−5G . The addition of magnetic fieldinfluence and vibration do not seem to modify the angle drift rates. All anglemeasurements can be approximated with a linear fitting curve except the Lear Astronicsyaw angle, which was approximated by an 8th-order polynomial, and the Microstrainacceleration along the z-axis, which was approximated by a 4th-order polynomialequation. Accelerations show a small decrease in drift rates when vibration was presentfor the Lear, Microstrain, and RGA300. The fibre-optic DMU-FOG also exhibited aslight increase in the order of magnitude in drift for experiment #1-3 (sensors attachedto vehicle, engine on).

Angular rate drift improved slightly under vibration in experiment #1-3 in comparisonwith the previous experiments.


Drift rateSensor Measurement Exp. 1-1 Exp. 1-2 Exp. 1-3

DMU-FOG Roll (degrees) -7.863e-05 1.2332e-06 9.89e-05Pitch (degrees) 2.3e-06 -6.7e-06 -9.68e-05

Gyro rate X (deg/s) 1.7e-06 -1.8e-07 -2.6289e-06Gyro rate Y (deg/s) -2.1e-07 2.7e-07 -7.1e-07Gyro rate Z (deg/s) -6e-07 1.1e-06 -1.3e-06Acceleration X (G) -4.6e-08 1e-07 2.8e-06Acceleration Y (G) -1.5e-06 4.6e-08 2.5e-06Acceleration Z (G) -5.19e-07 2.07e-07 -2.4e-06

Lear Astronics Roll (degrees) -1.3e-06 -5.7e-06 8.77e-06Pitch (degrees) 1.6e-05 7.81e-06 -7.463e-06Yaw (degrees) nonlinear 5.71e-04 5.02e-04

Gyro rate X (deg/s) 8e-10 6.9e-10 -2.5e-09Gyro rate Y (deg/s) 1.83e-09 8.9e-10 -2.9e-10Gyro rate Z (deg/s) -1.9e-09 1.2e-09 4.7e-10Acceleration X (G) 1.6e-07 6.8e-08 2.8e-06Acceleration Y (G) 5e-08 1.7e-07 2.5e-06Acceleration Z (G) -2.32e-08 -1.47e-08 2.4e-06

Microstrain Roll (degrees) -4.8e-05 -2.48e-05 -9.6e-06Pitch (degrees) 4.7e-05 5.35e-05 8.58e-05Yaw (degrees) -2.4694e-05 4.9e-04 9.82e-03

Gyro rate X (deg/s) -6.2e-07 1.2e-07 5.4e-07Gyro rate Y (deg/s) 8.3e-07 -1.5e-07 -2.9e-10Gyro rate Z (deg/s) 3.4e-07 8.7e-08 -3.8e-08Acceleration X (G) 8.4e-07 8.8e-07 1.4e-06Acceleration Y (G) 8.4e-07 4.2e-07 1.2e-07Acceleration Z (G) nonlinear 6.3e-07 2.46e-06

RGA300 Roll (degrees) -4.47e-05 -8.8e-06 -5.71e-05Pitch (degrees) 3.1e-06 5.4e-06 6.38e-05

Gyro rate Z (deg/s) 2.4e-05 1.7e-05 -1.3e-04Acceleration X (G) -6.5e-08 -8.6e-08 -1.1e-06Acceleration Y (G) -8e-07 -1.4e-07 -1e-06Acceleration Z (G) 8.19e-07 1.564e-07 5.5e-07

Table 2: Sensor drift rates for the static experiments. (Exp #1-1: sensors detached from vehicle, Exp #1-2: sensorsattached to vehicle, engine off and Exp #1-3: sensors attached to vehicle, engine on)


6.2 Statistical results

Sections 6.2.1, 6.2.2 and 6.2.3 presents the evaluation of mean, variance and standarddeviation for roll, pitch, yaw angles, gyro rates about X, Y, and Z, and accelerationsalong X, Y, and Z measured from each sensor.

6.2.1 Statistical results for experiment #1-1: sensors detached fromvehicle

Tables 3, 4 and 5 present statistical data from the static experiment withoutvehicle component electromagnetic field influence and vehicle vibration dueto the engine.

The roll and pitch variance from lowest to highest is Lear, Crossbow RGA300,Crossbow DMU-FOG, and Microstrain respectively. Yaw variance was loweron the Microstrain than the Lear. There were no roll and pitch readings fromthe Crossbow RGA300 nor the DMU-FOG. All measured variances for angleswere small enough to be used without a further prefiltering stage.

The Lear Astronics has the lowest variance for all three gyro rates with theMicrostrain, Crossbow DMU-FOG, and RGA300 increasing variance inorder. All measured variances for angular velocities are small enough to beused without a further prefiltering stage. The Crossbow DMU-FOG yaw rate,the only angular velocity it measures, has the highest variance.

Despite the different z-axis representations of the four NSUs, theirperformance was similar for acceleration. The Crossbow RGA300 has thelowest variance along all axes. The Lear Astronics had the highest variancefor all axes. All variances were on the order of 10−7. All measured variancesfor angles are small enough to be used without a further prefiltering stage.


Roll Mean (degrees) Variance (s2) Standard deviation (s)Microstrain 0.3791 0.0027 0.0517

Lear Astronics -0.7596 8.2407e-05 0.0091Crossbow RGA300 -0.4513 0.0008 0.0281

Crossbow DMU-FOG -3.9617 0.0025 0.0500

Pitch Mean (degrees) Variance (s2) Standard deviation (s)Microstrain 2.1577 0.0085 0.0924

Lear Astronics -0.7664 0.0002 0.0142Crossbow RGA300 -0.6619 0.0002 0.0144

Crossbow DMU-FOG -1.6586 0.0002 0.0151

Yaw Mean (degrees) Variance (s2) Standard deviation (s)Microstrain -177.5685 0.0096 0.0982

Lear Astronics 12.0278 0.0415 0.2038Crossbow RGA300 - - -

Crossbow DMU-FOG - - -

Table 3: Exp 1-1 (sensors detached from vehicle): Mean, variance and standard deviation for angle measurements

Gyro X Mean (deg/s) Variance (s2) Standard deviation (s)Microstrain 0.0004 2.8140e-06 0.0017

Lear Astronics 4.5543e-05 3.7968e-08 0.0002Crossbow RGA300 - - -

Crossbow DMU-FOG 0.0014 0.0187 0.1366

Gyro Y Mean (deg/s) Variance (s2) Standard deviation (s)Microstrain -0.0002 0.0002 0.0147

Lear Astronics -8.4617e-06 5.7892e-08 0.0002Crossbow RGA300 - - -

Crossbow DMU-FOG -0.0049 0.03086 0.1757

Gyro Z Mean (deg/s) Variance (s2) Standard deviation (s)Microstrain -5.8950e-05 6.0638e-05 0.0078

Lear Astronics -4.8603e-05 1.2882e-08 0.0001Crossbow RGA300 -0.4458 0.2280 0.4775

Crossbow DMU-FOG -0.0133 0.0184 0.1357

Table 4: Exp 1-1 (sensors detached from vehicle): Mean, variance and standard deviation for gyro ratemeasurements


Accel X Mean (G) Variance (s2) Standard deviation (s)Microstrain 0.0369 2.4534e-06 0.0016

Lear Astronics -0.0134 5.6182e-06 0.0024Crossbow RGA300 0.0115 1.5184e-07 0.0004

Crossbow DMU-FOG 0.0289 1.5360e-06 0.0012

Accel Y Mean (G) Variance (s2) Standard deviation (s)Microstrain -0.0066 8.2449e-07 0.0009

Lear Astronics 0.01334 4.1980e-06 0.0020Crossbow RGA300 -0.0079 3.4619e-07 0.0006

Crossbow DMU-FOG -0.0690 5.4770e-06 0.0023

Accel Z Mean (G) Variance (s2) Standard deviation (s)Microstrain -0.9739 1.1718e-06 0.0011



Table 5: Exp 1-1 (sensors detached from vehicle): Mean, variance and standard deviation for accelerationmeasurements

6.2.2 Statistical results for experiment #1-2: sensors attached to vehicle,engine off

Tables 6, 7 and 8 present statistical data from the static experiment withvehicle component electromagnetic field influence. This experiment wasconducted to what impact electromagnetic fields had on sensor readings. Ifthere were none, the results should be similar to those in 6.2.1.

As can be seen, the values of standard deviation are similar in general to thoseobtained in the previous experiment. The Microstrain yaw angle exhibited avariance 18 times larger than experiment #1-1 (sensors detached from vehicle)while the Lear yaw angle variance was 2 times larger. In the case of the gyrorates, the standard deviations are slightly smaller but still quite similar. Thesame observation can be made for the acceleration along X, Y and Z. Forangle measurements, the Lear has the smallest standard deviations. The gyrorates stayed largely the same as experiment #1-1. Acceleration measurementsfor all sensors exhibited the same variance and standard deviations.


Roll Mean (degrees) Variance (s2) Standard deviation (s)Microstrain -1.0798 0.0020 0.0442

Lear Astronics 0.8796 1.1106e-04 0.0105Crossbow RGA300 1.2255 4.2191e-04 0.0205



Lear Astronics -0.9383 9.1622e-05 0.0096Crossbow RGA300 -0.7245 2.5798e-04 0.0161





Table 6: Exp 1-2 (sensors attached to vehicle, engine off): Mean, variance and standard deviation for anglemeasurements

Gyro X Mean (deg/s) Variance (s2) Standard deviation (s)Microstrain 1.0503e-04 2.6856e-06 0.0016

Lear Astronics 4.2376e-05 2.7179e-08 1.6486e-04Crossbow RGA300 - - -

Crossbow DMU-FOG 0.0051 0.0165 0.1284

Gyro Y Mean (deg/s) Variance (s2) Standard deviation (s)Microstrain 2.1323e-04 1.7759e-04 0.0133

Lear Astronics -1.6866e-05 2.6126e-08 1.6164e-04Crossbow RGA300 - - -

Crossbow DMU-FOG 0.0025 0.0285 0.1688

Gyro Z Mean (deg/s) Variance (s2) Standard deviation (s)Microstrain -1.4825e-05 4.2962e-05 0.0066

Lear Astronics -4.6641e-05 2.3236e-08 1.5243e-04Crossbow RGA300 0.0115 0.2249 0.4742

Crossbow DMU-FOG -6.6027e-04 0.0173 0.1316

Table 7: Exp 1-2 (sensors attached to vehicle, engine off): Mean, variance and standard deviation for gyro ratemeasurements



Lear Astronics -0.0164 4.6784e-06 0.0022Crossbow RGA300 0.0126 2.1046e-07 4.5876e-04


Accel Y Mean (G) Variance (s2) Standard deviation (s)Microstrain 0.0187 5.8408e-07 7.6425e-04



Accel Z Mean (G) Variance (s2) Standard deviation (s)Microstrain -0.9818 1.4649e-07 3.8274e-04



Table 8: Exp 1-2 (sensors attached to vehicle, engine off): Mean, variance and standard deviation for accelerationmeasurements

6.2.3 Statistical results for experiment #1-3: sensors attached to vehicle,engine on

Tables 9, 10 and 11 present statistical data from the static experiment with theengine turned on. When the vehicle is started, the engine action inducesvibration of the entire platform and the alternator affects the previouselectromagnetic field. As the sensors are shaking, the readings should be lessprecise thus the variance should increase.

