UCGE Reports Number 20098

Department of Geomatics Engineering

Augmentation of GPS with a Barometer and a Heading Rate Gyroscope for Urban Vehicular Navigation (URL: http://www.geomatics.ucalgary.ca/links/GradTheses.html)

by

Nobuyuki Hayashi

December 1996

THE UNIVERSITY OF CALGARY

Augmentation of GPS with a Barometer and a Heading Rate Gyroscope

for Urban Vehicular Navigation

by

Nobuyuki Hayashi

A THESIS

SUBMITTE FACULTE TH O GRADUATDT F Y O E STUDIES

DEPARTMEN GEOMATICF TO S ENGINEERING

©Nobuyuki Hayashi 1996 PREFACE

unalteren Thia s i s d versioe author'th f o n s Maste f Scienco r Engineerinn i e g

Thesis of the same title. This thesis was accepted by the Faculty of Graduate Studies in

December 1996.

e facultTh y superviso r thi . Gerarfo rs Dr wor s dkwa Lachapell e otheth d r an e member examinine th f so g committe . Collins . J . Cannon . E M . . eM . M werDr , . Dr , eDr

Fattouche and Dr. G. Rogers. ABSTRACT

integratew ne A d DGP S/ sensor s land navigation syste s mintroducei d an d examined t incorporateI . s barometric heigh gyrd an to heading s verticawhica t d hac an l horizontal vehicle trajectory constraints to enhance position accuracy and availability in urba d forestean n d environments where satellite signal e frequentlar s y blockey b d obstructions e concepTh . f sensoo t r constrain S navigatioGP t s briefli n y discussed.

Decentralized two-state Kalman filter implementeare s to obtaid n smooth sensor informatio estimato t d nan e corrections. Error model r sensosfo r inpu developee ar t o dt evaluat e effec eth f correspondin o t g constraints. Augmented least square Kalmad an s n position estimator e chosear s r constrainenfo d position determination. Field tests were carried out and height and heading constraint DGPS solutions are compared with unaided

DGPS and barometric height aided DGPS solutions. For the cases tested, it improves the positioning availability by 24 to 35% while mostly maintaining the positioning accuracy within 10 metres DRMS. Conclusion presentee sar advantaged dan disadvantaged san f so this concept are discussed.

in ACKNOWLEDGEMENTS

I would like to thank my supervisor, Dr. Gerard Lachapelle, for his unlimited

support and encouragement. He gave me a tremendous opportunity to pursue the project,

showe a dremarkabl e patienc believed ability an em o completn t yi d e taske th e Th .

financial assistance gratefullarranges i e m r dyfo acknowledged.

Richard y besKlukam t s f becomo friendha s e r s lifethorougfo on eHi s . h

knowledg Godf e o Rockies e th , , Englis researcd han h topic trule sar y appreciated havI . e

been encourage sincers hi y db e attitude towards liflife y Canadn ei M . a woulr lesfa s e db

meaningful without him.

colleaguey m I f thano l Geomaticn kal i s s Engineerin r sharingfo ggreaa t time

during my program. I will carry this memory for a long time. John Brown, Jamie

Henriksen, Sun Huangqui, Chris Varner, Shawn Weisenburger, Kirk Collins and Brad

Groat are especially acknowledged for their help.

My family members, Yoshinori, Keiko, Yukiko Hayashi and Hide Yoshimura are

thanked for their continuous support from Japan. I would like to acknowledge Nahoko

Iguchi for her dedication and generous support. She is also a talented research assistant helpeo witwh e dm h testing.

IV DEDICATION

dedicateI this parents,thesismy to Yoshinori andKeiko

and

whatever brought me here. TABLE OF CONTENTS

APPROVAL PAGE...... ii ABSTRACT...... in ACKNOWLEDGEMENTS...... ^ DEDICATION...... ^ TABL CONTENTF EO S ...... i .v LIST OF TABLES ...... ix LIST OF FIGURES...... NOTATION...... xix

CHAPTER ONE: INTRODUCTION...... 1 1.1 Statement of Problem...... 2 1.2 Literature Review...... 4 1.3 System Requirements...... 7 1.4 Objectives...... 10

CHAPTER TWO: SYSTEM DESIGN...... 14 1 2. System Structure...... 4 1 . 2.2 Hardware Components...... 16 3 2. System Software...... 8 1 .

CHAPTER THREE: SENSOR DATA ACQUISITION PROCEDURE...... 22 3.1 Overvie f Sensowo r Technology...... 23 3.2 Description of Selected Sensors...... 36 3.2.1 Barometric Pressure Transducer...... 36 3.2.2 Fiber Optic Gyro...... 40 3 3. Sensor Error Models ...... 48 3.3.1 Barometric Height Error Model ...... 48 3.3.2 Gyro Heading Rate Error Model...... 0 .5 3.3.3 Sensor Heading Error Model...... 52

VI 3.3.4 Cross-Track Position Error Model...... 2 .5

CHAPTER FOUR: SENSOR CONSTRAINT POSITIONING THEORY...... 4 .5 4.1 Concept of Sensor Constraint Positioning...... 54 4.2 Mathematical Models...... 54 3 4. Augmented Least Squares Estimator...... 6 .5

CHAPTER FIVE: KALMAN FILTERS...... 64 5.1 KalmanFilter Algorithm...... 64 5.2 Sensor Filters...... 67 3 5. Kalman Position Estimator with Sensor Constraint ...... 75

CHAPTER SIX: SOFTWARE AND IMPLEMENTATION CONSIDERATIONS ...... 81 1 6. Overview...... 1 .8 6.2 Sensor Constraint Positioning Module...... 83 6.3 Miscellaneous Considerations...... 88 6.3.1 Position Estimator Breakdown Problem...... 88 6.3.2 Operational Considerations ...... 8 .8 6.3.3 Real-Time Implementation...... 9 .8 6.3.4 Optimal Estimator Configuration...... 9 8 .

CHAPTER SEVEN: SYSTEM TESTING AND RESULTS...... 92 7.1 Urban Environment Simulation...... 93 7.1.1 Route Description and Reference Trajectory ...... 93 7.1.2 Virtual Wall Concept...... 7 .9 7.1.3 Simulation Results...... 100 7.1.3.1 Cross-Track Cutoff Angle of 30 Degrees...... 103 7.1.3.2 Cross-Track Cutoff Angle of 45 Degrees...... 118 7.1.3.3 Cross-Track Cutoff AnglDegrees...... 0 6 f eo 3 13 . 7.2 Downtown Calgary Field Test...... 149 7.2.1 Objective Strategied san s ...... 9 14 . 7.2.2 Route Description...... 150

vii 7.2.3 Test Results...... 152 7.2.3.1 Unaide Results...... S dGP 2 15 . 7.2.3.2 Sensor Constrain Results...... S GP t 4 15 .

CHAPTER EIGHT: CONCLUSIONS AND RECOMMENDATIONS ...... 161 8.1 Conclusions...... 161 2 8. Recommendations...... 3 16 . REFERENCES...... 6 16 .

vin LIS TABLEF TO S

1.1 Single Point GPS Error Budgets...... 9 3.1 Relative Merits of Gyros from (Geieretal. 1993, Andrew 1994)...... 27 3.2 Viatran Mode Produc6 24 l t Specifications from (Viatran 1996)...... 37 3.3 Andrew AUTOGYRO™ Produce Specifications from (Andrew 1994)...... 41 1 7. Satellite Coverag DOPd ean , Springbank, Jun , 1996...... 9e29 4 2 7. Position Estimate Difference between SEMIKIN d C™an 3NAV ™ Solutions, Springbank, June29, 1996...... 95 7.3 Parameters Used in Error Models...... 96 4 7. Parameters Use Kalman di n Position Estimator ...... 96 5 7. Parameters Use n Kalmai d n Barometer Measuremen d Correctioan t n Filters...... 97 7.6 Parameters Used in Kalman Gyro Measurement, Correction and Heading Filters...... 97 7.7 Threshold Values for Acceptable GPS Estimate...... 102 7.8 Position Estimate Difference Between Reference Trajector Unaideand y d Least Squares Solutions, Springbank, June 29, 1996. (30° Cross-Track Cutoff Angle)...... 5 10 . 9 7. Position Estimate Difference Between Reference Trajector d Heighan y t Constraint Least Squares Solutions, Springbank, Jun , 1996e29 . (30° Cross-Track Cutoff Angle)...... 108 7.10 Position Estimate Difference Between Reference Trajector d Heighan y t and Heading Constraint Least Squares Solutions, Springbank, Jun, 29 e 1996. (30° Cross-Track Cutoff Angle)...... Ill 7.11 Position Estimate Difference Between Reference Trajectory and Height and Heading Constraint Kalman Filter Solutions, Springbank, Jun, 29 e 1996. (30° Cross-Track Cutoff Angle)...... 113

IX 7.12 Position Estimate Difference Between Reference Trajector Unaided an y d Least Squares Solutions, Springbank, Jun , 1996e29 . (45° Cross-Track Cutoff Angle)...... 118 7.13 Position Estimate Difference Between Reference Trajector Heighd an y t Constraint Least Squares Solutions, Springbank, Jun , 1996e29 . (45° Cross-Track Cutoff Angle)...... 3 12 . 7.14 Position Estimate Difference Between Reference Trajector d Heighan y t and Heading Constraint Least Squares Solutions, Springbank, June 29, 1996. (45° Cross-Track Cutoff Angle)...... 126 7.15 Position Estimate Difference Between Reference Trajectory and Height and Heading Constraint Kalman Filter Solutions, Springbank, June 29, 1996. (45° Cross-Track Cutoff Angle)...... 8 12 . 7.16 Position Estimate Availability, Springbank, June 29, 1996. (45° Cross-Track Cutoff Angle)...... 8 12 . 7.17 Position Estimate Difference Between Reference Trajectory and Unaided Least Squares Solutions, Springbank, June 29, 1996. (60° Cross-Track Cutoff Angle)...... 134 7.18 Position Estimate Difference Between Reference Trajector d Heighan y t Constraint Least Squares Solutions, Springbank, Jun , 1996e29 . (60° Cross-Track Cutoff Angle)...... 138 7.19 Position Estimate Difference Between Reference Trajector d Heighan y t and Heading Constraint Least Squares Solutions, Springbank, Jun, 29 e 1996. (60° Cross-Track Cutoff Angle)...... 145 7.20 Position Estimate Difference Between Reference Trajectory and Height and Heading Constraint Kalman Filter Solutions, Springbank, Jun, 29 e 1996. (60° Cross-Track Cutoff Angle)...... 148 7.21 Position Estimate Availability, Springbank, Jun , 1996e29 . (60° Cross-Track Cutoff Angle)...... 148 7.22 GPS Range Error Detection Thresholds, Downtown Calgary, August 17, 1996. (Height and Heading Constraint Least Squares)...... 156 7.23 GPS Range Error Detection Thresholds, Downtown Calgary, August 17, 1996. (Heigh Headind an t g Constraint Kalman Filter)...... 8 15 . 7.24 Position Estimate Availability, Downtown Calgary, August 17, 1996...... 159

XI LIST OF FIGURES

1.1 Trimble Placer™ GPS/DR System from (Geier et al. 1993)...... 5 1.2 Architectural Design of the AVLIN 2000™ Prototype System from (Harris 1989)...... 6 1.3 PortaNav Map-Aided GPS Navigation System from (Bullock 1995)...... 7 1.4 Weak Satellite Geometry. Three GPS Satellites are Aligned As Shown By Solie Th d Line...... 1 1 . 2.1 System Structur Sensof eo r Constrain NavigatioS GP t n System. SM = Carrier Phase Range Smoothing Algorithm, KF = Kalman Filter andL SLeas= t Squares...... 4 1 . 2.2 Hardware Configuratio Sensof no r Constrain NavigatioS GP t n System. (From top left to right) Viatran Model 246 Barometric Altimeter, Andrew AUTOGYRO™ Fiber Optic Gyro, NovAtel GPS Antenna, (centre) IBM- Compatible Laptop Computer Installed with NovAtel GPSCard™ 951R and AdvantechPCL-71 Board...... C 1DA 6 1 . 2.3 Typical Hardware Installation. (Top) Laptop Computer and Barometer in e Rearth , (centre VD2 1 ) C Power Suppl DC-Ad an y C Converted an r (bottom) AUTOGYRO™ Place Centre th n di e Console...... 20 3.1 Odometer...... 22 2 3. Differential Odometer Geometry from (Harris 1989)...... 24 3 3. KVHC100 Compass Engine from (KVH 1994)...... 6 .2 3.4 Spinning Rate Gyro from (Alan 1993)...... 28 3.5 Murata GYRO STAR™ Piezoelectric Vibratory Rate Gyro from (Nakamura 1990)...... 8 .2 3.6 Murata GYROSTAR™ Output Detection Theory from (Nakamura 1990)...... 29 3.7 Path Length Difference Generated by the Sagnac Effect from (Liu& Adams 1990)...... 30 3.8 The Spring-Supported Mass Accelerometer...... 33 9 3. Viatran Mode Electri6 24 l c Barometer from (Viatran 1996)...... 6 .3

xii 3.10 The US Standard Atmosphere Pressure-To-Height Conversion Chart from (Lutgens & Tarbuck 1982)...... 38 3.11 Viatran Mode Electri6 24 l c Barometer Measurement Erro a Typica n i r l Static Environment...... 9 .3 3.12 Viatran Mode Electri6 24 l c Barometer Measurement Erro Typicaa n i r l Dynamic Environment...... 40 3.13 Andrew AUTOGYRO™ from (Alien et al. 1994)...... 42 3.14 Andrew AUTOGYRO™ Configuration from (Bennet Eng& t e 1994)...... 43 3.15 Andrew AUTOGYRO™ Output Bias vs. Unit Temperature...... 44 3.16 Andrew AUTOGYRO™ Scale Factor vs. Unit Temperature...... 45 3.17 Sensor Heading Constraint Solutions Without Corrected Scale Factor. Default Scale Factor (0.00499 [deg/bit]) Used. Solid Line Indicates Reference Trajectory...... 47 3.18 Sensor Heading Constraint Solutions With Corrected Scale Factor. Solid Line Indicates Reference Trajectory...... 47 3.19 Cross-Track Position Displacement Induce Sensoy db r Heading Error...... 3 .5 4.1 Heading Computation...... 56 1 6. Flowchart of EC3...... 2 .8 2 6. Flowchar Sensof o t r Constraint Least Squares Position Estimator...... 4 .8 6.3 Flowchart of Sensor Constraint Kalman Position Estimator...... 85 6.4 Position Error of Optimal Estimator with Poor Initial Heading ...... 90 6.5 Position Erro Optimaf ro l Estimator with Good Initial Heading...... 91 7.1 Test Rout r Simulationefo ...... 93 2 7. Visible Satellites, Springbank, Jun , 1996...... 9e29 4 3 7. Virtual Wall Concept...... 8 .9 7.4 Visible Satellites with Virtual Wall Concept, Springbank, June 29, 1996...... 101 7.5 Visible Satellites, Springbank, June 29, 1996. (30° Cross-Track Cutoff Angle)...... 2 10 .