Angle measurements show an increase in variance compared to the two firstexperiments. The Crossbow RGA300 exhibits a standard deviation 20 timeslarger for roll and 83 times larger for pitch compared to experiment #1-1(sensors detached from vehicle). The DMU-FOG’s standard deviation is 8times larger for pitch angle. The Microstrain yaw angle is 52 times larger. Theother data in general remains in the same order of magnitude as the previousexperiments. The Lear Astronics has the smallest standard deviationscomparable to the first experiment. The Microstrain has second lowestvariance.

The analysis of the gyro rate shows differing results. The DMU-FOGdemonstrated the best variance at 3.6 times larger for gyro rate about the Xaxis, 2.6 times larger for the gyro rate about the Y axis and comparable for thegyro rate about the Z axis. However, it is the sensor with the highest standard


deviations. The RGA300 only reads the gyro rate in Z and has a largerdeviation than the DMU-FOG. The Lear has a standard deviation 3 timessmaller for the gyro Z, but as an important increment of deviation for the gyroX and Y. Even though, it is the sensor with the smallest variances to evaluategyro rates.

The two Crossbow (RGA300 and DMU-FOG) sensors were affectedsignificantly, by as much as several orders of magnitude, for accelerationmeasurements in presence of vibrations. The Lear demonstrated an increasein variances for all accelerations by as much as 100 times larger. TheMicrostrain exhibited the same variance for the X axis acceleration, slightlyincreased variance along the Y axis, and five times larger along the Z axis.

Roll Mean (degrees) Variance (s2) Standard deviation (s)Microstrain -0.8561 0.0042 0.0650

Lear Astronics 0.7059 1.8840e-04 0.0137Crossbow RGA300 1.2106 0.3151 0.5614

Crossbow DMU-FOG -2.0587 0.0078 0.0884


Lear Astronics -1.4799 1.4812e-04 0.0122Crossbow RGA300 -1.3018 1.4278 1.1949

Crossbow DMU-FOG -2.4091 0.0150 0.1225




Table 9: Exp 1-3 (sensors attached to vehicle, engine on): Mean, variance and standard deviation for anglemeasurements

6.3 Histograms

The histograms for all sensors are presented in Annex B. The population of data fromall sensors was insufficient, given a 40 minute duration per experiment, to concludetransducer characteristics would behave identically in all circumstances. Forexperiment #1-1 (sensors detached from vehicle), most sensors - with minimal externalinfluence - exhibited a normal distribution except for the Microstrain gyro rates aboutthe Y- and Z- axes which exhibited bimodal Gaussian behaviour, or having twoGaussian distributions conjoined. The Crossbow DMU-FOG exhibited a lognormaldistribution for the roll angle. For experiment #1-2 (sensors attached to vehicle, engine


Gyro X Mean (deg/s) Variance (s2) Standard deviation (s)Microstrain -1.6218e-04 1.6996e-04 0.0130

Lear Astronics 4.3538e-05 7.5674e-06 0.0028Crossbow RGA300 - - -

Crossbow DMU-FOG -0.0087 0.2400 0.4899

Gyro Y Mean (deg/s) Variance (s2) Standard deviation (s)Microstrain 3.5436e-04 2.9541e-04 0.0172

Lear Astronics -1.3790e-05 4.5228e-06 0.0021Crossbow RGA300 - - -

Crossbow DMU-FOG 0.0011 0.2159 0.4647

Gyro Z Mean (deg/s) Variance (s2) Standard deviation (s)Microstrain 2.4073e-04 5.3878e-05 0.0073

Lear Astronics -4.8398e-05 7.6853e-08 2.7722E-04Crossbow RGA300 -0.1397 0.2283 0.4778

Crossbow DMU-FOG 0.0023 0.0190 0.1377

Table 10: Exp 1-3 (sensors attached to vehicle, engine on): Mean, variance and standard deviation for gyro ratemeasurements


Lear Astronics -0.0259 4.9681-04 0.0070Crossbow RGA300 0.0226 6.0371e-04 0.0246


Accel Y Mean (G) Variance (s2) Standard deviation (s)Microstrain 0.0149 1.2476e-06 0.0011



Accel Z Mean (G) Variance (s2) Standard deviation (s)Microstrain -0.9840 5.0256e-06 0.0022

Lear Astronics -0.9990 2.7252e-04 0.0165Crossbow RGA300 0.9997 0.0064 0.0797

Crossbow DMU-FOG 1.0003 0.0098 0.0992

Table 11: Exp 1-3 (sensors attached to vehicle, engine on): Mean, variance and standard deviation for accelerationmeasurements


off), most sensors exhibited normal distributions with the exception of the LearAstronics yaw angle, and the Microstrain gyro rates about the X- and Z- axes. TheMicrostrain yaw angle distribution for experiment #1-2 shows a slight skew that may fitwith a Beta or Rayleigh density distribution[11]. For experiment #1-3 (sensors attachedto vehicle, engine on), more sensors exhibited the bimodal behaviour includingDMU-FOG roll angle, DMU-FOG acceleration along the X axis, DMU-FOGacceleration along the Z axis, Lear Astronics gyro rate about the X axis, Microstrainyaw angle, Microstrain gyro rate about the X axis, RGA300 roll angle, RGA300 pitchangle, RGA300 acceleration along the X axis, and RGA300 acceleration along the Zaxis.

6.4 Apparent Drift

The drift rates demonstrated in the preceding experiments was not sufficiently filteredto discern the gyro rate about the X (or Y depending on the NSU) axes on theMicrostrain, and Lear Astronics. DMU-FOG exhibited a mean of 0.0014 ◦/sec inexperiment #1-1 (sensors detached from vehicle), and 0.0051 ◦/sec in experiment #1-2(sensors attached to vehicle, engine off) and -0.0049 ◦/sec in experiment #1-3 (sensorsattached to vehicle, engine on) which are on the same order of magnitude as apparentdrift at this latitude.


7. Discussion

Tables 12, 13 and 14 demonstrate standard deviation comparisons for angle, gyro rate,and acceleration between static experiments for every sensor. Sections 7.0.1, 7.0.2 and7.0.3 describe the results respectively.

7.0.1 Angles

Comparing the standard deviations over the course of three experiments, thepresence or absence of the vehicle by itself did not impact the inclinometerssignificantly except for the Microstrain yaw angle. When subjected to theGOPHER’s electromagnetic field and the vibration of the engine the standarddeviations increased the most. These affects, as predicted, weresensor-dependent. It is interesting to note that the DMU-FOG was lessaffected by the vibration and additional electromagnetic field than theMEMS-based inclinometers. It would be reasonable to surmise that theimpact of a large electromagnetic field may be larger on the MEMS-basedinclinometers - which measure the DC offset voltage - and cause the decreasein consistent measurements compared to the engine vibration on the laser ringgyros in the Lear Astronics and the Crossbow DMU-FOG. This may be madeclearer with a further examination of the sensors in a similar experiment whilelogging the voltage and current data. The Lear Astronics was the mostconsistent, or least affected, by the electromagnetic field and the enginevibration of all four sensors in terms of angle measurements.

7.0.2 Gyro rates

The angular velocities logged in these experiments demonstrate the differencein impact of electromagnetic fields and engine vibration on the varioustransducers. In general, the influence of the engine and the electromagneticfield caused an increase in standard deviation for gyro rates. The standarddeviation ratios for experiment #1-2 (sensors attached to vehicle, engine off)demonstrate that the influence of the electromagnetic field alone does not alterthem substantially. At worst, gyro rate standard deviation in experiment #1-3(sensors attached to vehicle, engine on) increases were no more than 14 timesthe baseline Exp #1-1 (sensors detached from vehicle) values. This is incontrast to the 82 times increase the Crossbow RGA300 pitch angleexperienced or the 88 times increase of the Crossbow RGA300 accelerometeralong the Z axis. This would tend to be supported by the physical phenomenaused to infer angular velocity. The gyro rates for the Crossbow RGA300 andthe DMU-FOG were the most consistent of the four sensors. The gyro ratesfor the Lear Astronics were the least precise, or the most influenced by theelectromagnetic field and vehicle vibration. It is anticipated, however, thatonce data from the dynamic experiment is analyzed that the largest influence


Roll angle Exp 1-1 (degrees) (A) Exp 1-2 (B) Exp 1-3 (C)sA

sB

sA

sC

sA

Microstrain 0.0517 0.8549 1.2573Lear Astronics 0.0091 1.1538 1.5055

Crossbow RGA300 0.0281 0.7295 19.9786Crossbow DMU-FOG 0.0500 0.3 1.768

Pitch angle Exp 1-1 (degrees) (A) Exp 1-2 (B) Exp 1-3 (C)sA

sB

sA

sC

sA



Yaw angle Exp 1-1 (degrees) (A) Exp 1-2 (B) Exp 1-3 (C)sA

sB

sA

sC

sA


Crossbow RGA300 - - -Crossbow DMU-FOG - - -

Table 12: Comparison of angle standard deviations (s) between the three static experiments. The s ratio is obtainedby dividing the standard deviation of the current experiment by the standard deviation from Exp #1-1. (Exp #1-1:

sensors detached from vehicle, Exp #1-2: sensors attached to vehicle, engine off and Exp #1-3: sensors attached tovehicle, engine on)

on the accuracy of the rate gyros will be the moment arm of the sensorsmounted above the vehicle X-Y centre of gravity.

7.0.3 Accelerations

The most consistent sensor, in terms of acceleration measurements, was theMicrostrain; it exhibited at most a twofold increase in standard deviation inexperiment #1-3 (sensors attached to vehicle, engine on) from the baselineexperiment #1-1 (sensors detached from vehicle). The Crossbow RGA300experienced the most disruption, with an increase in standard deviation from19 to 88 times larger than the baseline experiment #1-1. It is suggested fromthe data, since the impact of the vehicle was not substantial on the CrossbowRGA300 in experiment # 1-2 (sensors attached to vehicle, engine off), that theimpact of the vibration was the major cause of imprecision. In general, theinterference of the vehicle’s presence in experiment #1-2 did not significantlyimpact the accelerations. For some transducers the standard deviationsactually decreased in ratio for experiment #1-2. In the case of the Lear


Gyro rate X Exp 1-1 (deg/s) (A) Exp 1-2 (B) Exp 1-3 (C)sA

sB

sA

sC

sA

Microstrain 0.0017 0.9412 7.6471Lear Astronics 0.0002 0.8243 14

Crossbow RGA300 - - -Crossbow DMU-FOG 0.1366 0.9400 3.5864

Gyro rate Y Exp 1-1 (deg/s) (A) Exp 1-2 (B) Exp 1-3 (C)sA

sB

sA

sC

sA


Crossbow RGA300 - - -Crossbow DMU-FOG 0.1757 0.9607 2.6448

Gyro rate Z Exp 1-1 (deg/s) (A) Exp 1-2 (B) Exp 1-3 (C)sA

sB

sA

sC

sA



Table 13: Comparison of gyro rate standard deviations between the three static experiments for every sensor. (Exp#1-1: sensors detached from vehicle, Exp #1-2: sensors attached to vehicle, engine off and Exp #1-3: sensors

attached to vehicle, engine on)

Astronics, the standard deviation for both experiment #1-2 and the baselineexperiment #1-1 was identical. A possible explanation for decrease in thestandard deviations in experiment #1-1 may be the wind that the devices wereexposed to while detached from the GOPHER vehicle and placed outdoors.During the conduct of experiment #1-2 the GOPHER was located indoors andon a flat concrete surface. Examining experiment #1-3, it is suggested fromthe data that vehicle vibration is a large source of imprecision for theaccelerometers.

7.0.4 Comparison Graphs

As another means of comparison, Figures 3, 4, and 5 demonstrate the normaldistributions for a sample of angles, angular velocities, and accelerations fromall four NSUs. These figures represent the normal distributions for experiment#1-1 (sensors detached from vehicle) shifted to zero and scaled appropriately.The Gaussian equation generated these figures using the variances measuredin experiment #1-1.


−0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distribution

Prob

abilit

y

MicrostrainLear AstronicsCrossbow RGA300Crossbow DMU−FOG

Figure 3: Comparison of NSU roll angle variance


−0.5 0 0.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distribution

Prob

abilit

y


Figure 4: Comparison of NSU gyro rates about the z-axis


−0.1 −0.05 0 0.05 0.1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distribution

Prob

abilit

y


(a)

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x 10−6

(b)

Figure 5: a) Comparison of NSU acceleration variance along the z-axis in experience #1-1. b) As all curves aresuperimposed, this second graph is generated by multiplying the variance by 10,000 to distinguish the distribution

separation order.DRDC Suffield TM 2005-213 23

Acceleration X Exp 1-1 (G) (A) Exp 1-2 (B) Exp 1-3 (C)sA

sB

sA

sC

sA



Acceleration Y Exp 1-1 (G) (A) Exp 1-2 (B) Exp 1-3 (C)sA

sB

sA

sC

sA

Microstrain 0.0009 0.8492 1.2222Lear Astronics 0.0020 1 2.05


Acceleration Z Exp 1-1 (G) (A) Exp 1-2 (B) Exp 1-3 (C)sA

sB

sA

sC

sA

Microstrain 0.0011 0.3479 2Lear Astronics 0.0020 0.95 8.25


Table 14: Comparison of acceleration standard deviations between the three static experiments for every sensor.(Exp #1-1: sensors detached from vehicle, Exp #1-2: sensors attached to vehicle, engine off and Exp #1-3: sensors

attached to vehicle, engine on)

8. Conclusions

This report covered an experiment held in April 2005 for various navigational sensorunits using the GOPHER platform. It aimed to collect identical condition data, discovererror characteristics, and observe individual sensor performance. The navigationalsensors used were: Lear Astronics, Crossbow DMU-FOG and Crossbow RGA300, andMicrostrain 3DM-G. This experiment tested the sensor performance in static conditionsto determine the influence of vehicle magnetic fields and of the engine vibrations on thesensor readings.

In general, the drift rates were on the order 10−4and smaller and for short termpurposes drift rates for most of these sensors could be considered negligible. The oneexception is the Microstrain yaw drift with a drift rate on the order of 10−3 that woulddrift substantially over long periods of time. The Lear, Microstrain, DMU-FOG, andRGA300 drifted linearly with and without the influence of the vehicle.

Most sensors, with minimal external influence, exhibited a normal distribution. As theinfluences were experienced these distributions changed in some cases from a normal


distribution to a bimodal Gaussian/normal. In the final experiment, more of thesesensors exhibited non-normal behaviour, which tends to support the original predictionof the behaviour when subjected to electromagnetic interference and vehicle vibration.It is important to be aware of the tendency towards bimodal behaviour because theactual mean and deviation will not hold and the measurement variance will be larger.

As predicted, the impact of electromagnetic interference and vehicle vibration wasmixed given the transducers in question. The impact of the magnetic field and vehiclevibration were more severe on the inclinometers and the accelerometers than the rategyros. In general, the rate gyros experienced the smallest impact, with limited changeto the standard deviation in experiment #1-2. The largest impact to the rate gyros wasexhibited by the Lear Astronics. This could be due to the specific transducer used or theKalman filter that was tuned for the on-board sensors.

The data suggests that vibration had the largest impact on the accelerometers, as waspredicted. The relative impact of the electromagnetic fields and vibrations was notdiscernable due to the lack of supporting data gathered. Future experiment shouldmeasure electromagnetic fields in experiments #1-1 through #1-3, voltage, and currenttogether to assist analysis of the relative impact.

Figures 3,4, and 5 demonstrate normal distributions for angle, angular velocity, andacceleration from all four NSUs. These figures demonstrate the smaller variances of theLear Astronics NSU in comparison to the other sensors. Compared to itself, the LearAstronics exhibited the least precision for angular velocity data over the course of thethree experiments. However, due to its internal system model, Kalman filter, andCourse Acquisition (C/A) GPS, the Lear was the most precise sensor when comparedto the others, offering the smallest variances and the best tolerance to electromagneticinterference and vehicle vibration. Even with a loss of precision, the variance of theLear Astronic’s angular velocity data was at least an order of magnitude smaller thanthe other sensors examined. In general, the smaller, less expensive NSUs have not yetsurpassed the precision of the Lear Astronics. The Microstrain exhibited moreconsistent accelerometer data, remaining within twice the variance of the baselineexperiment unlike the other sensors.

Further experiments should be held addressing the need to record additionalelectromagnetic data, voltage and current levels to better separate the impacts ofelectromagnetic influence and vehicle vibration on the sensors. Analysis shouldemploy a rotating table to examine the accuracy of the sensors as well as the precisionof the measurements. Experiments in the future should also involve larger data setstaken at various times of the day to negate the effects such as the diurnal cycle on thetemperature of the NSUs. Also, a rotation table should be used to examine the accuracyof the sensors at the same time as the precision.


References

1. R. Chesney (2001). Trial Plan for Navigation Data Collection. DRDCUnpublished Technical Report.

2. Chung H. and Ojeda L. and Borenstein J. (2001). Sensor fusion for Mobile RobotDead-reckoning With a Precision-calibrated Fiber Optic Gyroscope. In IEEE,(Ed.), 2001 IEEE International Conference on Robotics and Automation, pp.3588–3593. IEEE. Seoul : IEEE Press.

3. Georgiev A. and Allen P. (2004). Localization Methods for a Mobile Robot inUrban Environments. In IEEE, (Ed.), 2004 IEEE International Conference onRobotics and Automation, p. (to appear). IEEE/RSJ. Sendai: IEEE PRess.

4. Ojeda L. and Reina G. and Borenstein J. (2004). Experimental Results fromFLEXnav: An Expert Rule-based Dead-Reckoning System for Mars Rovers. InIEEE, (Ed.), Proceedings of the 2004 IEEE Aerospace Conference, IEEEAC. BigSky: IEEE Press.

5. Hogg R. and Rankin A. and Roumeliotis S. and McHenry M. and Helmick D. andBergh C. and Matthies L. (2002). Algorithms and Sensors for Small Robot PathFollowing. In IEEE, (Ed.), Proc. 2002 IEEE International Conference on Roboticsand Automation, pp. 3850–57. IEEE. Washington: IEEE Press.

6. Ojeda L. and Chung H. and Borenstein J. (2000). Precision-calibration ofFiber-optics Gyroscopes for Mobile Robot Navigation. In IEEE, (Ed.), Proceedingsof the 2000 IEEE International Conference on Robotics and Automation, pp.2064–2069. IEEE. San Francisco: IEEE Press.

7. Borenstein J., Everett H., Feng L. (1996). Where am I? Sensors and Methods forMobile Robot Positioning, 2nd ed. ed. A.K. Peters Ltd.

8. Borenstein J. and Feng L. (1996). Gyrodometry: A New Method for CombiningData from Gyros and Odometry in Mobile Robots. In IEEE, (Ed.), Proceedings ofthe 1995 Conference on Robotics and Automation (ICRA 96), IEEE. Minneapolis:IEEE Press.

9. Borenstein J. and Feng L. (1995). Correction of Systematic Odometry Errors inMobile Robotics. In IEEE, (Ed.), Proceedings of the 1995 Conference onIntelligent Robots and Systems (IROS 95), IEEE. August : IEEE Press.

10. Theory of Operation of Angular Rate Sensors, (Online) Crossbow. Rate GyroApplication Note. www.xbow.com/Support/ (1 Dec. 2005).

11. Athanasios Papoulis (1984). Probability, Random Variables, and StochasticProcesses, . New York: McGraw-Hill.


Annex AProcedure for Experiment # 1: Error characteristicsof NSUs caused by vehicle electromagnetic fieldand vehicle vibration

A.1 Experiment #1-1: Sensors detached from vehicle

1. Mount the NSUs and the data collection computer to the sensor platform.

2. Move the sensor platform to the location in Area 15 that testing will occur at.

3. Place the sensor platform on the ground facing north (use DGPS to find true north).

4. Power the computer and the NSUs and allow them to self calibrate (30 seconds).

5. Record the DGPS location of the sensor platform. Monitor the data collection forat least 30 minutes to 1 hour.

6. Power down the computer and the NSUs.

A.2 Experiment #1-2: Sensors attached to vehicle, engine off

1. Mount the sensor platform onto the GOPHER.

2. Move the GOPHER to the location in Area 15 that testing will occur at.

3. Place the GOPHER ground facing north (use DGPS to find true north).

4. Power the computer and the NSUs and allow them to self calibrate (30 seconds).

5. Record the DGPS location of the sensor platform.

6. Monitor the data collection for at least 30 minutes to 1 hour.


A.3 Experiment #1-3: Sensors attached to vehicle, engine on

1. Mount the sensor platform onto the GOPHER.

2. Move the GOPHER to the location in Area 15 that testing will occur at.

3. Place the GOPHER ground facing north (use DGPS to find true north).


4. Power the GOPHER, computer, and the NSUs and allow them to self calibrate (30seconds).

5. Record the DGPS location of the sensor platform.

6. Monitor the data collection for at least 30 minutes to 1 hour.


A.4 Experiment #1-4: Apparent Drift due to Earth’s Rotation

1. Examine the data from the previous experiments in either the gyro rate about theX-axis or the Y-axis for a constant drift in the roll/pitch (angular velocity about thex-axis/y-axis) which approaches 0.00319 ◦/sec.