xni 7.6 DOPs, Springbank, June 29, 1996. (30° Cross-Track Cutoff Angle, Unaided Least Squares)...... 103 7.7 2D Position, Springbank, June 29, 1996. (30° Cross-Track Cutoff Angle, Unaided Least Squares)...... 4 10 . 7.8 2D Position, Section A, Springbank, June 29, 1996. (30° Cross-Track Cutoff Angle, Unaided Least Squares)...... 4 10 . 7.9 Unaided Least Squares Position Errors, Springbank, June 29, 1996. (30° Cross-Track Cutoff Angle)...... 105 7.10 DOPs, Springbank, Jun , 1996e29 . (30° Cross-Track Cutoff Angle, Height Constraint Least Squares)...... 7 10 . Position7.1D 2 1 , Springbank, Jun , 1996e29 . (30° Cross-Track Cutoff Angle, Height Constraint Least Squares)...... 9 10 . Position7.1D 2 2 , Section A, Springbank, Jun , 1996e29 . (30° Cross-Track Cutoff Angle, Height Constraint Least Squares) ...... 109 7.13 Height Constraint Least Squares Position Errors, Springbank, Jun, 29 e 1996. (30° Cross-Track Cutoff Angle)...... 110 7.14 DOPs, Springbank, Jun , 1996e29 . (30° Cross-Track Cutoff Angle, Heigh d Headinan t g Constraint Least Squares and Kalman Filter)...... 112 7.15 2D Position, Springbank, June 29, 1996. (30° Cross-Track Cutoff Angle, Heigh d Headinan t g Constraint Least Squares)...... 114 7.16 2D Position, Section A, Springbank, June 29, 1996. (30° Cross-Track Cutoff Angle, Height and Heading Constraint Least Squares)...... 114 7.17 Heigh Headind an t g Constraint Least Squares Position Errors, Springbank, Jun , 1996e29 . (30° Cross-Track Cutoff Angle)...... 5 11 .

XIV 7.18 2D Position, Springbank, June 29, 1996. (30° Cross-Track Cutoff Angle, Height and Heading Constraint Kalman Filter)...... 116 Position7.1D 2 9 , Section A, Springbank, Jun , 1996e29 . (30° Cross-Track Cutoff Angle, Height and Heading Constraint Kalman Filter)...... 116 7.20 Heigh Headind an t g Constraint Kalman Filter Position Errors, Springbank, Jun , 1996e29 . (30° Cross-Track Cutoff Angle)...... 7 11 . 7.21 Visible Satellites, Springbank, Jun , 1996e29 . (45° Cross-Track Cutoff Angle)...... 119 7.22 DOPs, Springbank, Jun , 1996e29 . (45° Cross-Track Cutoff Angle, Unaided Least Squares)...... 119 7.23 2D Position, Springbank, June 29, 1996. (45° Cross-Track Cutoff Angle, Unaided Least Squares)...... 0 12 . 7.24 2D Position, Section A, Springbank, June 29, 1996. (45° Cross-Track Cutoff Angle, Unaided Least Squares)...... 120 7.25 Unaided Least Squares Position Errors, Springbank, Jun , 1996e29 . (45° Cross-Track Cutoff Angle)...... 121 7.26 DOPs, Springbank, June 29, 1996. (45° Cross-Track Cutoff Angle, Height Constraint Least Squares) ...... 123 PositionD 7.22 7 , Springbank, Jun , 1996e29 . (45° Cross-Track Cutoff Angle, Height Constraint Least Squares) ...... 4 12 . 7.28 2D Position, Section A, Springbank, June 29, 1996. (45° Cross-Track Cutoff Angle, Height Constraint Least Squares) ...... 124 7.29 Height Constraint Least Squares Position Errors, Springbank, June 29, 1996. (45° Cross-Track Cutoff Angle) ...... 5 12 . 7.30 DOPs, Springbank, Jun , 1996e29 . (45° Cross-Track Cutoff Angle, Height and Heading Constraint Least Square Kalmad san n Filter) ...... 7 12 .

XV 7.31 2D Position, Springbank, June 29, 1996. (45° Cross-Track Cutoff Angle, Height and Heading Constraint Least Squares)...... 129 Position7.3D 2 2 , Section A, Springbank, Jun , 1996e29 . (45° Cross-Track Cutoff Angle, Heigh d Headinan t g Constraint Least Squares)...... 129 7.33 Heigh Headind an t g Constraint Least Squares Position Errors, Springbank, June 29, 1996. (45° Cross-Track Cutoff Angle)...... 130 7.34 2D Position, Springbank, June 29, 1996. (45° Cross-Track Cutoff Angle, Heigh Headind an t g Constraint Kalman Filter)...... 131 PositionD 7.32 5 , Section A, Springbank, June , 199629 . (45° Cross-Track Cutoff Angle, Height and Heading Constraint Kalman Filter)...... 131 7.36 Heigh Headind an t g Constraint Kalman Filter Position Errors, Springbank, Jun , 1996e29 . (45° Cross-Track Cutoff Angle)...... 2 13 . 7.37 Visible Satellites, Springbank, Jun , 1996e29 . (60° Cross-Track Cutoff Angle)...... 133 7.38 DOPs, Springbank, Jun , 1996e29 . (60° Cross-Track Cutoff Angle, Unaided Least Squares)...... 4 13 . 7.39 2D Position, Springbank, June 29, 1996. (60° Cross-Track Cutoff Angle, Unaided Least Squares)...... 5 13 . Position7.4D 2 0 , Section A, Springbank, Jun , 1996e29 . (60° Cross-Track Cutoff Angle, Unaided Least Squares)...... 5 13 . 7.41 Unaided Least Squares Position Errors, Springbank, Jun , 1996e29 . (60° Cross-Track Cutoff Angle)...... 6 13 . 7.42 DOPs, Springbank, Jun , 1996e29 . (60° Cross-Track Cutoff Angle, Height Constraint Least Squares) ...... 138

XVI PositionD 7.42 3 , Springbank, Jun , 1996e29 . (60° Cross-Track Cutoff Angle, Height Constraint Least Squares) ...... 9 13 . PositionD 7.42 4 , Section A, Springbank, Jun , 1996e29 . (60° Cross-Track Cutoff Angle, Height Constraint Least Squares) ...... 9 13 . 7.45 Height Constraint Least Squares Position Errors, Springbank, June 29, 1996. (60° Cross-Track Cutoff Angle)...... 140 7.46 False Heading Constraint...... 1 14 . 7.47 DOPs, Springbank, June 29, 1996. (60° Cross-Track Cutoff Angle, Height and Heading Constraint Least Squares and Kalman Filter) ...... 142 PositionD 7.42 8 , Springbank, Jun , 1996e29 . (60° Cross-Track Cutoff Angle, Heigh d Headinan t g Constraint Least Squares)...... 143 PositionD 7.42 9 , Section A, Springbank, Jun , 1996e29 . (60° Cross-Track Cutoff Angle, Height and Heading Constraint Least Squares)...... 3 14 . 7.50 Heigh Headind an t g Constraint Least Squares Position Errors, Springbank, Jun , 1996e29 . (60° Cross-Track Cutoff Angle)...... 4 14 . 7.51 2D Position, Springbank, June 29, 1996. (60° Cross-Track Cutoff Angle, Heigh Headind an t g Constraint Kalman Filter)...... 6 14 . 7.52 2D Position, Section A, Springbank, June 29, 1996. (60° Cross-Track Cutoff Angle, Height and Heading Constraint Kalman Filter)...... 146 7.53 Heigh Headind an t g Constraint Kalman Filter Position Errors, Springbank, Jun , 1996e29 . (60° Cross-Track Cutoff Angle)...... 7 14 . 7.54 Test Route, Downtown Calgary, August 17, 1996...... 151 7.55 Visible Satellites, Downtown Calgary, Augus , 1996...... 17 t 2 15 . 7.56 DOPs, Downtown Calgary, August 17, 1996. (Unaided Least Squares)...... 153

XVll PositionD 7.52 7 , Downtown Calgary, Augus , 199617 t . (Unaided Least Squares) ...... 154 7.58 DOPs, Downtown Calgary, Augus , 199617 t . (Height and Heading Constraint Least Squares and Kalman Filter) ...... 155 PositionD 7.52 9 , Downtown Calgary, Augus , 199617 t . (Heigh Headind an t g Constraint Least Squares)...... 6 15 . 7.60 2D Position, Downtown Calgary, August 17, 1996. (Height and Heading Constraint Kalman Filter) ...... 158 7.61 Vertical Position, Downtown Calgary, August 17, 1996...... 160

XVlll NOTATION

Symbols: A amplitud signaf eo l (chapter one) A design matrix (chapter four) c spee ligh f vacuuda o n i t m C, covariance matrix of measurements cdt receiver clock offset error cdi receiver clock drift error

dCT cross-track distanc virtuao et l wall

df distance measure t timda elefy tb t wheel odometer df distance measured at time f. by right wheel odometer

dion ionospheric delay

dtrop tropospheric delay dp orbital error dt satellite clock error dT receiver clock error d§ distance between two epochs in latitude dk distance between two epochs in longitude h height

hb barometric height measurement Hj. design matrix which gives noiseless connection between the

measuremen statd an te vecto t tra k k adaptation gain constant

Kt Kalman filter gain at tk \ observation vector p range measurement p(t) PRN cod) e -1 (eithe r o 1 r+

XIX Pk smoothed range measurement at tk

Pk error covariance matrix associated with optimal estimate at tk

Pjt" error covariance matrix associated with projected estimat t tea k q spectral density

qcdt spectral density of receiver clock offset error

qcdi spectral densit receivef yo r clock drift error

qh spectral density of height position error q^ spectral densit heighf yo t rate error

q^ spectral density of longitude position error q^ spectral density of longitude rate error q^ spectral density of latitude position error

q^ spectral densit latitudf yo e rate error

Q process noise covariance

Q A adapted process noise covariance

Q k variance of process noise r position vector of a satellite R position vecto alanf ro d vehicle

RL radius of the left wheel's curvilinear path

RR radiurighe th f t so wheel' s curvilinear path

Rk varianc measuremenf eo t erro t tkra v velocity

\k measurement error assume white b o edt wit knowha n covariance structure W weight ° w misclosure vector

w t white noise with known covariance structure

XX w(/) random forcing function w cdt0 ( white noise inpu receivef o t r clock offset error wcdi 0 ( white noise inpu receivef o t r clock drift error wh(t) white noise inpu heighf o t t position error w^(0 white noise input of height rate error wx(0 white noise inpu longitudf o t e position error Wj_(0 white noise input of longitude rate error w^(t) white noise inpu latitudf o t e position error H^ (t) white noise input of latitude rate error

solution vector a priori position estimate vector

\k+l process state vector at time tk+\

\k updated estimate t ka x~ projected estimate at tk x(7) system state vector zk measurement vector at tk a.CT cross-track cutoff angle a. azimuth heading of vehicle's forward direction at epoch /, a k cutoff angle of a satellite P time constant for the process

$cdt time correlation constant of receiver clock offset estimate f>h time correlation constant of height estimate f>k azimuth of a satellite (chapter seven) P^ time correlation constant of longitude estimate P.J, time correlation constant of latitude estimate y k relative azimuth of a satellite with respect to the vehicle's heading

xxi 5 least squares adjustments to parameters d(t) Dirac delta function 8/i height position error dh height rate error d'k longitude position error 6A, longitude rate error 6(j) latitude position error 6(j> latitude rate error bd mean distance traveled over a data interval AZ, path length difference A

£ b (*k+\) barometric height error at time tk+l efc barometric height offset (residual) error ib linear barometric height drift rate s cr (*/fc+i) cross-track position error at tk+l e,('*+i) gyro error at tk+} eg gyro heading rate offset (residual) error eg gyro drift error

6GP5 GPS cross-track position estimate error e p receiver noise

e (*k\) heading error at t + k+l 8 e@ initial heading error

Qm relative multipath phase 0 vehicle heading X wavelength

Kk longitude positio t tna k

XXll K ratio of circumference of circle to its diameter

P geometric range

latitude positio t tna k (chapter six)

matrix relating \k and xAr+1 in absence of a forcing function (chapter five) o rotation

ok carrier phase measurement 1 variance

2 ab barometric height error variance a2 gyro heading rate error variance 8 o2 GPS range error variance P