Annex BData Graphs

This annex gives the experimental raw sensor data graphs for all the static experiments.Explanation for the graphs can be found in Section 6..

B.1 Experiment #1-1: Error Characteristics for static NSU awayfrom the vehicle influence

This section presents results for experiment 1-1 with NSU away from the GOPHERplatform. The graphs appear first, followed by the histograms.

Crossbow DMU-FOG

500 1000 1500 2000 2500−4.1

−4.05

−4

−3.95

−3.9

−3.85

−3.8

−3.75

−3.7

Time (s)

Roll (

deg)

y = − 7.863e−05*x − 3.845

Figure B.1: Exp 1-1: DMU-FOG graph of the roll angle vs time


500 1000 1500 2000 2500−1.72

−1.7

−1.68

−1.66

−1.64

−1.62

−1.6

−1.58

Time (s)

Pitc

h (d

eg)

y = 2.3e−06*x − 1.7

Figure B.2: Exp 1-1: DMU-FOG graph of the pitch angle vs time

500 1000 1500 2000 2500−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Time (s)

Gyr

o X

(deg

/s)

y = 1.7e−06*x − 0.0012

Figure B.3: Exp 1-1: DMU-FOG graph of the gyro rate about X vs time


500 1000 1500 2000 2500−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time (s)

Gyr

o Y

(deg

/s)

y = − 2.1e−07*x − 0.0046

Figure B.4: Exp 1-1: DMU-FOG graph of the gyro rate about Y vs time

500 1000 1500 2000 2500−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Time (s)

Gyr

o Z

(deg

/s)

y = − 6e−07*x − 0.012

Figure B.5: Exp 1-1: DMU-FOG graph of the gyro rate about Z vs time


500 1000 1500 2000 25000.022

0.024

0.026

0.028

0.03

0.032

0.034

0.036

0.038

0.04

Time (s)

Acce

l X (g

)

y = − 4.6e−08*x + 0.029

Figure B.6: Exp 1-1: DMU-FOG graph of the acceleration along X vs time

500 1000 1500 2000 2500−0.085

−0.08

−0.075

−0.07

−0.065

−0.06

Time (s)

Acce

l Y (g

)

y = − 1.5e−06*x − 0.067

Figure B.7: Exp 1-1: DMU-FOG graph of the acceleration along Y vs time


500 1000 1500 2000 25000.985

0.99

0.995

1

1.005

1.01

1.015

Time (s)

Acce

l Z (g

)

y = − 5.19e−07*x + 0.997

Figure B.8: Exp 1-1: DMU-FOG graph of the acceleration along Z vs time


−4.1

−4.0

5−4

−3.9

5−3

.9−3

.85

−3.8

−3.7

5−3

.70

1000

2000

3000

4000

5000

6000

7000

8000

9000

1000

0

Roll (

deg)

−1.7

2−1

.7−1

.68

−1.6

6−1

.64

−1.6

2−1

.6−1

.58

0

0.51

1.52

2.5

x 10

4

Pitc

h (d

eg)

N/A

a)b)

c)

−0.8

−0.6

−0.4

−0.2

00.

20.

40.

60.

80123456

x 10

4

Gyr

o X

(deg

/s)

−1−0

.8−0

.6−0

.4−0

.20

0.2

0.4

0.6

0.8

10

0.51

1.52

2.53

3.54

x 10

4

Gyr

o Y

(deg

/s)

−0.8

−0.6

−0.4

−0.2

00.

20.

40.

60.

80123456

x 10

4

Gyr

o Z

(deg

/s)

d)e)

f)

0.01

50.

020.

025

0.03

0.03

50.

040.

045

0

0.51

1.52

2.53

3.54

4.5

x 10

4

Acce

l X (g

)−0

.09

−0.0

85−0

.08

−0.0

75−0

.07

−0.0

65−0

.06

−0.0

550

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

Acce

l Y (g

)0.

980.

985

0.99

0.99

51

1.00

51.

011.

015

1.02

1.02

50

2000

4000

6000

8000

1000

0

1200

0

1400

0

Acce

l Z (g

)

g)h)

i)

Figure B.9: Exp 1-1: Crossbow DMU-FOG histograms a) roll b) pitch c) yaw d) gyro rate about X e) gyro rate aboutY f) gyro rate about Z g) acceleration along X h) acceleration along Y i) acceleration along Z


Lear Astronics

500 1000 1500 2000 2500−0.79

−0.78

−0.77

−0.76

−0.75

−0.74

−0.73

−0.72

Time (s)

Roll (

deg)

y = − 1.3e−06*x − 0.76

Figure B.10: Exp 1-1: Lear Astronics graph of the roll angle vs time

500 1000 1500 2000 2500−0.8

−0.79

−0.78

−0.77

−0.76

−0.75

−0.74

−0.73

−0.72

Time (s)

Pitc

h (d

eg)

y = 1.6e−05*x − 0.79

Figure B.11: Exp 1-1: Lear Astronics graph of the pitch angle vs time


500 1000 1500 2000 250011.7

11.8

11.9

12

12.1

12.2

12.3

12.4

12.5

12.6

Time (s)

Yaw

(deg

)

y = 0.00014*x + 12y = − 5.7e−24*x8 + 6.9e−20*x7 − 3.6e−16*x6 + 1e−12*x5 − 1.7e−09*x4 + 1.7e−06*x3 − 0.0011*x2 + 0.35*x − 37

data1 linear 8th degree

Figure B.12: Exp 1-1: Lear Astronics graph of the yaw angle vs time

500 1000 1500 2000 2500−6

−4

−2

0

2

4

6x 10−3

Time (s)

Gyr

o X

(deg

/s)

y = 8e−10*x + 4.4e−05

Figure B.13: Exp 1-1: Lear Astronics graph of the gyro rate about X vs time


500 1000 1500 2000 2500−8

−6

−4

−2

0

2

4

6

8x 10−3

Time (s)

Gyr

o Y

(deg

/s)

y = 1.83e−09*x − 1.12e−05

Figure B.14: Exp 1-1: Lear Astronics graph of the gyro rate about Y vs time

500 1000 1500 2000 2500−6

−4

−2

0

2

4

6x 10−4

Time (s)

Gyr

o Z

(deg

/s)

y = − 1.9e−09*x − 4.6e−05

Figure B.15: Exp 1-1: Lear Astronics graph of the gyro rate about Z vs time


500 1000 1500 2000 2500−0.022

−0.02

−0.018

−0.016

−0.014

−0.012

−0.01

−0.008

−0.006

−0.004

−0.002

Time (s)

Acce

l X (g

)

y = 1.6e−07*x − 0.014

Figure B.16: Exp 1-1: Lear Astronics graph of the acceleration along X vs time

500 1000 1500 2000 25000.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

Time (s)

Acce

l Y (g

)

y = 5e−08*x + 0.013

Figure B.17: Exp 1-1: Lear Astronics graph of the acceleration along Y vs time


500 1000 1500 2000 2500−1.02

−1.015

−1.01

−1.005

−1

−0.995

−0.99

−0.985

−0.98

Time (s)

Acce

l Z (g

)

y = − 2.32e−08*x − 0.999

Figure B.18: Exp 1-1: Lear Astronics graph of the acceleration along Z vs time


−0.8

−0.7

9−0

.78

−0.7

7−0

.76

−0.7

5−0

.74

−0.7

3−0

.72

0

2000

4000

6000

8000

1000

0

1200

0

1400

0

Roll (

deg)

−0.8

1−0

.8−0

.79

−0.7

8−0

.77

−0.7

6−0

.75

−0.7

4−0

.73

−0.7

20

1000

2000

3000

4000

5000

6000

Pitc

h (d

eg)

11.7

11.8

11.9

1212

.112

.212

.312

.412

.512

.60

500

1000

1500

2000

2500

Yaw

(deg

)

a)b)

c)

−0.0

15−0

.01

−0.0

050

0.00

50.

010.

015

0

2000

4000

6000

8000

1000

0

1200

0

1400

0

Gyr

o X

(deg

/s)

−0.0

15−0

.01

−0.0

050

0.00

50.

010.

015

0

5000

1000

0

1500

0

Gyr

o Y

(deg

/s)

−6−4

−20

24

6x

10−3

0

2000

4000

6000

8000

1000

0

1200

0

Gyr

o Z

(deg

/s)

d)e)

f)

−0.0

3−0

.025

−0.0

2−0

.015

−0.0

1−0

.005

00.

005

0

1000

2000

3000

4000

5000

6000

Acce

l X (g

)0

0.00

50.

010.

015

0.02

0.02

50.

030

2000

4000

6000

8000

1000

0

1200

0

1400

0

Acce

l Y (g

)−1

.02

−1.0

15−1

.01

−1.0

05−1

−0.9

95−0

.99

−0.9

85−0

.98

−0.9

750

1000

2000

3000

4000

5000

6000

7000

8000

9000

1000

0

Acce

l Z (g

)

g)h)

i)

Figure B.19: Exp 1-1: Lear Astronics histograms a) roll b) pitch c) yaw d) gyro rate about X e) gyro rate about Y f)gyro rate about Z g) acceleration along X h) acceleration along Y i) acceleration along Z


Microstrain

500 1000 1500 2000 2500

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Time (s)

Roll (

deg)

y = − 4.8e−05*x + 0.45

Figure B.20: Exp 1-1: Microstrain graph of the roll angle vs time

500 1000 1500 2000 25001.8

1.9

2

2.1

2.2

2.3

2.4

2.5

Time (s)

Pitc

h (d

eg)

y = 4.7e−05*x + 2.1

Figure B.21: Exp 1-1: Microstrain graph of the pitch angle vs time


500 1000 1500 2000 2500−177.9

−177.8

−177.7

−177.6

−177.5

−177.4

−177.3

−177.2

Time (s)

Yaw

(deg

)

y = − 2.4694e−05*x − 177.53

Figure B.22: Exp 1-1: Microstrain graph of the yaw angle vs time

500 1000 1500 2000 2500−6

−4

−2

0

2

4

6

8x 10−3

Time (s)

Gyr

o X

(deg

/s)

y = − 6.2e−07*x + 0.0013

Figure B.23: Exp 1-1: Microstrain graph of the gyro rate about X vs time


500 1000 1500 2000 2500−0.03

−0.02

−0.01

0

0.01

0.02

0.03

Time (s)

Gyr

o Y

(deg

/s)

y = 8.3e−07*x − 0.0014

Figure B.24: Exp 1-1: Microstrain graph of the gyro rate about Y vs time

500 1000 1500 2000 2500−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02

Time (s)

Gyr

o Z

(deg

/s)

y = 3.4e−07*x − 0.00056

Figure B.25: Exp 1-1: Microstrain graph of the gyro rate about Z vs time


500 1000 1500 2000 25000.032

0.034

0.036

0.038

0.04

0.042

0.044

Time (s)

Acce

l X (g

)

y = 8.4e−07*x + 0.036

Figure B.26: Exp 1-1: Microstrain graph of the acceleration along X vs time

500 1000 1500 2000 2500−10

−9

−8

−7

−6

−5

−4

−3x 10−3

Time (s)

Acce

l Y (g

)

y = 8.4e−07*x − 0.0079

Figure B.27: Exp 1-1: Microstrain graph of the acceleration along Y vs time


500 1000 1500 2000 2500−0.976

−0.975

−0.974

−0.973

−0.972

−0.971

−0.97

−0.969

Time (s)

Acce

l Z (g

)

y = − 6e−16*x4 + 3.8e−12*x3 − 5.5e−09*x2 − 2.3e−06*x − 0.97

Figure B.28: Exp 1-1: Microstrain graph of the acceleration along Z vs time


0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0

200

400

600

800

1000

1200

Roll (

deg)

1.8

1.9

22.

12.

22.

32.

42.

50

100

200

300

400

500

600

Pitc

h (d

eg)

−177

.9−1

77.8

−177

.7−1

77.6

−177

.5−1

77.4

−177

.3−1

77.2

0

100

200

300

400

500

600

700

800

Yaw

(deg

)

a)b)

c)

−0.0

15−0

.01

−0.0

050

0.00

50.

010.

015

0

200

400

600

800

1000

1200

1400

Gyr

o X

(deg

/s)

−0.0

4−0

.03

−0.0

2−0

.01

00.

010.

020.

03050100

150

200

250

Gyr

o Y

(deg

/s)

−0.0

25−0

.02

−0.0

15−0

.01

−0.0

050

0.00

50.

010.

015

0.02

0.02

5050100

150

200

250

300

350

Gyr

o Z

(deg

/s)

d)e)

f)

0.02

50.

030.

035

0.04

0.04

50.

050

100

200

300

400

500

600

Acce

l X (g

)−1

6−1

4−1

2−1

0−8

−6−4

−20

2x

10−3

0

200

400

600

800

1000

1200

Acce

l Y (g

)−1

.02

−1.0

15−1

.01

−1.0

05−1

−0.9

95−0

.99

−0.9

85−0

.98

−0.9

750

1000

2000

3000

4000

5000

6000

7000

8000

9000

1000

0

Acce

l Z (g

)

g)h)

i)

Figure B.29: Exp 1-1: Microstrain histograms a) roll b) pitch c) yaw d) gyro rate about X e) gyro rate about Y f) gyrorate about Z g) acceleration along X h) acceleration along Y i) acceleration along Z


Crossbow RGA300

500 1000 1500 2000 2500−0.65

−0.6

−0.55

−0.5

−0.45

−0.4

−0.35

Time (s)

Roll (

deg)

y = − 4.47e−05*x − 0.385

Figure B.30: Exp 1-1: Crossbow RGA300 graph of the roll angle vs time


500 1000 1500 2000 2500−0.74

−0.72

−0.7

−0.68

−0.66

−0.64

−0.62

−0.6

−0.58

−0.56

Time (s)

Pitc

h (d

eg)

y = 3.1e−06*x − 0.67

Figure B.31: Exp 1-1: Crossbow RGA300 graph of the pitch angle vs time

500 1000 1500 2000 2500−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

Time (s)

Gyr

o Z

(deg

/s)

y = 2.4e−05*x − 0.48

Figure B.32: Exp 1-1: Crossbow RGA300 graph of the gyro rate about Z vs time


500 1000 1500 2000 25000.0095

0.01

0.0105

0.011

0.0115

0.012

0.0125

0.013

0.0135

Time (s)

Acce

l X (g

)

y = − 6.5e−08*x + 0.012

Figure B.33: Exp 1-1: Crossbow RGA300 graph of the acceleration along X vs time

500 1000 1500 2000 2500−11

−10

−9

−8

−7

−6

−5x 10−3

Time (s)

Acce

l Y (g

)

y = − 8e−07*x − 0.0067

Figure B.34: Exp 1-1: Crossbow RGA300 graph of the acceleration along Y vs time


500 1000 1500 2000 25000.994

0.996

0.998

1

1.002

1.004

1.006

1.008

1.01

Time (s)

Acce

l Z (g

)

y = 8.19e−07*x + 0.999

Figure B.35: Exp 1-1: Crossbow RGA300 graph of the acceleration along Z vs time


−0.6

5−0

.6−0

.55

−0.5

−0.4

5−0

.4−0

.35

0

0.2

0.4

0.6

0.81

1.2

1.4

1.6

1.82

x 10

4

roll (

deg)

−0.7

4−0

.72

−0.7

−0.6

8−0

.66

−0.6

4−0

.62

−0.6

−0.5

8−0

.56

0

0.51

1.52

2.53

3.54

x 10

4

Pitc

h (d

eg)

N/A

a)b)

c)

N/A

N/A

−3−2

.5−2

−1.5

−1−0

.50

0.5

11.

52

0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

Gyr

o Z

(deg

/s)

d)e)

f)

0.00

40.

006

0.00

80.

010.

012

0.01

40.

016

0.01

80.

020123456

x 10

4

Acce

l X (g

)−0

.016

−0.0

14−0

.012

−0.0

1−0

.008

−0.0

06−0

.004

−0.0

020

0

0.51

1.52

2.53

3.54

4.55

x 10

4

Acce

l Y (g

)0.

985

0.99

0.99

51

1.00

51.

011.

015

0

0.51

1.52

2.53

3.5

x 10

4

Acce

l Z (g

)

g)h)

i)

Figure B.36: Exp 1-1: Crossbow RGA300 histograms a) roll b) pitch c) yaw d) gyro rate about X e) gyro rate aboutY f) gyro rate about Z g) acceleration along X h) acceleration along Y i) acceleration along Z


B.2 Exp 1-2: Error Characteristics for static NSU, sensors on thevehicle

This section presents results for experiment 1-2 with NSU’s installed on the GOPHERplatform. The graphs appear first, followed by the histograms.

Crossbow DMU-FOG

0 200 400 600 800 1000 1200 1400 1600 1800−2.26

−2.24

−2.22

−2.2

−2.18

−2.16

−2.14

−2.12

−2.1

−2.08

−2.06

Time (s)

Roll (

deg)

y = 1.2332e−06*x − 2.1565

Figure B.37: Exp 1-2: DMU-DOG graph of the roll angle vs time


0 200 400 600 800 1000 1200 1400 1600 1800−1.94

−1.92

−1.9

−1.88

−1.86

−1.84

−1.82

−1.8

−1.78

−1.76

Time (s)

Pitc

h (d

eg)

y = − 6.7e−06*x − 1.8

Figure B.38: Exp 1-2: DMU-DOG graph of the pitch angle vs time

0 200 400 600 800 1000 1200 1400 1600 1800−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

Time (s)

Gyr

o X

(deg

/s)

y = − 1.8e−07*x + 0.0053

Figure B.39: Exp 1-2: DMU-DOG graph of the gyro rate in X vs time


0 200 400 600 800 1000 1200 1400 1600 1800−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Time (s)

Gyr

o Y

(deg

/s)

y = 2.7e−07*x + 0.0023

Figure B.40: Exp 1-2: DMU-DOG graph of the gyro rate in Y vs time

0 200 400 600 800 1000 1200 1400 1600 1800−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Time (s)

Gyr

o Z

(deg

/s)

y = 1.1e−06*x − 0.0016

Figure B.41: Exp 1-2: DMU-DOG graph of the gyro rate in Z vs time


0 200 400 600 800 1000 1200 1400 1600 18000.024

0.026

0.028

0.03

0.032

0.034

0.036

0.038

0.04

0.042

Time (s)

Acce

l X (g

)

y = 1e−07*x + 0.032

Figure B.42: Exp 1-2: DMU-DOG graph of the acceleration in X vs time

0 200 400 600 800 1000 1200 1400 1600 1800−0.055

−0.05

−0.045

−0.04

−0.035

−0.03

−0.025

Time (s)

Acce

l Y (g

)

y = 4.6e−08*x − 0.037

Figure B.43: Exp 1-2: DMU-DOG graph of the acceleration in Y vs time


0 200 400 600 800 1000 1200 1400 1600 18000.98

0.985

0.99

0.995

1

1.005

1.01

1.015

Time (s)

Acce

l Z (g

)

y = 2.07e−07*x + 0.995

Figure B.44: Exp 1-2: DMU-DOG graph of the acceleration in Z vs time


−2.2

6−2

.24

−2.2

2−2

.2−2

.18

−2.1

6−2

.14

−2.1

2−2

.1−2

.08

−2.0

60

0.51

1.52

2.53

x 10

4

Roll (

deg)

−1.9

6−1

.94

−1.9

2−1

.9−1

.88

−1.8

6−1

.84

−1.8

2−1

.8−1

.78

−1.7

60

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

Pitc

h (d

eg)

N/A

a)b)

c)

−0.8

−0.6

−0.4

−0.2

00.

20.

40.

60

0.51

1.52

2.53

3.54

4.55

x 10

4

Gyr

o X

(deg

/s)

−1−0

.8−0

.6−0

.4−0

.20

0.2

0.4

0.6

0.8

0

0.51

1.52

2.53

3.5

x 10

4

Gyr

o Y

(deg

/s)

−0.6

−0.4

−0.2

00.

20.

40.

60.

80

0.51

1.52

2.53

3.54

4.5

x 10

4

Gyr

o Z

(deg

/s)

d)e)

f)

0.01

50.

020.

025

0.03

0.03

50.

040.

045

0.05

0

0.51

1.52

2.53

x 10

4

Acce

l X (g

)−0

.06

−0.0

55−0

.05

−0.0

45−0

.04

−0.0

35−0

.03

−0.0

25−0

.02

0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

Acce

l Y (g

)0.

975

0.98

0.98

50.

990.

995

11.

005

1.01

1.01

51.

021.