2 o® gyro heading error variance

2 a Sdt satellite clock error variance

2 oSiono ionospheric delay variance

2 oStrop tropospheric delay variance

2 a 8p orbital error variance

a2 measurement noise variance o

(0 gyroscope heading change

C00 carrier frequency plus Doppler shift a angular velocity

Operators: AT matrix transpose A"1 matrix inverse a| length of the vector a a*b dot product of vectors a and b

XXlll a xb cross produc vectorf b o t d an sa

partial derivative of the function/ with respect to x dx

Acronyms: 2D dimensionao tw l space 3D three dimensional space AS Anti-Spoofmg AVL Automatic Vehicle Location C/A code Coarse/Acquisition code (1.023 MHz) DOD US Department of Defense DGPS Differential GPS DR Dead Reckoning DRMS Distance Root Mean Square ECEF Earth-Centre Earth-Fixed EDOP East Dilution of Precision FOG Fiber Optic Gyro FM Frequency Modulation GDOP Geometric Dilution Of Precision GPS Global Positioning System HDOP Horizontal Dilution Of Precision IVHS Intelligent Vehicle Highway System LI LI carrier (1575.42 MHz) L2 L2 carrier (1227.6 MHz) MS-DOS Microsoft Disk Operating System MSPE Mean Square Positional Error NAVSTAR Navigation Satellite Timing and Ranging NDOP North Dilutio Precisiof no n OEM Original Equipment Manufacturer

XXIV P code Precision code (10.23 MHz) PC Personal Computer PCMCIA Personal Computer Memory Card International Association PDOP Positional Dilutio Precisiof nO n PRN Pseudo Random Noise RAM Random Access Memory RLG Ring Laser Gyro S RM Root Mean Square K RT Real-Time Kinematic A S Selective Availability SV Space Vehicle TDOP Time Dilutio Precisiof nO n UHF Ultra High Frequency VDOP Vertical Dilutio Precisiof nO n 4 8 S WorlWG d Geodetic Syste mf 198o 4 Y code Encrypte coddP e

XXV CHAPTER ONE

INTRODUCTION

The field of land vehicle navigation is growing rapidly with the maturation of the

Global Positioning System (GPS) and the advancement of positioning-related technologies

in recent years. GPS is a satellite based radionavigation system developed by the U.S.

Departmen f Defenso t e (Spilker 1980) t includeI . constellatioa s satellite4 2 x f no si n si

orbital planes, which are strategically arranged so that a minimum of six satellites are

visibl usero et s anywher worle l times al th satellite t n dea i Th . e altitud approximatels ei y

19,652 km (Spilker 1980). One requirement of GPS positioning is that one must be able to

observe these multiple satellite signals simultaneously without mutual interferencee Th . receiveS t leasGP a f to r fout usese rs a satellite range measurement calculato st receiveea r

position with respect to a earth-centre earth-fixed (ECEF) coordinate system. The 1.6GHz signalS GP essentialle sar y line-of-sight.

Vehicle navigation and tracking is a topic of great interest today due to the large

potential market for both consumer and business vehicles. All of the major automobile

manufacturers have been developing in-vehicle navigation systems. They guide travelers

and motorist desireo st d destinations, help them find correct road highwayd san givd san e

them various data such as current location, distance to the destination and estimated

arrival time. Recent Japanese car navigation units are capable of receiving traffic

informatio wavM F beaconr eo a nvi thed suggesn san yca "lease th t t clogged" route th n ei

real-time. Some have bi-directional communication functions to send back the location of 2 a vehicl a contro o t e l statio r advancefo n d traffic controls (Sakata 1996). Another extensive market is the tracking of commercial vehicles. In the United States alone, the total numbe f commerciao r l vehicles exceed 7 millio1 s n (Brown 1992) w cosLo t. electronics are already permitting the introduction of navigation systems into emergency vehicles (fire engines, polices cars, ambulances) and into truck fleets. Other vehicle tracking applications include deliver couried yan r services, armore r servicesdca , utility companies, private security companies, stolen cars, high value goods delivery, automobile towing service, dispatching taxi cabs, shuttle vans and so on (Brown 1992).

1.1 Statemen Problef to m

The major problem of GPS land navigation is insufficient satellite signal observations in heavily populated and forested areas due to shadowing (signal blockage).

Shadowing occurs when tall buildings, bridges, overpasses, highways, tunnels and trees cover the sky partially or entirely. Since the minimum signal strength of LI C/A code is define s -16a d 0 dBW t stronsignalS no GP e , gar s enoug penetrato ht e these structures

(Spilker 1980). Becaus positioninS eGP g require t leassa t four satellite signal computo st e a 3D position estimate and a receiver clock offset relative to GPS time, these obstructions severely reduce the position availability in such areas. Lachapelle et al. (1994) also suggest limited performance of GPS under tree branches and leaves where GPS UHF signals are largely attenuated sucn I . h environments coveragS GP ,longe o n y s ei ma r e optimaon d an l frequently encounter a GPS position outage period. Studies have shown that in inner city downtown locations with buildings greater tha storiesn nte , four satellites wil visible b l e 3 e timeth les f , o swhicr fro thafa % ms h50 ni acceptable coverag r lanfo e d navigation

applications (Sushko 1993).

Another outstanding proble urbamn i foreste d nan d e presencareath n s a i s f eo

unpredictable error called multipath. Multipath is defined as the error caused by the

reflection, receivere refractionth o t y ,bouncinr o resultinwa , signas e it e th th n f go lo n g i

same signal arrivin receivee th t g a mor y rb e thapate non h (Navtech Seminars Inc. 1996).

Multipath provides a false position estimate to the user. Braasch (1996) gives the

mathematical mode multipath-contaminatea f o l signaS dGP l (direct signal plus multipath

rays) as

~-~a

1=1

where

A amplitude of direct signal [W],

/?(/) PRN code (eithe -1)r o ,1 r+

o 0 carrier frequency plus Doppler shift [Hz],

a, amplitude of the /th multipath component relative to the direct path

[W],

5. time delay of the ith multipath component relative to the direct path

(which mus negative b t e when given sign conventio useds ni ) [s], 4

0m/ e ftphashth f multipato e h component relativ e directh o et path

[rad],

n number of multipath signals.

Several attempts have been mad o modet e e signath l l structur e multipatth f o e o t h

minimize its error (Van Nee & Siereveld 1994). Multipath range error is typically in the

order of 0-50 metres depending on the environment, antenna type, receiver type and user

dynamics. Multipath error f ovemetre0 o s 10 r s have been reported near skyscrapers

(Braasch 1996) urban I .foreste d nan d environment multipate th , severely hma y degrade positionine th g accuracy. Wit hredundancy o littln r eo positioa , n estimat becomy ma e e

highly vulnerabl contaminateo et observationsS dGP .

1.2 Literature Review

becoms ha t I e common inexpensivs a , reliabld ean e positioning sensor beine ar s g

introduced (Nakamura 1990, Phillips 1993, Alie t alne . 1994, Martinell Iked& i a 1995)o t ,

combin witS hGP e other positioning device o enhanct s e navigation capabilit urban yi n

canyons. Most commercial GPS land navigation systems are capable of utilizing distance

sensors (e.g. odometer) and heading rate sensors to enable GPS-independent positioning,

called dead reckoning (DR), in the absence of sufficient GPS signals. Dead reckoning uses

headin distancd gan e sensor measuro st displacemene eth t vectors whic thee har n usea n di

recursive manner to determine the current vehicle position. Kao (1991) examine possible dth systemR eD combinatiod obtaio an st S nGP f no superior performance e suggesteH . combinatioe dth gyroa f no , magnetic compasd an s odometer in the DR system. Gyro measurements are used to eliminate the short term magnetic anomalie compasn si s heading measurements. Geie t ale r. (1993) too ksimplea r approach as shown in Figure 1.1. They integrated an odometer and gyro into the Trimble

Placer™ GPS/DR system. This DR sensor configuration is used in many DR and GPS/DR systems systee Th . m use filteree sth d position solutions which provid leveea f multipato l h rejection.

Analog Digital Input inputs Odom

Alarm DR GPS _Y

Back-up

NMEA RTCM or Configuration TANS Pkts RS-232 ports

Figure 1.1. Trimble Placer™ GPS/DR System from (Geier et al. 1993) NU-METRICS Odometers Vol2 1 t Battery

Figure 1.2. Architectural Desig AVLIe th f no N 2000™ Prototype System from (Harris 1989)

Harris (1989) employed the differential odometry theory with a map database sees a Figurel.2 n i S modul GP d eacs ean A . h odometer only measures distances traveled

requiree wheele ar b yon o r differentiatw dfo , l odometry. This technique eliminatee sth

need for rotation sensors since differential odometry can provide heading change

information matchin p methodR D Ma . d usee gan sar updato dt e positions i wheS nGP

not available. Ishikawa et al. (1995) utilized map matching technology in addition to a

distance sensor, fibre opti receiveS cGP gyr d o improvt roan e position accuracy. This

system employed another technique to obtain a smooth trajectory. When a fibre optic gyro

readin belos gi threshole wth d value vehicle th ,straigha n assumes ei o e tb linee o dt Th .

system then solve regressioa s n line equatio o smootnt vehicle hth e trajectory. Bullock Magnetic mount Active matrix GPS antenna colour LCD Etak digital road map storen do hard drive

Track ball pointing device receiveS GP r with PCMCIA card interface (plugge) din VersC NE a notebook computer

Figure 1.3. PortaNav Map-Aide NavigatioS dGP n System from (Bullock 1995)

(1995) propose portablda e land navigation system which doe t requirsno odometen ea r ro gyro as shown in Figure 1.3. He selected the Etak digital road maps and a Trimble

MobileGPS, a PCMCIA card-type GPS receiver with six parallel channels and eight track satellites d createan , e PortaNath d p aideS navigatioma vGP d n system e systeTh . m features an 8-state Kalman position filter, various route finding algorithms and map aiding logic.

1.3 System Requirements

The requirement navigatioe th f so n system proposed ) portabilityherei(1 e nar ) (2 , acceptabl costew accuraclo .) Requiremen(3 d yprimarf an o s i ) y(1 t importance th o t e edu nature of the research project. A dedicated test vehicle would be ideal since certain sensors, such as an odometer, could be installed permanently. A vehicle equipped with anti-lock brake havy esma odometer(s monitoo )t rotatioe wheelse th r th f no . However, 8 such a vehicle still requires the installation of an odometer output reader. Since most testin s donwa g e wit a hrenta l vehicle, modifyinn optiona t e no vehicl.th gs wa e

Requirement (2) depends on the system configuration, particularly that of GPS. Table 1.1

shows the error budgets of single point GPS positioning.

In single point mode, a GPS receiver is subject to errors from the atmosphere, multipath, satellite orbits, satellite clocks and receiver noise (Bullock 1995). However, it is known that the spatial correlation of satellite orbit and clock errors (includes selective

availability atmospherid an ) c error reasonable sar y hig r shorhfo t baseline differentian i s l mode. Differential GPS takes advantage of this by placing a GPS monitor station at a

control point. Given the accurate coordinate of the control point, the monitor receiver can

comput rangS GP eea error mostly induce spatially db y correlated errors rangee Th . error is then sent to the remote GPS receiver as a range correction. This technique reduces the

GPS positioning error dramatically, from 100 m to several metres for a code solution. Table 1.1. Single Point GPS Error Budgets from (Lachapelle 1995, Braasch 1996, Bullock 1995) Error source Typica codA C/ el range error Tropospheric delay 2-30m Ionospheric delay 2-50m Satellite orbit errors 5- 10m Satellite clock errors 10m Selective availability (SA) 5-80m Measurement noise 0.1 -3m Multipath 0-50m

For land navigation applications, it is desirable that the user be able to determine the location of a vehicle both on the highway and in dense downtown regions. US

Departmen f Transportatioo t n define e minimuth s m accuracy requiremene th r fo t automatic vehicle location (AVL) applications as 30m 2DRMS (US Department of

Transportation and Defense 1990). For the intelligent vehicle highway system (IVHS), required accuracie betweee metre7 sar d urbaan n si n1 n area 10-3d san 0 metre ruran si l

areas (Chadwick 1994). For this project, the accuracy requirement is set to 10 m DRMS whic typicaa s hi l widt two-lana f ho e roadconsequencea s A . , differentia modS GP s le i

chosen to fulfill this requirement. The challenge lies in maintaining positioning accuracy while improving the position availability under the condition that the incoming GPS signal

is insufficient and contaminated, satellite geometry is weak or even singular.

Requiremen t importan no researce s i th ) r (3 tfo t h projec t absolutelbu t y criticar fo l

commercial applications. The proposed system is flexible in that the system can accept 10 input from sensor f diverso s e quality without redesignin e entirth g e algorithml Al .

hardware components used in this system may be easily obtained. The current system

supports the NovAtel GPSCard™ as the GPS receiver but should work with any GPS

receiver which generate datw ra a tim S d includinesan GP g pseudorang carried ean r phase

(for smoothing) observations.

1.4 Objectives

researce Th h project presente thin di s thesi primarils si y aime t overcominda g poor

positioning performance in urban areas by introducing constraints on a vehicle's vertical

and horizontal trajectory. The author initially tested a barometric height aided GPS system d stilan l encountered poor horizontal geometr urban yi n areas which resulte poon i d r

horizontal position estimates e pooTh .r performanc e s faccauseth wa te y b thatd ,

ironically, height aided GPS navigation was capable of three-satellite positioning and three

satellites formed weak geometry more often than foure desirW . widela e y distributed

satellite constellation to ensure that the solution is not weak in any given direction.