025

0

0.51

1.52

2.53

3.54

x 10

4

Acce

l Z (g

)

g)h)

i)

Figure B.45: Exp 1-2: Crossbow DMU-FOG histograms a) roll b) pitch c) yaw d) gyro rate about X e) gyro rateabout Y f) gyro rate about Z g) acceleration along X h) acceleration along Y i) acceleration along Z


Lear Astronics

0 200 400 600 800 1000 1200 1400 1600 18000.85

0.86

0.87

0.88

0.89

0.9

0.91

0.92

Time (s)

Roll (

deg)

y = − 5.7e−06*x + 0.88


0 200 400 600 800 1000 1200 1400 1600 1800−0.97

−0.96

−0.95

−0.94

−0.93

−0.92

−0.91

−0.9

Time (s)

Pitc

h (d

eg)

y = 7.81e−06*x − 0.945



0 200 400 600 800 1000 1200 1400 1600 1800

20.4

20.6

20.8

21

21.2

21.4

Time (s)

Yaw

(deg

)

y = 0.00057078*x + 20.234


0 200 400 600 800 1000 1200 1400 1600 1800−4

−3

−2

−1

0

1

2

3

4

5

6x 10−3

Time (s)

Gyr

o X

(deg

/s)

y = 6.9e−10*x + 4.2e−05

Figure B.49: Exp 1-2: Lear Astronics graph of the gyro rate in X vs time


0 200 400 600 800 1000 1200 1400 1600 1800−5

−4

−3

−2

−1

0

1

2

3

4

5x 10−3

Time (s)

Gyr

o Y

(deg

/s)

y = 8.9e−10*x − 1.8e−05

Figure B.50: Exp 1-2: Lear Astronics graph of the gyro rate in Y vs time

0 200 400 600 800 1000 1200 1400 1600 1800−4

−3

−2

−1

0

1

2

3

4

5x 10−3

Time (s)

Gyr

o Z

(deg

/s)

y = 1.2e−09*x − 4.8e−05

Figure B.51: Exp 1-2: Lear Astronics graph of the gyro rate about Z vs time


0 200 400 600 800 1000 1200 1400 1600 1800−0.026

−0.024

−0.022

−0.02

−0.018

−0.016

−0.014

−0.012

−0.01

−0.008

Time (s)

Acce

l X (g

)

y = 6.8e−08*x − 0.016

Figure B.52: Exp 1-2: Lear Astronics graph of the acceleration in X vs time

0 200 400 600 800 1000 1200 1400 1600 1800−0.024

−0.022

−0.02

−0.018

−0.016

−0.014

−0.012

−0.01

−0.008

−0.006

−0.004

Time (s)

Acce

l Y (g

)

y = 1.7e−07*x − 0.016

Figure B.53: Exp 1-2: Lear Astronics graph of the acceleration in Y vs time


0 200 400 600 800 1000 1200 1400 1600 1800−1.008

−1.006

−1.004

−1.002

−1

−0.998

−0.996

−0.994

−0.992

−0.99

Time (s)

Acce

l Z (g

)

y = − 1.47e−08*x − 0.999

Figure B.54: Exp 1-2: Lear Astronics graph of the acceleration along Z vs time


0.84

0.85

0.86

0.87

0.88

0.89

0.9

0.91

0.92

0.93

0

2000

4000

6000

8000

1000

0

1200

0

Roll (

deg)

−0.9

8−0

.97

−0.9

6−0

.95

−0.9

4−0

.93

−0.9

2−0

.91

−0.9

0

1000

2000

3000

4000

5000

6000

Pitc

h (d

eg)

20.3

20.4

20.5

20.6

20.7

20.8

20.9

2121

.121

.20

200

400

600

800

1000

1200

1400

1600

1800

Yaw

(deg

)

a)b)

c)

−0.0

1−0

.005

00.

005

0.01

0.01

50

1000

2000

3000

4000

5000

6000

7000

Gyr

o X

(deg

/s)

−0.0

1−0

.008

−0.0

06−0

.004

−0.0

020

0.00

20.

004

0.00

60.

008

0.01

0

1000

2000

3000

4000

5000

6000

7000

8000

gyro

Y (d

eg/s

)−0

.01

−0.0

08−0

.006

−0.0

04−0

.002

00.

002

0.00

40.

006

0.00

80.

010

2000

4000

6000

8000

1000

0

1200

0

Gyr

o Z

(deg

/s)

d)e)

f)

−0.0

35−0

.03

−0.0

25−0

.02

−0.0

15−0

.01

−0.0

050

0

1000

2000

3000

4000

5000

6000

7000

Acce

l X (g

)−0

.03

−0.0

25−0

.02

−0.0

15−0

.01

−0.0

050

0

2000

4000

6000

8000

1000

0

1200

0

Acce

l Y (g

)−1

.02

−1.0

15−1

.01

−1.0

05−1

−0.9

95−0

.99

−0.9

850

2000

4000

6000

8000

1000

0

1200

0

Acce

l Z (g

)

g)h)

i)



MicroStrain

0 200 400 600 800 1000 1200 1400 1600 1800−1.25

−1.2

−1.15

−1.1

−1.05

−1

−0.95

−0.9

−0.85

Time (s)

Roll (

deg)

y = − 2.48e−05*x − 1.06


0 200 400 600 800 1000 1200 1400 1600 18001.7

1.75

1.8

1.85

1.9

1.95

2

2.05

2.1

2.15

2.2

Time (s)

Pitc

h (d

eg)

y = 5.35e−05*x + 1.87



0 200 400 600 800 1000 1200 1400 1600 1800−34

−33.5

−33

−32.5

−32

−31.5

−31

Time (s)

Yaw

(deg

)

y = 0.00049*x − 33


0 200 400 600 800 1000 1200 1400 1600 1800−8

−6

−4

−2

0

2

4

6x 10−3

Time (s)

Gyr

o X

(deg

/s)

y = 1.2e−07*x + 4.4e−06

Figure B.59: Exp 1-2: Microstrain graph of the gyro rate in X vs time


0 200 400 600 800 1000 1200 1400 1600 1800−0.025

−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02

0.025

Time (s)

Gyr

o Y

(deg

/s)

y = − 1.5e−07*x + 0.00034

Figure B.60: Exp 1-2: Microstrain graph of the gyro rate in Y vs time

0 200 400 600 800 1000 1200 1400 1600 1800−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02

Time (s)

Gyr

o Z

(deg

/s)

y = 8.7e−08*x − 9.1e−05

Figure B.61: Exp 1-2: Microstrain graph of the gyro rate in Z vs time


0 200 400 600 800 1000 1200 1400 1600 18000.029

0.03

0.031

0.032

0.033

0.034

0.035

0.036

0.037

0.038

0.039

Time (s)

Acce

l X (g

)

y = 8.8e−07*x + 0.032

Figure B.62: Exp 1-2: Microstrain graph of the acceleration in X vs time

0 200 400 600 800 1000 1200 1400 1600 18000.015

0.016

0.017

0.018

0.019

0.02

0.021

Time (s)

Acce

l Y (g

)

y = 4.2e−07*x + 0.018

Figure B.63: Exp 1-2: Microstrain graph of the acceleration in Y vs time


0 200 400 600 800 1000 1200 1400 1600 1800−0.9835

−0.983

−0.9825

−0.982

−0.9815

−0.981

−0.9805

−0.98

Time (s)

Acce

l Z (g

)

y = 6.3e−07*x − 0.98

Figure B.64: Exp 1-2: Microstrain graph of the acceleration in Z vs time


−1.2

5−1

.2−1

.15

−1.1

−1.0

5−1

−0.9

5−0

.9−0

.85

0

200

400

600

800

1000

1200

Roll (

deg)

1.6

1.7

1.8

1.9

22.

12.

22.

30

200

400

600

800

1000

1200

Pitc

h (d

eg)

−34

−33.

5−3

3−3

2.5

−32

−31.

5−3

10

200

400

600

800

1000

1200

1400

Yaw

(deg

)

a)b)

c)

−0.0

15−0

.01

−0.0

050

0.00

50.

010.

015

0

200

400

600

800

1000

1200

1400

Gyr

o X

(deg

/s)

−0.0

3−0

.02

−0.0

10

0.01

0.02

0.03

050100

150

200

250

Gyr

o Y

(deg

/s)

−0.0

2−0

.015

−0.0

1−0

.005

00.

005

0.01

0.01

50.

020.

025

0

100

200

300

400

500

600

Gyr

o Z

(deg

/s)

d)e)

f)

0.02

40.

026

0.02

80.

030.

032

0.03

40.

036

0.03

80.

040.

042

0.04

40

100

200

300

400

500

600

Acce

l X (g

)0.

010.

012

0.01

40.

016

0.01

80.

020.

022

0.02

40.

026

0.02

80

500

1000

1500

2000

2500

Acce

l Y (g

)−0

.99

−0.9

88−0

.986

−0.9

84−0

.982

−0.9

8−0

.978

−0.9

76−0

.974

0

500

1000

1500

2000

2500

3000

Acce

l Z (g

)

g)h)

i)

Figure B.65: Exp 1-2: Microstrain histograms a) roll b) pitch c) yaw d) gyro rate about X e) gyro rate about Y f) gyrorate about Z g) acceleration along X h) acceleration along Y i) acceleration along Z


Crossbow RGA300

0 200 400 600 800 1000 1200 1400 1600 1800

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

Time (s)

Roll (

deg/

s)

y = − 8.8e−06*x + 1.2



0 200 400 600 800 1000 1200 1400 1600 1800−1.1

−1

−0.9

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

Time (s)

Pitc

h (d

eg)

y = 5.4e−06*x − 0.73


0 200 400 600 800 1000 1200 1400 1600 1800−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

Time (s)

Gyr

o Z

(deg

/s)

y = 1.7e−05*x − 0.0035

Figure B.68: Exp 1-2: Crossbow RGA300 graph of the gyro rate in Z vs time


0 200 400 600 800 1000 1200 1400 1600 18000.005

0.01

0.015

0.02

Time (s)

Acce

l X (g

)

y = − 8.6e−08*x + 0.013

Figure B.69: Exp 1-2: Crossbow RGA300 graph of the acceleration in X vs time

0 200 400 600 800 1000 1200 1400 1600 18000.01

0.012

0.014

0.016

0.018

0.02

0.022

0.024

0.026

0.028

Time (s)

Acce

l Y (g

)

y = − 1.4e−07*x + 0.022

Figure B.70: Exp 1-2: Crossbow RGA300 graph of the acceleration in Y vs time


0 200 400 600 800 1000 1200 1400 1600 18000.985

0.99

0.995

1

1.005

1.01

1.015

1.02

1.025

Time (s)

Acce

l Z (g

)

y = 1.564e−07*x + 1.002

Figure B.71: Exp 1-2: Crossbow RGA300 graph of the acceleration in Z vs time


0.7

0.8

0.9

11.

11.

21.

31.

41.

51.

60

0.51

1.52

2.53

3.5

x 10

4

Roll (

deg)

−1.1

−1−0

.9−0

.8−0

.7−0

.6−0

.5−0

.4−0

.30

0.51

1.52

2.53

3.54

4.5

x 10

4

Pitc

h (d

eg)

N/A

a)b)

c)

N/A

N/A

−2.5

−2−1

.5−1

−0.5

00.

51

1.5

22.

50

0.2

0.4

0.6

0.81

1.2

1.4

1.6

1.82

x 10

4

gyro

Z (d

eg/s

)

d)e)

f)

00.

005

0.01

0.01

50.

020.

025

01234567x

104

Acce

l X (g

)0.

005

0.01

0.01

50.

020.

025

0.03

0.03

50123456

x 10

4

Acce

l Y (g

)0.

980.

985

0.99

0.99

51

1.00

51.

011.

015

1.02

1.02

501234567

x 10

4

Acce

l Z (g

)

g)h)

i)



B.3 Exp 1-3: Error Characteristics for static NSU, vehicle engineon

This section presents results for experiment 1-3 with NSU installed on the GOPHERplatform and the engine is turned ON. The graphs appear first, followed by thehistograms.

Crossbow DMU-FOG

0 200 400 600 800 1000 1200 1400 1600−2.5

−2.4

−2.3

−2.2

−2.1

−2

−1.9

−1.8

Time (s)

Roll (

deg)

y = 9.89e−05*x − 2.14

Figure B.73: Exp 1-3: DMU-FOG graph of the roll angle vs time


0 200 400 600 800 1000 1200 1400 1600−3.2

−3

−2.8

−2.6

−2.4

−2.2

−2

−1.8

Time (s)

Pitc

h (d

eg)

y = − 9.68e−05*x − 2.33

Figure B.74: Exp 1-3: DMU-FOG graph of the pitch angle vs time

0 200 400 600 800 1000 1200 1400 1600−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

Time (s)

Gyr

o X

(deg

/s)

y = − 2.6289e−06*x − 0.0066369

Figure B.75: Exp 1-3: DMU-FOG graph of the gyro rate in X vs time


0 200 400 600 800 1000 1200 1400 1600−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

Time (s)

Gyr

o Y

(deg

/s)

y = − 7.1e−07*x + 0.0017

Figure B.76: Exp 1-3: DMU-FOG graph of the gyro rate in Y vs time

0 200 400 600 800 1000 1200 1400 1600−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Time (s)

Gyr

o Z

(deg

/s)

y = − 1.3e−06*x + 0.0033

Figure B.77: Exp 1-3: DMU-FOG graph of the gyro rate in Z vs time


0 200 400 600 800 1000 1200 1400 1600−0.1

−0.05

0

0.05

0.1

0.15

Time (s)

Acce

l X (g

)

y = 2.8e−06*x + 0.036

Figure B.78: Exp 1-3: DMU-FOG graph of the acceleration in X vs time

0 200 400 600 800 1000 1200 1400 1600−0.12

−0.1

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

Time (s)

Acce

l Y (g

)

y = 2.5e−06*x − 0.04

Figure B.79: Exp 1-3: DMU-FOG graph of the acceleration in Y vs time


0 200 400 600 800 1000 1200 1400 1600

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

Time (s)

Acce

l Z (g

)

y = − 2.4e−06*x + 1

Figure B.80: Exp 1-3: DMU-FOG graph of the acceleration in Z vs time


−2.5

−2.4

−2.3

−2.2

−2.1

−2−1

.9−1

.80

1000

2000

3000

4000

5000

6000

7000

Roll (

deg)

−3.2

−3−2

.8−2

.6−2

.4−2

.2−2

−1.8

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

1000

0

Pitc

h (d

eg)

N/A

a)b)

c)

−2−1

.5−1

−0.5

00.

51

1.5

20

2000

4000

6000

8000

1000

0

1200

0

Gyr

o X

(deg

/s)

−2−1

.5−1

−0.5

00.

51

1.5

20

2000

4000

6000

8000

1000

0

1200

0

1400

0

Gyr

o Y

(deg

/s)

−0.8

−0.6

−0.4

−0.2

00.

20.

40.

60.

80

0.51

1.52

2.53

x 10

4

Gyr

o Z

(deg

/s)

d)e)

f)

−0.1

−0.0

50

0.05

0.1

0.15

0

1000

2000

3000

4000

5000

6000

7000

8000

Acce

l X (g

)−0

.14

−0.1

2−0

.1−0

.08

−0.0

6−0

.04

−0.0

20

0.02

0.04

0

1000

2000

3000

4000

5000

6000

7000

8000

Acce

l Y (g

)0.

70.

80.

91

1.1

1.2

1.3

1.4

0

1000

2000

3000

4000

5000

6000

Acce

l Z (g

)

g)h)

i)

Figure B.81: Exp 1-3: Crossbow DMU-FOG histograms a) roll b) pitch c) yaw d) gyro rate about X e) gyro rateabout Y f) gyro rate about Z g) acceleration along X h) acceleration along Y i) acceleration along Z


Lear Astronics

0 200 400 600 800 1000 1200 1400 16000.64

0.66

0.68

0.7

0.72

0.74

0.76

Time (s)

Roll (

deg)

y = 8.77e−06*x + 0.699



0 200 400 600 800 1000 1200 1400 1600−1.54

−1.52

−1.5

−1.48

−1.46

−1.44

−1.42

Time (s)

Pitc

h (d

eg)

y = − 7.463e−06*x − 1.474


0 200 400 600 800 1000 1200 1400 160016.6

16.8

17

17.2

17.4

17.6

17.8

Time (s)

Yaw

(deg

)

y = 0.00050239*x + 16.791



0 200 400 600 800 1000 1200 1400 1600−0.015

−0.01

−0.005

0

0.005

0.01

0.015

Time (s)

Gyr

o X

(deg

/s)

y = − 2.5e−09*x + 4.6e−05

Figure B.85: Exp 1-3: Lear Astronics graph of the gyro rate in X vs time

0 200 400 600 800 1000 1200 1400 1600−0.015

−0.01

−0.005

0

0.005

0.01

0.015

Time (s)

Gyr

o Y

(deg

/s)

y = − 2.9e−10*x − 1.4e−05

Figure B.86: Exp 1-3: Lear Astronics graph of the gyro rate in Y vs time


0 200 400 600 800 1000 1200 1400 1600−6

−4

−2

0

2

4

6

8x 10−3

Time (s)

Gyr

o Z

(deg

/s)

y = 4.7e−10*x − 4.9e−05

Figure B.87: Exp 1-3: Lear Astronics graph of the gyro rate in Z vs time

0 200 400 600 800 1000 1200 1400 1600−0.1

−0.05

0

0.05

0.1

0.15

Time (s)

Acce

l X (g

)

y = 2.8e−06*x + 0.036

Figure B.88: Exp 1-3: Lear Astronics graph of the acceleration in X vs time


0 200 400 600 800 1000 1200 1400 1600−0.12

−0.1

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

Time (s)

Acce

l Y (g

)

y = 2.5e−06*x − 0.04

Figure B.89: Exp 1-3: Lear Astronics graph of the acceleration in Y vs time

0 200 400 600 800 1000 1200 1400 1600

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

Time (s)

Acce

l Z (g

)

y = − 2.4e−06*x + 1

Figure B.90: Exp 1-3: Lear Astronics graph of the acceleration in Z vs time


0.64

0.66

0.68

0.7

0.72

0.74

0.76

0

1000

2000

3000

4000

5000

6000

7000

8000

Roll (

deg)

−1.5

6−1

.54

−1.5

2−1

.5−1

.48

−1.4

6−1

.44

−1.4

2−1

.40

500

1000

1500

2000

2500

3000

3500

4000

4500

Pitc

h (d

eg)

16.6

16.8

1717

.217

.417

.617

.80

500

1000

1500

2000

2500

3000

3500

4000

4500

Yaw

(deg

)

a)b)

c)

−0.0

2−0

.015

−0.0

1−0

.005

00.

005

0.01

0.01

50.

020

500

1000

1500

2000

2500

Gyr

o X

(deg

/s)

−0.0

2−0

.015

−0.0

1−0

.005

00.

005

0.01

0.01

50.

020

500

1000

1500

2000

2500

3000

Gyr

o Y

(deg

/s)

−0.0

15−0

.01

−0.0

050

0.00

50.

010.

015

0

2000

4000

6000

8000

1000

0

1200

0

Gyr

o Z

(deg

/s)

d)e)

f)

−0.0

7−0

.06

−0.0

5−0

.04

−0.0

3−0

.02

−0.0

10

0.01

0

500

1000

1500

2000

2500

3000

3500

4000

Acce

l X (g

)−0

.04

−0.0

3−0

.02

−0.0

10

0.01

0.02

0

1000

2000

3000

4000

5000

6000

Acce

l Y (g

)−1

.08

−1.0

6−1

.04

−1.0

2−1

−0.9

8−0

.96

−0.9

4−0

.92

−0.9

0

500

1000

1500

2000

2500

3000

3500

Acce

l Z (g

)

g)h)

i)



MicroStrain

0 200 400 600 800 1000 1200 1400 1600−1.3

−1.2

−1.1

−1

−0.9

−0.8

−0.7

−0.6

−0.5

Time (s)

Roll (

deg)

y = − 9.6e−06*x − 0.85


0 200 400 600 800 1000 1200 1400 16001.9

2

2.1

2.2

2.3

2.4

2.5

2.6

Time (s)

Pitc

h (d

eg)

y = 8.58e−05*x + 2.26



0 200 400 600 800 1000 1200 1400 1600−110

−105

−100

−95

−90

−85

Time (s)

Yaw

(deg

)

y = 0.00982*x − 108


0 200 400 600 800 1000 1200 1400 1600−0.05

−0.04

−0.03

−0.02

−0.01

0

0.01

0.02

0.03

0.04

Time (s)

Gyr

o X

(deg

/s)

y = 5.4e−07*x − 0.00059

Figure B.95: Exp 1-3: Microstrain graph of the gyro rate in X vs time


0 200 400 600 800 1000 1200 1400 1600−0.015

−0.01

−0.005

0

0.005

0.01

0.015

Time (s)

Gyr

o Y

(deg

/s)

y = − 2.9e−10*x − 1.4e−05

Figure B.96: Exp 1-3: Microstrain graph of the gyro rate in Y vs time

0 200 400 600 800 1000 1200 1400 1600−0.03

−0.02

−0.01

0

0.01

0.02

0.03

Time (s)

Gyr

o Z

(deg

/s)

y = − 3.8e−08*x + 0.00027

Figure B.97: Exp 1-3: Microstrain graph of the gyro rate in Z vs time


0 200 400 600 800 1000 1200 1400 16000.034

0.036

0.038

0.04

0.042

0.044

0.046

Time (s)

Acce

l X (g

)

y = 1.4e−06*x + 0.039

Figure B.98: Exp 1-3: Microstrain graph of the acceleration in X vs time

0 200 400 600 800 1000 1200 1400 16000.008

0.01

0.012

0.014

0.016

0.018

0.02

Time (s)

Acce

l Y (g

)

y = 1.2e−07*x + 0.015

Figure B.99: Exp 1-3: Microstrain graph of the acceleration in Y vs time


0 200 400 600 800 1000 1200 1400 1600−1

−0.995

−0.99

−0.985

−0.98

−0.975

Time (s)

Acce

l Z (g

)

y = 2.46e−06*x − 0.986

Figure B.100: Exp 1-3: Microstrain graph of the acceleration in Z vs time


−1.3

−1.2

−1.1

−1−0

.9−0

.8−0

.7−0

.6−0

.50

100

200

300

400

500

600

700

Roll (

deg)

1.9

22.