Consider the satellite constellation projected in the horizontal plane. If satellites are

located on a line, the horizontal position accuracy of the direction perpendicular to the

solid line shown in Figure 1.4 suffers greatly. This geometric weakness may be manifested

as inaccurate position estimates as well as an unexpectedly high Horizontal Dilution of

Precision (HDOP). 11

270

Figure 1.4. Weak Satellite Geometry. Three GPS Satellites are Aligned As Shown By The Solid Line

urban I n environments, weak satellite geometr frequentls yi y observe termn di f so

e cross-tracth k satellite geometry a directio, n perpendicula e vehiclth o t re trajectory.

Consider driving a vehicle in a downtown area. There are more obstructions on each side vehicle th f o e (e.g. multi-storey buildings) tha behinr fronn o i f o . tThes dit e obstructions

block incoming GPS signals from the receiver and cause inferior cross-track satellite

geometry. The poor satellite geometry, combined with the limited signal availability,

increases the dilution of precision (DOP) in the cross-track direction by one to numerous

orders of magnitude and causes poor positioning accuracy. Therefore, there is a need to

enhanc satellite eth e geometr orden yi improvo rt cross-trace eth k position accuracy.

In this project, the author is proposing an inexpensive urban navigation system.

Dead reckoning (DR) system relativele sar cost requirw ylo bu t distancea e sensor sucs ha

an odometer. Sinc e systeeth r thim fo se portabl b researc o t thao d s e t coulhi ha t e db 12 moved from vehicle to vehicle, a DR system could not be implemented. A new concept

developee hab o dt orden di increaso rt positioe eth n availabilit accuracd yan y withou. DR t

The concept is called sensor constraint GPS navigation. It employs a barometric pressure

transducer (barometer) and a fibre optic gyro (FOG) in addition to a GPS navigation unit.

verticae Th horizontad an l l (cross-track) position displacemen constraines i t d accordino gt

sensoe th r information alss i t oI . capabl two-satellitf eo navigatioS eGP n which increases

position availability.

As mentioned earlier, solutions in urban and forested environment are more

vulnerable to GPS range errors. Providing height and heading constraints implies that the

position estimat alss ei o "constrained" agains erroneoue th t s signal. Thus, this technology

may als usee ob reduco dt e multipath error arisine Th . g correctl o problet w ho ms yi detect

e solutioth n containin e multipatth g h error. Ther e somar e e approache o detect s t

multipath. Since the vehicle dynamics is limited, we may use this fact as an error threshold.

Another idea is to monitor the excessively large GPS range residuals.

wile W l develo lanw dne pnavigatioa n syste followine th mn i g chapters. Chapter describeo Tw overviee sth proposee th f wo d system configuration Chapten I . r Threee th ,

current sensor technolog presenteys i specificatione th d dan barometee th f so headind ran g

rate gyro, which are employed in the project, are also given. The sensor constraint

positioning algorith mdevelopes i Chapten di r Four. Various Kalman filter developee ar s d

in Chapter Five. In Chapter Six, the navigation software is described. Two field

experiments, opey testinsk nr simulationfo g d downtowan n Calgary testing, were

conducted and results are given in Chapter Seven. The least squares approach is compared 13 to the Kalman filter approach. Finally, conclusions and recommendations are presented in

Chapter Eight. 14 CHAPTEO RTW

SYSTEM DESIGN

Syste1 2. m Structure

The structure of the sensor constraint GPS navigation system is shown in Figure

2.1. Basic hardware includes a GPS receiver, barometer and heading rate gyro. Data from e GPSth , baromete ratd an er gyr"augmentede e usedth oar n i " navigation algorithm.

Differential GPS was selected to increase the positional accuracy. Thus, another GPS

receive employes i r monitoe th t da r station systee Th .adoptes mha modulae dth r concept

GPS Antenna

Barometer

Heading Rate Gyro

GPS P SM •*

Gyro correction 4 KF 1^,^ "%^ Navigation Gyro heading rate ^O"————————— », Heading Algorithm ————^ KF to KF 0 LS/KM

KF * /» Barometer height .-v6/ KF /ib " - /)b+<5r?

Figure 2.1. System Structure of Sensor Constraint GPS Navigation System. Carrie= M S r Phase Range Smoothing Algorithm Kalma= F K , n Filter Leas= an S dL t Squares 15 to maintain flexibility. It operates with GPS alone, GPS and barometer, GPS and gyro or

all three sensors.

The system utilize a decentralizes d filter approach (Abousalem 1993). This approac s i specificallh y user multi-sensofo d r systems (Abousalem 1993)e Th .

decentralized filtering algorithm is applied to smooth out the raw and noisy sensor

measurements and to estimate their errors. This approach has a clear advantage over the

conventional centralized filtee computation termth i r f o s n timd versatilityan e A . barometric pressure transducer inpu transformeis t d int barometrioa c height, corrected

and serves as a sensor height. At each epoch, the gyro sensor input is corrected and

converted int a vehiclo e heading S dat . s insufficienti GP aWhe e th n , corrupter o d geometrically weak, the sensor height and heading data are utilized to constrain the

position estimate. These data are treated as measurements that reduce the number of

necessar S observationsGP y , normall D solutione 4 numbeth ya y fouf r b o ,rfo r

independent sensor constraints. Thus, the minimum number of GPS observations

necessary for a position computation with the sensor height and heading information becomes two. It is possible to further reduce the number of required satellites by adding

another sensor information. For instance, an estimated receiver clock offset in addition to

the current system could reduce the required GPS observations to one. In addition, an

odometer, or distance sensor, could be used for DR positioning during the GPS outage

period. 16 2.2 Hardware Components

hardware Th e component designee ar s mountee b o dt vehicla n di e withouy an t modification. This feature is important because rental cars were used for the project.

Consequently e systeth , m need o maintait s n portability s showA . Figurn i n e 2.2e th , hardware system consists of a Viatran Model 246 barometric pressure transducer, an

Andrew AUTOGYRO™ digital fibre optic gyro, a NovAtel GPSCard™ 951R GPS receive d antennaan r Advantecn a , h PCL-711 12-bit data acquisition board IBMn a , - compatible laptop computer and 12 VDC power supply. Another NovAtel GPSCard™ is

Figure 2.2. Hardware Configuration of Sensor Constraint GPS Navigation System. (From top left to right) Viatran Model246 Barometric Altimeter, Andrew AUTOGYRO™ Fiber Optic Gyro, NovAte AntennaS GP l , (centre) IBM- Compatible Laptop Computer Installed with NovAtel GPSCard™ 951R and Advantech PCL-71 BoarC 1DA d 17 used at the monitor station to generate differential GPS corrections.

NovAtee Th l GPSCard Advantece th d ™an h PCL-71 cardE ID se installe1ar n di

expansioe th n IBM-compatibln slota f so e laptop computer computee Th . thes i r n placed

bace onth teske necessarseath e t b f vehicle o ty ma securt o yI t . computee eth seae th t n ro

by straps when dynamic maneuver expectede sar antennS GP mountes A .ai rooe th fn do

attaio t n maximum signal reception.

The Viatran Mode 6 baromete24 l s locatee reai r th r n o sead s s welli a t t I .

preferabl instalo t t barometea no le trune th minimizo kt n i r e unexpecteeth d pressure r flowai chango .t Thie du es baromete s specificalli r y designe o measurdt e barometric

pressure (Viatran 1996) unie Th t. sense ambienn sa t barometric pressur translated ean t si

into an output of voltage ranging from zero to five volts. The voltage output is converted

into digital for e processeorden mi b o t r d wit e computerhth e barometeTh . r voltage

output is converted into 12-bit digital data by the PCL-711 data acquisition board. A

supply voltag usee VDeb 0 provid 4 o dbetween t Cd ca an 5 e2 n1 8. powe unit e e th Th .o rt

VDC car battery powers the barometer.

The Andrew AUTOGYRO™ heading rate gyro is located in the centre console as

shown in Figure 2.3. A gyro is a device to measure the rotation rate of its axis. An

AUTOGYRO one-axia ™s i s gyro that measure headine sth g chang vehiclea f eo e Th .

gyro unit should be mounted on a flat surface in order to avoid a misalignment error. The

manufacturer suggests that the mounting surface be parallel to the road surface within

approximately 5 degrees (Andrew Corp. 1994). The gyro's minimum detectable angle is

approximately 0.005 degrees. The AUTOGYRO ™ continuously generates heading rate 18 data wit intervan ha 0.f o l1 seconds. Thi digitaa s si l fibre optic gyro (FOG than i ) t doei t s

t requirno datea a acquisition board outpue Th . t connecto AUTOGYROn a f o r e th ™s i

DB-9P, also known as the COM port, although its pin layout is not a standard one. A

special cabl therefors ei e require conneco dt computer'e gyre th th to ot s communication

(COM) port AUTOGYROe Th . ™designes i operatee b o dt d r battery2 wit1 ca he a Th .

VDC car battery is also used to power the gyro.

12 VDC car batteries were needed to power the laptop computer. With a fully-

charged generic 50 Ah 12 V DC power supply and a Compaq 386 computer, this system

operates for two hours. This was sufficient for this project since its typical operation

perio s approximateldwa houre operatioe yon Th . extendee nb timy ema d significantlf yi

the vehicle's battery, which is constantly recharged by its alternator, is also used as a

power supply.

Syste3 2. m Software

Most land navigation applications require the real-time position determination.

Although this system is intended for real-time operation, post processing was selected due complexite th o t obtaininf yo g differentia correctionS GP l real-timen si consequencea s A . ,

a data logger and position computation program were needed to operate the system. Real-

time implementation, which largely relie advancen so d wireless communications r lefs i , fo t

a future project.

datw Ne a logging softwar s writtewa er thifo ns e authorprojecth y b t. This

program, called ELGO, (1) sends appropriate commands to a GPS receiver and a data 19 acquisition boar generato dt e specific informatio desirea t na d interval ) collect(2 , S sGP

data, (3) stores asynchronous gyro data into its buffer in the background, (4) collects

baromete gyrd an ro datstored aan s them wit hcurrena timS r synchronizatioefo GP t n

during post-processing ) show(5 d s an ,curren t status. Essentially, ELGO operateS GP sa

receiver, a data acquisition board and a digital gyro simultaneously.

epoch0 1 Dat r second spe an a supported e 5 interval d, ar 2 , 1 f so . Barometric data

is sampled at 100 Hz and averaged over the data interval period, i.e. one barometer output

is an average of 20 raw barometer measurements if operated at 5 epochs per second.

Heading rate data from the AUTOGYRO™ is asynchronous. This gyro has its own clock

and continuously produces heading rates every 0.1 seconds. ELGO stores these data into a

temporary storage space (buffer). Whe datS obtaineds ani GP , ELGO immediately addo st buffere date th th n al i tim,i S al t addeGP marsa k extracte dataS d GP fro, e storemth e sth

gyro data timwitS clear d nexe ehan buffeGP e th tsth r datafo r t becomeI . s clear that

ther possibilita s ei missinf yo g inexpensivgyrn a oo t date adu e oscillato gyroe e th n Th .ri

manufacturer specifie date sth a spacing accurac 0.00e b o yt 1 seconds. This could leao dt

e possibilitth f missinyo g data ever epochs0 10 y . ELGO monitor e numbeth s f dato r a

stored in the buffer and corrects the output if possible. If the buffer contains k fewer data

tha t shouldni , ELGO compute e averagth s e heading rate fro e remaininmth g datd an a

adds this averaged rat outputek e time th o st . useELGe b S dy OwitonlS GP ma r yho GP

and other sensor(s). Option strings allow ELGO to disable logging of barometer and / or

gyro data. 20

Figure 2.3. Typical Hardware Installation. (Top) Laptop Computer and Barometer Reare inth , (centre VD2 )1 C Power Suppl DC-Ad yan C Converte (bottomd ran ) AUTOGYRO™ Placed in the Centre Console

navigatioe Th n progra mbases i Cn do 3NAV™ , develope Universite Th t da f yo

Calgary (Cannon & Lachapelle 1992). This is a between-receivers, single difference, carrier phase smoothed code DGPS navigation program t doeI .t solvsno e carrier phase ambiguities and the differential GPS position accuracy is known to be at the metre-level 21 with NovAtel GPSCards™ in ideal conditions (Cannon & Lachapelle 1992). For this project, this progra extensivels mwa y modifie authoe th y accommodato db rt externae eth l sensor information e modificationTh . s includ e sensoth e r data interfacee th , implementation of augmented position estimation routines for sensor constraint positioning and Kalman filters, and the GPS range error detection logic. This program is capabl generatinf eo g receiver location, satellite location, receiver clock offset, dilutiof no precision (DOP) and vehicle's heading and velocity. Other features include new position estimation methods (least squares with inequality constraint and the Kalman filter in addition to standard least squares) and sensor constraint positioning (least squares or

Kalman filter mode may be selected). Vehicle trajectory may be constrained in terms of heading, heigh bothr o t .

All program languagC e writtee ar sth d compile n an ei n y Borlanb d+ + C d compiler version 3.1 on an IBM-compatible 486 computer. Currently, all programs run on

MS-DO graphicao n d San l user interfac supporteds ei . 22 CHAPTER THREE

SENSOR DATA ACQUISITION PROCEDURE

A sensor is a device for receiving an external information such as heat, light, or pressure and transmitting it to a user. For most low cost land navigation applications, certain type f sensoro s e commonlar s y used, namely distance, rotation, pressurd an e acceleration sensors. An inertial system is a unit in which rotation and acceleration sensors are integrated. Dead reckoning positioning systems have become common among commercial land navigation units aime t urbada (Sakate nus a 1996). They employ eithera differential odometer or an odometer and a heading sensor to update a two dimensional position estimat absence (GeieS th GP n t ei ale f r. eo 1993). Although sensor vere sar y useful devices, they require certain procedures to achieve their best performance. This chapter gives a brief overview of the current technology of some of inexpensive (< $1000)

magnetometer

Figure 3.1. Odometer 23 sensors. Specific discussions of the barometric pressure transducer and the heading rate gyro employed in the current system are presented. Finally, the error models of barometric height, gyro heading rate, sensor headin cross-tracd gan k position, whic e explicitlhar y utilize Chapten di r Four developede ar , .

3.1 Overview of Sensor Technology

Odometer

An odometer s showa , n Figure a devic3.1 s i , o providt e e systeth e m with distance information. Using two odometers on each of the wheels of the vehicle may provide heading change information by taking the difference of the two odometer outputs.

A distance is computed by observing the number of pulses detected from targets equally spaced around each whee thed nan l multiplying these pulse count constana y sb t value/

(scale factor) which depend perimetee th wheele n so th f ro . Factors suc vehicls ha e speed, tire pressure, vehicle payload and tire tread wear affect the actual tire size and thus the accuracy of measured distances.

Harris (1989) proposed the following theory of determining a heading change from differential odometers. Heading change is observed by differentiating the two odometer distance measurements from differential odometers as shown in Figure 3.2. The mean distance traveled ove datra a interval A^ determines fi y db 24

a . North i+1

e\ pa^ \ett^e ^ ceove V\ne

ee — ^1-Tr\gW^

i.i+1

,i •*•

Figure 3.2. Differential Odometer Geometry from (Harris 1989)

(ML-MR) (3.1) where

(3.2) and

d1^ distance measured at time /. by left wheel odometer,

df distance measured at time ti by right wheel odometer,

L dt +] distance measured at time ti+l by left wheel odometer, 25

df+l distance measure t timda e righty i+lb t wheel odometer.

headinA g change ove data r a interval A computes i a d using equations (3.1d )an

(3.2) and the width of the vehicle's wheel path, TRACK, as

_ A(X ~ TRACK (3.3) , -a,

TRACK R= L -RR (3.4) where

a, azimuth heading of vehicle's forward direction at epoch tf,

al+l azimuth headin vehicle'f go s forward directio t epocna h ti+l,

RL radius of the left wheel's curvilinear path,

RR radiurighe th f t so wheel' s curvilinear path.

The measurement accuracy of the differential odometer heading change is affected by distance measurement errors.

Flux Gate Compass

A flux gate compass is a device which provides heading information by measuring the intensity of a local external magnetic field as shown in Figure 3.3. Thus, the heading angle is measured relative to the Earth's magnetic pole, not to geodetic north. Flux gate 26 compasse paia perpendiculaf e o r sus r coil measuro st directioe eth magneti e th f no c field.

By measuring a vector direction from the two coil voltages, the direction of the magnetic field may be determined (Kao 1991).

Sinc steee eth l structur magnetizede vehicla b f y eo ema actuae th , l magnetic field

direction measured by a compass in the vehicle becomes that of the combined magnetic

field of the Earth and the vehicle itself. Kao also writes that the compass measurements

suffer from the large electric current generated by the rear defroster and short term

magnetic anomalies due to power lines, steel structures, freeway underpasses and tunnels.

Compasses rely on gravity to isolate the Earth's horizontal magnetic field, and thus

acceleration and platform motion create short term compass errors (KVH 1994). Replaced

72.69 41.60 2.5P TY 4 3.18 BREAKAWAY AREA I s- SENSOR J1

45.72 40.64 J2 02.54 Q PL

2.54-1 66.04 74.30 109.22 TYP MI O-. 11/I U 1 xn --—•____" ~• _ j—

3.43 -i MAX 1.58

BOARD CLEARANCE | CONNECTOR \ WATTACHETH D TYPICAL DIMS. IN mm

Figur eC10 H 3.3.0KV Compass Engine from (KVH 1994) 27 by gyros which have become availabl t reasonablea e prices, compasse rarele sar y usen di current land vehicle navigation systems due to the above problem.

Rate Gyro

A rate gyro measures an angular velocity with respect to its rotation axis. Most gyro r lanfo s d vehicle navigatio e singlnar e axis heading rate sensors a constan r Fo . t sampling rate angulae th , r speed proportionae sar relative th o t l e headings. Gyros suffer from drifting caused by system noise, vibration, operation temperature change and other factors. Rate gyros are generally classified as one of these types: spinning rate, vibratory ratopticad ean l gyros. Their relative merit showe sar Tabln i e 3.1.

Table 3.1 Relative Merits of Gyros from (Geier et al. 1993, Andrew 1994) Typ Gyrf eo o Drift [deg/hr] Reliability Pros Cons Spinning rate 100 Fair High accuracy Short life Vibratory rate 100-3600 Good Small size Errors causey db Long life vibration Low cost Temperature sensitive Optical 10-18 Excellent Very high Expensive accuracy (FOG) movino N g parts

Traditionally the angular momentum of a spinning rotor is used to determine angular rate of displacement. Spinning rate gyros use a motor to spin a thin disk, as shown in Figure 3.4. When the axis of rotation of the disk is changed, gyroscopic forces occur which resis change th t direction ei f disk'no s momentum. These gyroscopic forces cause

flexinsprine th f go spoke dise th k f sresultino changa n gi disn ei k position with respect 28

CAPAOnVB PLATES

/ SPRING ELECTRONICS MOTOR BOARD DISK Figure 3.4. Spinning Rate Gyro from (Phillips 1993) to the motor and chassis. These positional changes are detected by measurement of capacitance between the disk and the plates on the circuit board (Phillips 1993).

As the technology matures, cost and reliability continue to be of concern.

Currently mose th , t popular typ f gyroeo piezoelectrie sar c vibratory rate gyros. Although their reliability and stability are inferior to interferometric gyros, such as FOG, they are of

Output from gyro left-handed

Force generated when the 0 rotation Is added O Tne vibration transmitted to the cerami ccompoun e Isth d of xandy

Piezoelectric ceramics for feedback

Elastic Invariable steel

Figure 3.5. Murata GYROSTAR™ Piezoelectric Vibratory Rate Gyro from (Nakamura 1990) 29 exceptionall costw ylo . Piezoelectric vibratory rate gyros utiliz physicaea l phenomenon calle Coriolie dth s effect s showA . Figurn ni e 3.5 elastin a , piezoelectrid c an stee r ba l c ceramic plates are pasted together and the vibrator is driven at the x axis. When the unit is rotated angulan a , r velocit applies y i centra e vibratoth e ) axith o Coriolida t f (z l sd o an r s force develops in the direction perpendicular to the vibration direction (Nakamura 1990).

The structure of the GYROSTAR™ rate gyro of Murata Corp. is in the shape of an equilateral triangle to improve sensitivity and stability. This vibrating unit allows the left and right piezoelectric ceramic arrangee b directioe o st th compoune n di th f no d vibration mode same Th . e ceramic usee b bot n di y hsma excitatio angulad nan r velocity detection, making both the structure and circuit simple. When rotating, the left and the right detection value e subtractear s d from each othe s showa r n Figuri n e 3.6. Thuse th , detection voltage is

(A+a)-(A-a)= (3.5)

Kon Rotating Rotating

R-L . 0Note_ * t* cancaltod Defection volUg«

Figure 3.6. Murata GYROSTAR,T1 MV1 Output Detection Theory from (Nakamura 1990) 30 which yield a relativels y large detection outpu0 degree9 f r o secont pe s d (Nakamura

1990).

Significant progress has been made in recent years towards the realization of practical interferometric fiber optic gyros (FOGs). Fiber optic gyros are beginning to replace mechanical gyro theis sa r prices rapidly drop. FOG phenomeno e basee th s ar n do n calle Sagnae dth c effect tha circuia t t syste differens mha t optical pato h tw length e th n si propagation directions whe rotates i t ni d (Perlmutter coheren1993)o tw f I . t light beams emanating from a common source travel in opposite directions around a stationary circular pat r ringh (o f radiu o ) (witsR source hth ring)ee fixeth n phas,n do i the e eyar when they return to the source as shown in Figure 3.7. If the ring is now rotated around its axis with a velocit ybeae vth , m rotating longea wit e rins hth gha r optical path thae n th tha f o t counter-rotating beam by a distance AL given by

Figure 3.7. Path Length Difference Generate Sagnae th y db c Effect from (Li Adamu& s 1990) 31

A£ = d—' ,- — 1=-^- [m] (3.6)

where

c the speed of light in a vacuum [m/s],

circumferenc e ratie th th f oo 7i circla diameters f it eo o et ,

R Radiu interferometee th f so d ran ] coi[m l

v velocit rotatioe th f yo n [m/s].

r monochromatiFo c ligh wavelengtf o t h Athi, , s chang optican ei l path length

A£ = [m] (3.7)

result non-reciprocaa n si l Sagnac phase difference

, A* = — • ——— - -r—— [rad] (3.8) A C AC

between the two beams after a single pass around the ring. For a single ring (loop)

enclosin are- n TiR ga A a 2, havin turngN fibre f rotatinsd o an , g wit angulan ha r velocity

Q = v IR, equation (3.8) becomes 32

(3.9)

Alternatively expresy ma resultan e e sth w , t phase shif termn i t f coiso l diameteR 2 = D r

and fiber lengt iiDN= hL ,

[rad]'

Note that a constant angular velocity yields a constant phase difference. We may therefore

think of a FOG as a rate gyro.

Barometric Pressure Transducer

Pressure transducers measure ambient pressures. A pressure transducer which is

designe measuro dt e barometri r pressurecai calles si barometrida c pressure transducer,

barometric altimete r simplro y barometer pressurr Ai . measures ei comparisoy db n witn ha

opposing pressure. Mercury barometers use a mercury column. The aneroid barometer

uses the tension of a spring connected to a vacuum box. Many portable altimeters used by

hikers employ these principles. Different technique e use ar sn newe i d r high-precision

barometers. One technique used in military and commercial engine pressure sensors relies vibratina n o g cylinder surrounde vacuuma pressure y db th s A . e changes e resonanth , t

frequency of the hoop mode of vibration also changes in a predictable fashion (Copley

1994). The conversion from air pressure to altitude is based on a theoretical standard 33 atmosphere and a corresponding pressure versus altitude curve. In reality, the real atmosphere varies widely from the theoretical standard and is quite dynamic. These variations mus takee b t n into account when usin gbarometera .

Accelerometer

Accelerometer usee sar measuro dt acceleratione eth vehiclea f so . Detaile th f so principle f accelerometerso givee sar Lawrencn ni e (1993) l accelerometerAl . s operaty eb measuring the inertia force generated when a mass accelerates. The inertia force may

Figure 3.8. The Spring-Supported Mass Accelerometer 34 deflect a spring, whose deflection can be measured; it may change the tension in a string and hence its vibrating frequency; or it may move a capacitor plate closer to one fixed plat furthed ean r from another, causin gmismatca value th f thein eo hi r capacitancd ean producin n outpua g t signal. Generally r navigatiofo , n purposes, onle longitudinath y l acceleratio vehicla f f interestno o s ei acceleratioe Th . n measurement integratee ar s o dt obtain vehicle velocities and traveling distances. Drifting problems are usually experienced durin integratioe gth n operations (Kao 1991).

The spring-supported mass is a basic single degree of freedom accelerometer and is shown in Figure 3.8. The relationship between the size of the proof mass and the dampin stiffnesd sprine gan th f go s determine characteristicss sit response Th . f suceo ha system to a force applied to the frame along the spring's axis may be determined by summin force gth e from inertia, fluid dampin sprind gan g displacemens a t

(3.11) vary \av where

m weight of the mass [kg]

x displacement from the mass' rest position [m],

c damping coefficient [kg/s],

2 Kx spring stiffness [kg/s ]. 35 In some instrument dampine sth g outweigh inertie sth a ter thamo s t equation (3.11y )ma

e considereb s firsa d t order s mori t I .ee inerti usuath r afo l ter mo dominatet e th d an ,

equatio secone b o nt d order.

If the acceleration is steady and the mass displacement is steady, initial transient

oscillations have subsided and the result is

e inertith Tha , ais t forc s balancei ee opposin th y b de b g y sprinma gx forcd an e

considered as a measure of the acceleration. 36 Descriptio2 3. Selectef no d Sensors

3.2.1 Barometric Pressure Transducer

A Viatran Mode barometri6 24 l c pressure transducer, show Figurn i e 3.9 uses ,i d

for this projec o measurt t e barometric heights. This baromete s designei r o measurdt e

barometric pressures to within 0.01" Hg (Viatran 1996). Its full scale pressure range is

25" Hg to 32" Hg absolute which corresponds to a linear output of approximately 0 to 5

VDC (Viatran 1996). Specifications for the Viatran Model 246 are given in Table 3.2.