12.

22.

32.

42.

52.

62.

7050100

150

200

250

300

350

400

450

Pitc

h (d

eg)

−110

−105

−100

−95

−90

−85

0

200

400

600

800

1000

1200

Yaw

(deg

)

a)b)

c)

−0.0

5−0

.04

−0.0

3−0

.02

−0.0

10

0.01

0.02

0.03

0.04

0.05

050100

150

200

250

300

350

400

450

500

Gyr

o X

(deg

/s)

−0.0

6−0

.04

−0.0

20

0.02

0.04

0.06

0

100

200

300

400

500

600

700

800

Gyr

o Y

(deg

/s)

−0.0

4−0

.03

−0.0

2−0

.01

00.

010.

020.

030

100

200

300

400

500

600

700

800

900

1000

Gyr

o Z

(deg

/s)

d)e)

f)

0.02

50.

030.

035

0.04

0.04

50.

050.

055

0

200

400

600

800

1000

1200

1400

Acce

l X (g

)0

0.00

50.

010.

015

0.02

0.02

50

100

200

300

400

500

600

700

Acce

l Y (g

)−1

−0.9

95−0

.99

−0.9

85−0

.98

−0.9

75−0

.97

−0.9

650

200

400

600

800

1000

1200

1400

Acce

l Z (g

)

g)h)

i)

Figure B.101: Exp 1-3: Microstrain histograms a) roll b) pitch c) yaw d) gyro rate about X e) gyro rate about Y f)gyro rate about Z g) acceleration along X h) acceleration along Y i) acceleration along Z


Crossbow RGA300

0 200 400 600 800 1000 1200 1400 1600−0.5

0

0.5

1

1.5

2

2.5

3

3.5

Time (s)

Roll (

deg)

y = − 5.71e−05*x + 1.25



0 200 400 600 800 1000 1200 1400 1600−6

−5

−4

−3

−2

−1

0

1

2

3

Time (s)

Pitc

h (d

eg)

y = 6.38e−05*x − 1.35


0 200 400 600 800 1000 1200 1400 1600−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

Time (s)

Gyr

o Z

(deg

/s)

y = − 0.00013*x − 0.043

Figure B.104: Exp 1-3: Crossbow RGA300 graph of the gyro rate in Z vs time


0 200 400 600 800 1000 1200 1400 1600−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

0.1

Time (s)

Acce

l X (g

)

y = − 1.1e−06*x + 0.023

Figure B.105: Exp 1-3: Crossbow RGA300 graph of the acceleration in X vs time

0 200 400 600 800 1000 1200 1400 1600−0.03

−0.02

−0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Time (s)

Acce

l Y (g

)

y = − 1e−06*x + 0.021

Figure B.106: Exp 1-3: Crossbow RGA300 graph of the acceleration in Y vs time


0 200 400 600 800 1000 1200 1400 16000.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

Time (s)

Acce

l Z (g

)

y = 5.5e−07*x + 1

Figure B.107: Exp 1-3: Crossbow RGA300 graph of the acceleration in Z vs time


−0.5

00.

51

1.5

22.

53

3.5

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Roll (

deg)

−6−5

−4−3

−2−1

01

23

0

2000

4000

6000

8000

1000

0

1200

0

1400

0

1600

0

1800

0

Pitc

h (d

eg)

N/A

a)b)

c)

N/A

N/A

−2.5

−2−1

.5−1

−0.5

00.

51

1.5

22.

50

0.51

1.52

2.5

x 10

4

Gyr

o Z

(deg

/s)

d)e)

f)

−0.0

8−0

.06

−0.0

4−0

.02

00.

020.

040.

060.

080.

10.

120

1000

2000

3000

4000

5000

6000

7000

8000

Acce

l X (g

)−0

.04

−0.0

20

0.02

0.04

0.06

0.08

0

2000

4000

6000

8000

1000

0

1200

0

1400

0

Acce

l Y (g

)0.

750.

80.

850.

90.

951

1.05

1.1

1.15

1.2

1.25

0

2000

4000

6000

8000

1000

0

1200

0

Acce

l Z (g

)

g)h)

i)



Annex CInitialisms

AO Area of Operations

AOR Area of Responsibility

C/A Course Acquisition GPS

DMU Dynamic Measurement Unit

DGPS Differential GPS

ECEF Earth-Centred, Earth-Fixed

FOG Fibre Optic Gyroscope

GPS Global Positioning System

HAAW Heavy Anti-Armour Weapon

IMU Inertial Measurement Unit

LAAW Light Anti-Armour Weapon

LAN Local Area Network

NSU Navigational Sensor Unit

OPI Office of Primary Interest

PID Proportional Integral Differential

RGA Rate Gyro Accelerometer

RPG Rocket Propelled Grenade

RTK Real Time Kinematic

SMA Senior Military Advisor

TNA Thermal Neutron Activation

UAV Unmanned Aerial Vehicle

UGV Unmanned Ground Vehicle

UUV Unmanned Underwater Vehicle

USV Unmanned Space Vehicle

UxV Unmanned (Aerial, Ground, Underwater, Space) Vehicle


Annex DNotation

α latitude angle

β longitude angle

σ2 Variance of a variable population

σ Standard deviation of a variable population

θ rotation about the modified y-axis in radians for Euler RPY

φ rotation about the modified x-axis in radians for Euler RPY

ψ rotation about initial z-axis in radians for Euler RPY

` Local Coordinate Frame of Reference (Robot ego-centric)

p` Local Coordinate Frame pose (Robot ego-centric)

prpy JAUS-compliant

pW World Coordinate Frame pose

pW−UTM World Coordinate Frame pose with UTM

q quaternion vector

q? quaternion conjugate

qs quaternion scalar component

qx quaternion imaginary projection along the i axis

qy quaternion imaginary projection along the j axis

qz quaternion imaginary projection along the k axis

s2 Variance of a variable sample

s Standard deviation of a variable sample

x` x displacement in local pose

xW x displacement in global pose

y` y displacement in local pose

yW y displacement in local pose

z` z displacement in global pose


zW z displacement in global pose

D Displacement vector

G Units of gravity (9.81 ms2 )

R Rotation Matrix

T Transformation Matrix

W World Coordinate Frame of Reference


Annex EEquipment Specification

Thread 1/4"-20Load, lbs. 24

Compression Maximum Deflection@ Max. Load 0.01"Durometer 50A

(A) 1 1/8"(B) 2 3/8"(C) 2 19/64"(E) 1 15/16"

Flange Hole Dia. 0.196"Part No. S/N 6188K412

Table E.1: GOPHER Shock Mount Specifications for 6188K412, Steel Cup Vibration Damping Mount Neoprene,1/4"-20 Thread, 24 Lbs Max Load


DOCUMENT CONTROL DATA(Security classification of title, body of abstract and indexing annotation must be entered when document is classified)

1. ORIGINATOR (the name and address of the organization preparing the document.Organizations for whom the document was prepared, e.g. Centre sponsoring acontractor’s report, or tasking agency, are entered in section 8.)

Defence R&D Canada – SuffieldPO Box 4000, Medicine Hat, AB, Canada, T1A 8K6

2. SECURITY CLASSIFICATION(overall security classification of the documentincluding special warning terms if applicable).

UNCLASSIFIED

3. TITLE (the complete document title as indicated on the title page. Its classification should be indicated by the appropriateabbreviation (S,C,R or U) in parentheses after the title).

Static Localization Sensor Experiment 2005

4. AUTHORS(Last name, first name, middle initial. If military, show rank, e.g. Doe, Maj. John E.)

Vincent, I. ; Erickson, D.

5. DATE OF PUBLICATION (month and year of publication of document)

March 2006

6a. NO. OF PAGES (totalcontaining information. IncludeAnnexes, Appendices, etc).

119

6b. NO. OF REFS (total cited indocument)

11

7. DESCRIPTIVE NOTES (the category of the document, e.g. technical report, technical note or memorandum. If appropriate, enter the type of report,e.g. interim, progress, summary, annual or final. Give the inclusive dates when a specific reporting period is covered).

Technical Memorandum

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9a. PROJECT OR GRANT NO. (if appropriate, the applicable research anddevelopment project or grant number under which the document waswritten. Specify whether project or grant).

9b. CONTRACT NO. (if appropriate, the applicable number under whichthe document was written).

10a. ORIGINATOR’S DOCUMENT NUMBER (the official document numberby which the document is identified by the originating activity. Thisnumber must be unique.)

DRDC Suffield TM 2005-213

10b. OTHER DOCUMENT NOs. (Any other numbers which may beassigned this document either by the originator or by the sponsor.)

11. DOCUMENT AVAILABILITY (any limitations on further dissemination of the document, other than those imposed by security classification)( X ) Unlimited distribution( ) Defence departments and defence contractors; further distribution only as approved( ) Defence departments and Canadian defence contractors; further distribution only as approved( ) Government departments and agencies; further distribution only as approved( ) Defence departments; further distribution only as approved( ) Other (please specify):

12. DOCUMENT ANNOUNCEMENT (any limitation to the bibliographic announcement of this document. This will normally correspond to the DocumentAvailability (11). However, where further distribution beyond the audience specified in (11) is possible, a wider announcement audience may beselected).

Unlimited

13. ABSTRACT (a brief and factual summary of the document. It may also appear elsewhere in the body of the document itself. It is highly desirable that theabstract of classified documents be unclassified. Each paragraph of the abstract shall begin with an indication of the security classification of theinformation in the paragraph (unless the document itself is unclassified) represented as (S), (C), (R), or (U). It is not necessary to include here abstracts inboth official languages unless the text is bilingual).

This document presents the background, objectives, experimental procedure and the results of the exper-iments held during April 2005 on the GOPHER platform for the following navigational sensor units (NSU):Lear Astronics Corporation’s NSU, Crossbow Dynamic Measurement Unit DMU-FOG, Crossbow Rate GyroAccelerometer RGA300CA and MicroStrain 3DM-G. These sensors were tested concurrently in static anddynamic situations, with the presence and absence of the vehicle and its influences. This report presentsthe static experiment results. These trials are a unique opportunity to collect identical condition data, dis-cover systematic/nonsystematic error sources in aggregate across sensor types, observe individual sensorperformance and compare the capability of these sensors under identical conditions.

14. KEYWORDS, DESCRIPTORS or IDENTIFIERS (technically meaningful terms or short phrases that characterize a document and could be helpful incataloguing the document. They should be selected so that no security classification is required. Identifiers, such as equipment model designation, tradename, military project code name, geographic location may also be included. If possible keywords should be selected from a published thesaurus. e.g.Thesaurus of Engineering and Scientific Terms (TEST) and that thesaurus-identified. If it not possible to select indexing terms which are Unclassified, theclassification of each should be indicated as with the title).

localization, mobile robots, inertial navigation, dead-reckoning, GPS/DGPS

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Static Localization Sensor Experiment 2005