In orde o examint r e pressurth e I uniS e te outpu Pascalth n i e followint th , g

conversio s necessaryni e particulaTh . r barometer uses preciselwa d y calibratee th t a d

factory for

0.006 volts at 25.0" Hg and

4.988 volt 32.0t sa . "Hg (3.13)

3.45 • BREATHER ELEMENT .441—— .50

H L

NOTE: UNfT INFORMATION 1. ALL DIMENSIONS ARE NOMINAL. IN INCHES LASER MARKED AND FOR REFERENCE PURPOSES ONLY ON HOUSING

Figure 3.9. Viatran Model 246 Electronic Barometer from (Viatran 1996) 37 Pressure expressed in inches of Hg may be converted to Pascal using

Pasca g-l= p-mm Hg-1000. (3.14)

valuee th r (3.13)f so Fo ,

Table 3.2 Viatran Model 246 Product Specifications from (Viatran 1996) Full Scale Pressure Range 25" to 32" Hg absolute Total Erro rNon-Linearit o Bant e ddu Hysterisiy& s <±0.01"Hg Repeatabilit& y Response Time < ±5 msec Zero Repeat After 100°F Temperature Shift < ±0.007" Hg Compensated Temperature Range 0° +200°Fo t F Operating Temperature Range -40°F to +250°F Temperature Effec Zern o t o < ±0.0018" Hg per 1°F Temperature Effec Span o t n < ±0.0018" Hg peF 1° r Long Term Stability < ±0.035g "H pe monthr6 s Supply Voltage 8.5to40VDC Power Supply Regulation < ±0.000007g "H per Volt Output Signal 0 to 5 VDC Output Signal Noise Levels < 10 mV peak to peak 38 25"Hg = 635mmHg = 84464.31164 Pa and

32" Hg = 812.8 mm Hg= 108114.3189 Pa (3.15) where

g = 9.78049 [m/s2] gravity force,

p = 13600 [kg m3] density of Hg.

A linear relation between pressure in Pascal/? and output voltage v is given from equations

(3.13) and (3.15) as

(84464.3116= p 4735.684273(4+ 0.006)v+ ) [Pa]. (3.16)

Equation (3.16) gives air pressure in Pascals from the Viatran Model 246 barometer. The

110 T

0 500 1000 1500 2000 2500 3000 3500 4000 Height[m]

Figur StandarS U ee 3.10Th d. Atmosphere Pressure-To-Height Conversion Chart from (Lutgen Tarbucs& k 1982) 39 U.S. Standard Atmosphere (Lutgen Tarbucs& k 1982pressure-to-heighe th uses i )r dfo t

conversion as shown in Figure 3.10. Since this table only defines the theoretical

relationship between pressure and height, following errors must be taken into account in

orde compensato rt deviatioe eth n from this model.

erroe Th r characteristic barometee th f so r vary dependin environmente th n go a n I .

static environment, major error sources are the bias of the sensor and long term drift change th mainlo locat n ei e yldu pressur shows ea Figurn i e 3.11 r vehiclFo . e navigation,

the barometer is commonly located in a car. As a result, barometric measurements are

disturbe changey db ambienn si t pressure causeacceleratioe th y db deceleratiod nan f no vehiclee th . Figure 3.12 shows thi svehicle effectth s A e. accelerates t createi , rissa f eo

pressure in the vehicle which pushes down the measured height. At the same time, a

20T

' ' TI ' ' I ' '' ' I ' 0 I '' ' ' ' I ' ' I ''' I ' 501000 502000 503000 504000 505000 506000 507000 508000 509000 GPS Time [sec]

Figure 3.11. Viatran Mode Electroni6 24 l c Barometer Measurement Error inTypicaa l Static Environment 40 v^O-DecelerationUs

574008.9 574070.9 574130.9 574190.9 574250.9 574310.9 574370.9 GPS Time [sec] Figure 3.12. Viatran Model 246 Electric Barometer Measurement Error i nTypicaa l Dynamic Environment certain amount of air escapes from the vehicle's compartment and the barometric height increases to a certain extent. Other measurement errors may include a deviation from theoretical standard atmosphere caused by non-standard humidity and temperature, nonlinearities cause vertically db y moving air, wind, weather front conversiod an s n error.

It is nearly impossible to distinguish the causes of error in dynamic environments and these error generalle sar y insignificant (Lutgen Tarbucs& k 1982). Therefore, these errore sar grouped int constane oth driftte biath r .so

3.2.2 Fiber Optic Gyro

For land vehicle navigation purposes, a single axis gyro is commonly used to determine vehicle headings. An Andrew AUTOGYRO™, shown in Figure 3.13, was 41 selected for this project. This gyro is a single axis, digital output, interferometric fiber

optic rate gyroe AUTOGYROTh . ™ configuratio s givei n n Figuri n e 3.14e .Th

AUTOGYRO™ employs an analog electronic signal processor and an all-fiber optical

system (Andrew Corp. 1994). The fiber consists of a elliptical core of germanium

surrounded by a fluorine-doped inner cladding (Alien et al. 1994). This fiber exhibits

significantly lower coefficient o t thermas d stresan l s environments e AndreTh . w

AUTOGYRO™ specifications are given in Table 3.3. The device measures angular rate which allow vehicle sth e turning anglaccuratelye b o et measured. Powere VD2 1 Ca y db

car battery, the AUTOGYRO™ produces a digitized output of incremental angular

rotation every 0.1 second. The output is equivalent to the average rotation rate over that

period (Andrew Corp. 1994).

Tabl Andre3 e3. w AUTOGYRO™ Product Specifications from (Andrew 1994) Input Rotation Rate ±100deg/sec Minimum Detectable Rotation Rate ± 0.02 deg/sec (60 deg/hr) lOOHn (i z bandwidth) Angle Random Walk Bias Drif stabilize(at t d temperature) 0.005 deg/sec, rms (18 deg/hr) Scale Factor Non-Linearity 0.25%, rms Scale Factor Temperature Stability 0.5%s rm , (over temperature range) Warm-up Time 1 second Operating Temperature -40°C to +75°C Power +9 to+18 VDC, 630mA Sensor Output RS-232E, 9600 baud Connector Type 9-pin subminiature (DB-9 plug) 42

Figure 3.13. Andrew AUTOGYROT1M*1 from (Alie t alne . 1994) 43

3dB Directional 3dB Directional Coupler Coupler

PZT Phase Modulator Sine Wave Generator

Rotation Rat r Angulaeo r Position Output a) Open-Loop

Multifunction Integrated-Optics Circuit 3 dB Directional Coupler

Rat r Angulaeo r Position Output b) Closed Loop

Figure 3.14. Andrew AUTOGYRO™ Configuration from (Bennett & Enge 1994) 44

0.01 T

0 6 0 5 0 4 30 Unit Temperature [deg. C]

Figure 3.15. Andrew AUTOGYRO™ Output Bias vs. Unit Temperature

Figure 3.15 shows the relationship between unit temperature and gyro output bias.

Although the bias can be largely corrected by the temperature-bias compensation table

provided by the manufacturer, it is likely that a residual bias will remain. Appropriate

calibration procedure carefud san l gyro temperature control should reduce this error.

Previous gyro experiment, Figure 3.16, have indicated thagyre th t o scale factor

increase unexpecten a t sa dunie ratth t s temperaturea e rises, thereforeis t I . , necessaro yt

correc e unith t t scale facto functioa s a r f unio n t temperature scalA . ee b facto y ma r

determined by rotating a gyro unit a certain number of degrees while recording its outputs.

scale Th e facto thes i r n computey db 45 (3.17) where

/ gyro scale factor,

O rotation unigivee degreesn th i t o nt ,

n digital gyro output count.

Performing this procedure at the desired unit temperature gives a gyro scale factor for that temperature, provided that the unit has an acceptable repeatability. Figure 3.16, obtained from a laboratory experiment conducted on August 23, 1996, shows the relationship between the scale factor and unit temperature. Since unit temperature will vary with the testing environment, appropriate scale factors must be determined with

0.004 20 30 40 50 Unit Temperature [deg.C]

Figure 3.16. Andrew AUTOGYRO™ Scale Factor vs. Unit Temperature 46 respec o actuat t l operating temperature e scalTh .e facto d ordes modelei 3r r a r y b d polynomial equation (curv figurn ei e 3.16s )a

2 3 f(x) = a0 + alx+a2x + a3x (3.18) where

x is gyro unit temperature [°C],

a0 =0.00253199307659,

a0.0001687807126= , 1,

a2 = -0.00000439984368 ,

0.00000005296039= a . 47

0 80 0 70 0 60 0 50 0 40 0 30 0 20 100 900 1000 Easting [m]

Figure 3.17. Sensor Heading Constraint Solutions without Corrected Scale Factor. Default Scale Factor (0.00499 [deg/bit]) Used. Solid Line Indicates Reference Trajectory

-80 -90 -100 100 200 300 400 500 600 700 800 900 1000 Easting[m]

Figure 3.18. Sensor Heading Constraint Solutions with Corrected Scale Factor. Solid Line Indicates Reference Trajectory 48

The effect of appropriate scale factor determination is obvious from figures 3.17

and 3.18. Forward and reverse runs are shown in each figure. Improper scale factor may

cause severe position estimate displacemen filtea d r an tbreakdow Kalmae th f ni n position

estimato s employedi r . Equation (3.18 s implementei ) e navigatioth n i d n modulo t e

comput scale eth e facto functioa s a r f unino t temperature date Th a. logging softwars ei

designed to include gyro unit temperature output. As the unit ages, the scale factor may

change because of the mechanical degradation. Therefore, the coefficients of (3.18) should

periodicall updatede yb .

Senso3 3. r Error Models

In this section, sensor error models are developed. It is necessary to determine

error modelbarometrie th r sfo c height, gyro heading ratsensod ean r headin evaluato gt e

the weights of the sensor measurements. The sensor heading error model is then

implemented in the cross-track position error model. These models are used in Chapter

Fou calculato rt e weight varianced san sensof so r measurements.

3.3.1 Barometric Height Error Model

For barometric height, the primary error source is the barometric height offset with

heightS respecGP o e initia.t t Thith s o mainlli t s sensoe du y r bias e disagreementh , t

between barometri orthometricr c(o heighe heightS )th heighd GP t d an ,offse an t t between antennaS sensoe GP th bia e e srTh th . unierrod an tconstans i r t and, thereforee b y ma t i , 49 remove initiay db l calibration e residuaTh . l (non-constant) error e absorbear se th y b d second error source, heigh ttake e drift b need t nan ,dno int o accoun t thia t s point.

e secondarTh y error source heighth s i et drift cause y changeb d n pressuri s e around the barometer. The ambient barometric pressure slowly changes as high and low pressure systems approach stationara n I . y environment barometrie th , c height changf eo approximately 50 metres in an hour has been observed by the author. For land navigation applications, height drift is also caused by in-vehicle pressure disturbances due to the acceleratio deceleratiod nan vehiclee th f no , temperature changes, etc. Additional errors may include the aging of the sensor unit as well as hardware and software limitations.

Assuming that GPS updates are obtained consistently (e.g. every 10 minutes), we may conside heighe th r heighe t th offse d t an drift tconstant e b rat o e t heighe Th . t error model may then be defined as

(3.19) efra*+ ,e)= fc (/ t8)+ i (/Jk)A/ where

8 fc (^t+i ) barometric height error at time tk+l [m],

efc barometric height offset (residual) error at the calibration time t0

[m],

ib linear barometric height drift rate [m/s],

A/ update interval betwee ntd k+l tan k [s]. 50

Modeling the long-term behavior of efc is extremely difficult since there are many factors whic alten ambiene hca th r t pressure whe vehicle t stationarynth no s ei thin I . s project, ib is assumed constant between calibration periods. Calibration may be performed when good GPS solutions are available. Therefore, good GPS coverage is periodically necessary (e.g. every ten minutes).

3.3.2 Gyro Heading Rate Error Model

mose Th t significant gyro error sourc headine th s ei g rate offsee th t o t erro e du r gyro biase headinTh . g rate offse temperature-dependens i t e manufacturth d an t e often provides rate offset versus temperature charts (Andrew Corp. 1994). This error may be considered constant by stabilizing the gyro unit temperature at a certain value. Stabilizing the unit temperature is strongly suggested since it stabilizes the scale factor error as well.

anothee Th r significant error sourc gyre th os ei scale factor error scale Th .e factor erro s negligibli r e vehicl s lonth a e s ga e follow a straighs t line. However t becomei , s obviou headine th s sa g rate increases (e.g. sudden heading change). Thus scale th , e factor erro functioa e substantias i rth f o n l heading rateauthoe Th s foun. ha r d thae scalth t e factor error fluctuates with unit temperature. This error may be minimized by calibrating the gyro at the operational unit temperature.

The gyro drift error is an outstanding error source as well. This may be caused by temperature change, instability of the unit, environmental stresses, mechanical failures, and so on. Other errors such as g-sensitivity, cross-axis sensitivity, nonlinear errors (Abbott & 51 Powell, 1995) and the effect of the earth rotation (Da & Dedes, 1995) are ignored in this thesis since the negligible yar mosr efo t land navigation applications.

Assuming that the gyro unit temperature is stabilized, the gyro error model may be expresses da

where

C*+i) gyro erro t tra k+l [rad/s],

gyro heading rate offset (residual) error at t0 [rad/s],

gyro drift error [rad/s2],

update interval between tk and tk+l [s].

Note that in this thesis the gyro offset is calibrated when the vehicle is stationary ane headindth thay ge gyr sa th changt t expectedoy no drif ma s i e e t W erro. r s ei g constant between calibrations. Needless to say, periodic calibration is recommended to validate this assumption. Although the scale factor error and gyro offset may be evaluated with respect to the reference heading rate, this technique is not implemented in the current system. 52 3.3.3 Sensor Heading Error Model

Since the fibre optic gyro only senses the change in vehicle heading, the initial heading mus e obtaineb t r otheo d S fror msourcesGP e headinTh .n a go t erro e du r inaccurate initial heading should be included. The sensor heading error may be written as

( 8e('*+.) = 8e(^) + 8f('t+,) ' where

8 ©(**+i ) heading error at tk+l [rad],

6e initial heading error [rad],

8g (A+i ) gyro error at *k+i computed from equation (3.18) [rad/s].

Since the gyro error grows over time, the heading error may become intolerable afte a certair n period. GooS geometrGP d y (e.g t intersectionsa . e useb o t dy ma ) frequently update the gyro (e.g. every five minutes).

3.3.4 Cross-Track Position Error Model

Finally, the cross-track position error model is obtained using equation (3.21). The cross-track position error may be expressed as

8crvo) ~ 8GF5 .,- 53 where

8 cr (*k+\) cross-track position error at tk+l [m],

'GPS cross-tracS GP k position estimate error [m],

vk vehicle velocity [m/s],

8 e (*k+i) heading erro t trk+la obtained from equation (3.21) [rad],

A/ update interval between tk and tk+l [s].

These parameter illustratee sar Figurn di e 3.19.

It is uncertain in urban areas when good GPS coverage can be obtained.

Therefore, the system is designed to initiate the calibration process whenever the good

GPS coverage is obtained..

Figure 3.19. Cross-Track Position Displacement Induced by Sensor Heading Error. 54 CHAPTER FOUR

SENSOR CONSTRAINT POSITIONING THEORY

This chapter discusses the sensor constraint positioning algorithm. In sensor

constraint positioning, position estimates are constrained by the sensor measurements

whemeasurementS nGP weake sar , erroneou r absentso implemeno T . t sensor constraint

positioning, an augmented least squares estimator is introduced and developed.

Concep1 4. Sensof to r Constraint Positioning

In sensor constraint positioning, information regarding the relative position of a

vehicle is provided by non-GPS sensors and used to constrain the position estimate so that

s lesi t s affectee numberth y b d , qualit geometrd S measurementsan y GP f yo thin I . s

project, the vehicle height and heading information, which may be obtained from the

barometer and gyro, are selected as constraints. A barometric height constrains vertical

position while a sensor heading constrains horizontal position.

Mathematica2 4. l Models

mathematicaA rangS lGP e mode e measurementh f o l gives i t y nb

(4.1) 55 p = ||r - R|| geometric range [m],

r position vector o satellitefa ,

R position vecto lana f dro vehicle,

dp range error induced by orbital error [m],

dt satellite clock error [s],

T d receiver clock error [s],

dim' dtrop ionospheric and tropospheric delays [m],

6 p receiver noise [m]. barometrie th r Fo c height measurement mathematicae th , lsimplifie e modeb y ma l s da

hhb= +zb (4.2)

where

hb barometric height measurement [m],

h true height [m],

efe barometric height measurement error [m].

For the horizontal heading measurement, as shown in Figure 4.1, two consecutive

coordinates are required to construct a mathematical model as

(4.3) 56 where

0 heading defined clockwise from zer 2no t relativ norto et h [rad],

distance between two consecutive epochs in latitude [m],

dk distance between two consecutive epochs in longitude [m],

heading error [rad].

Note that the barometric height and heading errors are evaluated by equations (3.17) and

(3.19).

Figure 4.1. Heading Computation

4.3 Augmented Least Squares Estimator

This section describe algorithn sa sensor mfo r constraint least squares positioning. facn i augmenten a ts i t I d weighted least squares estimator. Conside e parametrith r c

weighted least squares equation. Given the design matrix A, the covariance matrix of 57

measurements C/3 the a priori position estimate vector x° and the misclosure vector w°,

solutioa n vecto obtainee b followine y rth ma xy d b g equations (Krakiwsky, 1990)

(4.4)

(4.5)

(4.6)

where

1 observation vector,

5 least squares adjustment parameterso st .

An augmented desig obtainee b n y matri lineariziny ma db xA g equations (4.1 (4.3o )t )

with respec geodetie th o t c coordinate syste received man r cloc rangeS kGP offset,a r Fo .

A.. = (4.7)

fo barometria r c height,

] 0 A,=[0, 1 , 0 , (4.8)

r headinfo d an g 58

, o, o (4.9)

where

distance betwee consecutivo ntw e epoch latitudn si e [m],

dk distance betwee consecutivo ntw e epoch longitudn si e [m].

Equations (4.7) to (4.9) form an augmented design matrix. Sensor height and heading inputs are treated as the measurements in this augmented least squares estimator. Solving equations (4.4) to (4.6) with the augmented design matrix yields height and heading constraint position estimates.

e constrain e effecth f Th o t s definee diagonai t th y b d l element e weighth f o st matrix C/'1

"of 0 ••• 0 0 0~ 0 oj ... 0 0 0

C ' = (4.10) ^/ 0 0 ... a> 0 0 0 0 ••• 0 a* 0 0 0 ••• 0 0 a®_ where

GPS range error variances [m2], 59 barometric height error variance [m2], * sensor heading error variance [rad2].

navigatioe Th n progra mbases i Cn do NAV ™ develope Universite th t da f Calgaryyo t I . 3 is capable of smoothing range measurements by carrier phase observations to improve the

accuracy (Cannon & Lachapelle 1992). A smoothed range measurement may be given by

Pk=WPt+(\- W)(P («t_,+ 4 -0t_,)} (4.

where

Pk, Pk_l smoothed range measuremen td k _t t}an a kt [m],

W weight of a range measurement that is decreased from 1.0 to zero

b yspecifiea d numbe t eacra h epoch,

Pk raw range measurement at tk [m],

W \- weigh carrief o t r phase measurements,

C^, O^ measured carrier phase measurement at tk and tk_l [m]. 60 The variance of smoothed range measurements may be expressed as a function of the range and carrier phase errors. The smoothed range measurement variance may be given as

vrop °+ * ° + ° ,+ (4. 12) where

measurement noise [m2],

tropospheric delay [m2],

2 alion ionospheric delay [m ],

2 Ogp orbital error [m ],

2 •\dt satellite clock error [m ].

Martin (1980) gives tropospheric and ionospheric error models as a function of elevation as 61 {AC;V(/Ocsc(£)} -0.034

-b 2 2 0.5 2 rl 7v{csc(£ +20.3 )} 47CV (4.14)

where

N(h) linear integra usef o l satellito rt e refractivity function,

AC residual compensation magnitud, m) 1 «e0. C (A

temperature,

vehicle altitude,

satellite elevatio degreesn i ,

1= .610x constan3= MKn i t S unit,

/ carrier frequency in Hz,

vertical electron content in electrons / m2,

AK fractional value of reduced ionospheric delay ( 0.5 < AAT < 5 m). 62 The smoothed range measurement variance should decrease proportiona weighe th o f t lo t carriee th r phase measurement resultine Th . g measurement varianc expressee b y ema s da

(4.15)

where

W weigh ranga f o t e measurement,

range measurement error variance [m2]

carrier phase measurement error variance [m2].

Equations (4.12) to (4.15) are used to compute a GPS range variance.

The measurement error variances of barometric height and sensor heading at tk givee ar y nb 63 where

£b(tk) barometric height error at tk from equation (3.17),

sensor heading error at tk from equation (3.19).

Note that the variances computed by equations (4.16) and (4.17) increase with time, reflecting the cumulative sensor measurement errors. Equations (4.15) to (4.17) allow a navigation algorith mfin o optimat n da l position estimat givey an nt e a time . 64 CHAPTER FIVE

KALMAN FILTERS

This chapter describe Kalmae sth n filter algorith s implementationit d man . First, the general Kalman filter algorithm is briefly presented. Then, the sensor filters are developed. Finally, a Kalman filter version of the sensor constraint position estimator is designed and discussed.

5.1 Kalman Filter Algorithm

e generaTh l discrete Kalman filter algorith ms briefli y describe thin di s section.

Detailed discussion Kalmaf so n filter givee sar Brown i Hwann& g (1992 . Geld al )an t b e

(1974)s assumu t Le .e tharandoe th t m proces estimatee b modelee o b st e n th dca n di linear form

where

xjt+1 process state vector at time 4+1,

transition matrix relating x^and xAr+1 in absence of a forcing

function,

white noise with known system noise covariance structure 65 and measurement of the process is assumed to occur at discrete points in time according lineae th o rt relationship

z*=AAxt+vt (5.2)

where

zk measurement vector at tk,

Ak design matrix which gives noiseless connection between the

measurement and state vector at lk,

v k measurement error assumed to be white with a known covariance

structure.

The covariance matrice give e \d kar \vr y nan b ksfo

0. (5-5)

where

Qk variance matrix of process noise at 4,

CJk variance matri measuremenf xo t erro t 4ra - 66

The standard Kalman filter equations are derived as follows (Brown & Hwang

1992). The blending factor called Kalman filter gain is given by

(5.6)

where Perros ^i r covariance matrix associated with projected estimate. e optimaTh l estimat t s obtainei tea k linearly db y blendin e noisgth y measurement

projected estimate x~ and the filter gain Kk

(5.7)

The covariance matrix associated with the optimal estimate may be computed by

or

Pt=(l-KtA>; (5.9) 67

where the optimal gain has been substituted in. Since wk in equation (5.1) has zero mean t correlateanno s d i previou e definitiony th b df s ' o wit y contributiow se han th , f wno o t ^

the projected estimate may be ignored. Thus, the projected estimate at tk+l is given by

The error covariance matrix associated with the projected estimate is obtained by

(5.11)

Equations (5.6 (5.11o t ) ) constitut Kalmae eth n filter recursive equations e KalmaTh . n

filter is an algorithm for making optimal estimates from discrete measurements.

5.2 Sensor Filters

Ther mane ear y factor consideo st r when implementin Kalmaga n filte r sensorsfo r .

In the most common implementation, one Kalman filter takes all measurements into

accoun updated an t estimatel sal same th t esa time. This approac calles hi centralizee dth d

Kalman filter (e.g. Carlson 198 Abousaled 7an m 1993) r efficienn a fo .t y Thino wa ts i s

this project since the sensor measurements are independent and the update intervals are

not identical. For instance, the gyroscope measurement bias estimate may be updated only

whe vehicle nth e heading rat perfectls ei y known (e.g. heading rate shoul zere db o whena 68 vehicle is not moving). Also, it is preferable to keep the size of matrices used in the filter as small as possible since a matrix inversion is required to calculate the Kalman gain.

Another concer s flexibilityni r t instancedesirablno Fo . s i t o updati t e, e gyrth e o bias estimate when the gyro measurement is absent.

Considering these factors, an array of independent two-state Kalman filters is implemented t consist I .measuremen o tw f so t filters erroo tw , r corrector headina d san g filter, which are developed in the following sections. The strengths of this approach are tha intervae th t ladjustede epocb y systee hma th de-activat,y mma ecertaia n filter whet ni is unnecessary and the computational load is less than the centralized Kalman filter. This approach was selected as it conforms to the modular programming concept. Every software component may be transported to any other program to reduce programming and debugging timee navigatioTh . n program presente n Chaptei d x useSi rs these filters extensively.

generae Th l dynamic mode describes i l d immediately below behavioe th f a I . f o r phenomeno sensee b o n t modele s di lineaa y db r parameter system dynamice th , f sucso ha representesystee b y mfirst-ordee ma th y db r equation (Gel t albe . 1974)

(0 (5.12) where

\(t) system state vector,

w(/) random forcing function, 69 , G(t) matrices arising in the formulation.

Several researchers suggest that the integrated Gauss-Markov process may be

appropriat e sensoth r refo filter models (e.g. Brow Hwann& g 1992, Abbo Powell& t ,

1995) generaA . l continuous mode thin i l s cas (Brows ei Hwann& g 1992)

0 IT,' + 1 (5.13) 0 -pi

wher tims i eP constan processe th r fo t .

For the Kalman filter, the transition matrix and the covariance matrix associated e derivewitar hw d using this model transitioe Th . n matri s determinexi (Browy db n&

Hwang 1992)

-\ s -1 = L 0 5 + p

1 1 s s(s + P) (5.14) o —-

where L'inverss i 1 e Laplace transform operator. 70

Although analytical evaluatio covariance th f no e matri triviaa t x no l Q s taski fc , a goothi s i s d opportunit o derivyt . Formallyit e , Q^s expressei . integran di l fors ma

(Brown & Hwang 1992, Gelb et al. 1974)

(5.15) ^

where the matrix £|u(£)ur(r|)| is a matrix of Dirac delta functions

whic zers hi o anywhere excep s infiniti t t i t thar|y £T £ a = t= e ,, Jsuc A n .i e wa th t ha integral of the function across the singularity is unity (Gelb et al. 1974). An important property of the delta function, which follows from this definition, is

(5.17) 71 Substituting equations (5.3), (5.13), (5.14), (5.16) and (5.17) into equation (5.15) yields

=nr -\T =r

=r 1 -l-e-K Jo = J

(5.18)

The integration of each element gives the final form

Q _ 2,2 (5.19) i^2 where a. = f

(5.20)

+ tf, + 72

(52i)

Af

(5.22) zpy

2|3 '~

and

(5.23)

Note that there is an important distinction to be made between q and Q . The # is an elemen spectrae th f o t l densit calles i Q dcovariancya e matrith d xan e matrix (Gelt be al. 1974) spectraA . l density e converte matrib y covarianca xma o dt e matrix through multiplicatio Dirae th y cnb delta function (Gel. 1974)al relationshie t be Th . p betweee nth variance of the process noise a2, the spectral density #and the correlation time P is defined as (Bullock 1995) 73

q =2pa2. (5.24)

The above discussion facilitates the development of the sensor filters. All sensor

integratee filterth e us s d Gauss-Markov mode f equatioo l n (5.13) barometrie Th . c height

dynamic expresse e modeb y ma l s da

0 IT*' (5.25) o -

gyroscopThe e heading rate modeis l

To1 0' (5.26)

The barometric height bias model is

1 T6/r"0 " (5.27) dh

gyroscope Th e heading rate bias modes i l 74 8c6 "0 1 8co (5.28) 5d) 0 -

Finally sensoe th , r heading modes i l

0 0 1 T0" (0 (5.29) 0 0 -Pel®.

wher time th e es f>i correlatio n constan correspondine th r tfo g sensor input.

Note that although equations (5.25) to (5.29) are of the same form, an appropriate time constan whitd an t e noise variance mus e determineb t r eacdfo h model taking into account the measurement characteristics, operation environment, and so on. For this thesis, these parameters were selected and listed in Chapter Seven. The significance of these filter thas i systee s th t m accept widsa e rang f sensoreo s with various accuracies.

Adjustment to a new sensor may be done by choosing a proper P and q. The bases determinatioi laboratorn q d o d an P y f nexperimento specificationd san s provided manufacturere byth . Corresponding transition matrice noisd san e covariance matricey sma be evaluated using equations (5.14) and (5.19), or by less demanding numerical evaluations based on approximations (Brown & Hwang 1992). For this thesis, these parameters were selecte listed d an Chapten di r Seven. 75 K3 5. ai Positiomn a n Estimator with Sensor Constraint

Designing a Kalman filter with sensor constraints involves the filter dimension, the

determinatio propea f no r mathematical mode implementatiod an l sensoe th f no r constraint

strategy. In many land vehicular applications, a constant velocity model is often chosen

since the introduction of the acceleration state does not significantly improve positioning

accuracy for moderate vehicle dynamics (e.g. Cannon 1991, Gao 1992, Bullock 1995).

The estimate state consists of eight parameters

5<> 8X 8 8/? 8/ cdt c5i (5.30)

where

84>,8(j) latitude position and rate errors,

8A,, 8l longitude position and rate errors,

5/7, 8/i height position and rate errors,

c5/, c$i receiver clock offse drifd an t errors.

An integrated Gauss-Markov model is used as the sensor filter model. The dynamic model

of the position estimate may be described by 76

"0 1 0 0 0 0 0 0 " 1%(0~ 0 -p* 0 0 0 0 0 0 v> 0 0 0 1 0 0 0 0 »x(') 0 0 0 --Px 0 0 0 0 i»i(0 X — X ~4~ (5.31) 0 0 0 0 0 1 0 0 **(') 0 0 0 0 0 - P, 0 0 W*C) 0 0 0 0 0 0 0 1 wcdl(t) 0 0 0 0 0 0 0 -pj J--«J

where

p* time correlation constan tlatitudf o e estimate

p, time correlation constan tlongitudf o e estima

p, time correlation constant of height estimate,

time correlation constant of receiver clock offset estimate,

0 ( white noise inpu latitudf o t e positio ratd nean errors,

WK (/), w j_ (t) white noise input of longitude position and rate errors,

\vh (t), w^ (t) white noise input of height position and rate errors,

aft(0» «fwhit0 ( f e noise inpu receivef o t r clock offse drifd an t errors. w w

state Th e transition matri thif xo s mode derives i l s da 77

1 ±(l-e-W ) ° 0 0 0 0 0 0 e * 0 0 0 0 0 0 1 , . 0 0 1 — (1 — e~ ') ° 0 0 0 PV 0 0 0 e~^ 0 0 0 0 0 0 0 0 1 J-(l-e-p^) ° 0 0 0 0 0 0 c 0 0 0 0 0 0 0 0 1 ,*A0 - A1 ( /e*-*i ) Pcdt 0 0 0 0 0 0 0 e-Pc,*Ar

(5.32)

The corresponding process noise covariance matrix may be obtained from equations

(5.15) and (5.32s )a

0 0 0 " "a. Gl2 0 0 0 G2i 622 0 0 0 0 0 0 0 0 2 0 0 0 0 33 G34 0 0 £43 0 0 0 0 &4 (5.33) 0 0 0 0 0 0 655 056 0 0 0 0 0 0 065 Q66 0 0 0 0 0 0 G77 &8 0 0 0 0 0 0 G87 G88_ where oo r- OO co en co CO

" ca CN ca<< ca CO.

ca ca

<^

^

O) d 79

687=278, (5-48)

and

5 49 88 ', v( - ')

where

q^ , q^ spectral density of latitude position and rate errors,

q^ , q^ spectral densit longitudf yo e positio ratd nean errors,

qh,q^ spectral density of height position and rate errors,

Qcdtrfcdi spectral densit receivef yo r clock offse drifd an tt errors.

Determination of spectral densities for the position random process is at best a

"guesstimate" roughly based on expected vehicle dynamics (Brown & Hwang 1992). In

many vehicular applications randoe th , m perturbation intendee th o st d pat greatee har n i r

horizontae th l plan evertical.e thath n ni

The same augmented design matrix shown in equations (4.7) to (4.9) is used in the

Kalman position estimator to implement the sensor constraint. The Kalman filter sensor

constraint algorith midenticas i lease th thao t ltf o tsquare s estimator effectivenese th , f o s

e constrainth s controllei t e measurementh y b d t variance matrix e KalmaTh . n filter

position estimates ten oscillato dt e afte tigha r vehiclte turth f no e becaus presence th f eo e velocite th f o y state .t desirabl Thino s si sensor efo r constraint positioning sinc initiae eth l 80 heading is determined by previous position estimates. Thus, it may introduce a significant initial heading bias into the Kalman position estimator and cause a filter to breakdown. An adaptive process noise covariance matrix routin s thuwa es create o t avoid d such oscillation. This routine takes the gyroscope heading change into account in order to increas procese eth s horizonta e noisth f eo l plane components sa

Q = Q-ekM (5.50) where

Q adapted process noise covariance,

Q initial process noise covariance,

k adaptation gain constant,

The adapted value is exponentially proportional to the initial value and is a function of the heading change n appropriatA . e adaptation gain constant mus e selecteb t o avoit d d possible filter breakdow givey an nr nheadinfo g change r thiFo s. thesis, adaptation gaif no

10.0 was selected. This value yields k\o^ = 1.0 when CD is approximately 5.7 [deg/s]. 81 CHAPTER SIX

SOFTWAR IMPLEMENTATIOD EAN N CONSIDERATIONS

This chapter describes the navigation software algorithm. The program, called

EC3 s basei , n Co d3NAV™ , develope e UniversitTh t a d f Calgaro y y (Canno& n

Lachapelle 1992). C3NAV™ is a between-receiver, single difference, carrier phase

smoothed code DGPS navigation program. EC3 uses the basic components of C NAV™ 3 such as satellite ephemeris decoding, satellite orbit computation, satellite clock

computation, ionospheric and tropospheric corrections, generating or applying differential

corrections, carrier smoothed code generatio standard nan d least squares estimationw Ne .

modules were developed to accommodate sensor constraint positioning. EC3 is written in

C language e chapteTh . r concludes with discussion f sensoo s r constraint position

estimators and operational considerations.

6.1 Overview

Figure 6.1 show overvien sa navigatioe th f wo n program. Basic flo identicaws i o t l

tha f Co t3 NAV™ (Canno Lachapell& n e 1992). There are, however a numbe, f o r

enhancements for sensor constraint positioning. The barometer and/or gyro data for the

vertical and horizontal constraint may be applied to solutions. EC3 has two position

estimators lease th , t square Kalmad san n thesf use a filterseleco n d e rca e an ,on t estimato r

for computations. Utilizing this feature enable o compart s e least squares solutiono t s

Kalman filter ones. The barometer and gyro measurement data reader obtains the 82 corresponding senso e rcurren th S timdat r f eaco fo GP eat h epoch. Thesw ra e measurement sensoe th sene sar o t rt constraint positioning module with correcteS dGP observations, satellite coordinate initiad san l receiver coordinates positionine Th . g module return a valus o flae succest e th g e r positiofailuro sth f o e n estimate process. Upon success receivee th , r coordinate updatede sar , displaye storedd dan . Filterin sensoe th f go r measurements is done in the sensor constraint positioning module and is therefore not seen at this level.

Yes

Compute Satellite Coordinates Compute and Apply Satellite Clock, Troposphere and Ionosphere Correction Compute Carrier Phase Smoothed Range Reject Satellites Under Cutoff Angle

Compute Position Estimates - Least Squares or Kalman - Standar r Sensodo r Constraint

Comput d Storan e e Corrections

I Output Result\ s Figure 6.1 Flowchart of EC3 83

Senso2 6. r Constraint Positioning Module

Flowchart sensoe th r rsfo constraint positioning modul showe ear Figurn ni 2 e6.

(least squares) and Figure 6.3 (Kalman). Although they appear identical, fault tolerant

routine e implementear s e Kalmath n i d n position estimato s explainea r d late n thii r s

chapter. Kalman sensor measurement filter e firsar st use o obtait d n filtered sensor

measurements "standardA . " DGPS position estimator, without sensor constraint, first

tries to find a solution without the aid of sensor constraints. The routine evaluates the

resul immediateld an t y decides whether sensor constraint positioning shoul usee db r do

not. The current criteria for acceptable position estimates are (1) the range residuals and

) satellit(2 e geometry expresse dilutioe th y df b precisio no n (DOP) thin I . s thesis, these

values are taken to achieve the best result. These values used for computation are

explicitly writte Chapten i r Seve whicn i h testing result presentede sar .

If a position estimate without sensor constraints is acceptable, the routine tries to

update sensor measurement errors and heading. First, it initiates the Kalman barometric

height error corrector usin n updatea g S heightGP d . Then e Kalmath , n gyro error

corrector is activated if the receiver is stationary, i.e. the reference heading change is zero.

Finally, it determines an estimated maximum GPS heading error with respect to the

velocity of the vehicle as

=s m. - i ——————P0fs, J»0«.-— ff-^(6.1) 84

Kalman Measurement Filters Get Filtered Barometer Height and Gyro Heading Rate

Standard Least Squares Estimator (No Constraint)

Good Position Estimate?

Kalman Barometer Apply Barometed ran Error Corrector Gyro Error Update 8/24 Corrections

Kalman Heading Vehicle Estimator with Gyro tationarv? Data

Kalman Gyro Error Corrector Updat) e86

Previous Position Available? No Is Last Position Goo Vehicld& e peed Reasonable"£ i Apply Gyro Error Sensor Constraint Sensor Constraint Corrections Least Squares Least Squares Estimator Using Estimator Using GPS, h ,© GPS, h Kalman Heading Kalman Heading b b Estimator with Estimator with Gyro GPS Data Data

No Position Available at This Epoch

Figur Flowchar2 e6. Sensof o t r Constraint Least Squares Position Estimator 85

Kalman Measurement Filters Get Filtered Barometer Height and Gyro Heading Rate

Standard Kalman Position Estimator (No Constraint)

Good Position Estimate?

Kalman Barometer Apply Barometed ran Error Corrector Gyro Error Update Corrections

Kalman Heading Estimator with Gyro Data

Kalman Gyro Error Corrector Update

Previous Position Is Last Position Available? No Good & Vehicle Reasonabld ee e

Apply Gyro Error Sensor Constraint Sensor Constraint Corrections Kalman Position Kalman Position Estimator Using Estimator Using GPS, h ,® GPS, h Kalman Heading Kalman Heading b b Estimator with Estimator with Gyro GPS Data Data

Positioo N n Available at This Epoch

Figure 6.3 Flowchart of Sensor Constraint Kalman Position Estimator 86

where

8 Pars* S' *».*-! GPS P°Siti°n eiTOr at '

vk vehicle velocit t tya k .

This erro inversels ri y proportiona vehicle th o t l e velocity. Therefore reasonabla , e vehicle

velocity yield acceptabln sa headingS erroe GP th belos f ri I . wpredeterminea d threshold, datS uses ai GP updato dt headine eth s ga

where

£, £_! latitude position estimat d t kt _etan a k } ,

^AA-I longitude position estimat fd t _jt tean a k.

Otherwise, the latest gyro heading change, which is filtered and corrected at an earlier

stage appendes i , lase th t headino dt g

(6.3)

headine Th thes gi n filtereKalmae th y db n heading estimator with appropriate parameters. 87 algorithe Th m constantly monitorsolutioS GP e nsth whethe error-fres i t ri r noteo .

The error may be exposed as excessively large range residuals, intolerably high dilution of

precision (DOP) e.g. GDOP of over 10, large position change, or lack of solution due to

insufficient GPS range observations. If the position estimate, without sensor constraints, is

not acceptable e routinth , e initiates necessary procedure o perfort s m sensor constraint

positioning. First t updatei , headine sth g wit gyrha o heading change measurement. Next,

if a barometer measurement is available, the barometric height constraint is activated and s erroit s calculatei r d from equation (3.17) e routinTh . e then determine a previou f i s s

position is available to construct the heading row of the design matrix of equation (4.9). If

this is the case, the heading constraint is applied and its error computed from equation

(3.19). The augmented position estimator then computes a sensor constraint position

estimate. The result is evaluated and, if acceptable, returned.

e resul Th s consideredi t unacceptable whe o ) estimatn n(1 o t s givei ee du n

insufficient numbe measurementf o r ) divergenc(2 r so e (least squares only). Conditio) n(1

will be due to a shortage of GPS measurements. Note that with height and heading

constraints activated, there is still a minimum requirement of two GPS measurements for

computation. With only one constraint, three or more satellites are needed to complete the

calculation .cause e Conditiob y corruptey db ma ) rangesnS (2 dGP , failur correco et S GP t

ranges a poo, r initial position estimate, weak satellite geometry, inaccurate barometric

height and/or heading measurements, sensor error(s) and/or heading determination failure

or linear approximation errors. 88 Miscellaneou3 6. s Considerations

6.3.1 Position Estimator Breakdown Problem

Sinc standare eth d Kalman estimator cannot diverge, ther reaa s ei l possibilitf yo

poor estimat somf ei e measurement intolerable sar y erratic lease Th .t square Kalmad san n

estimator givy ema s very inaccurate estimates whe e qualitth n f sensoo y r constraint

information is poor. For the Kalman position estimator, a least squares estimator is used to

get the a priori estimate if (1) no a priori estimate is available, (2) the a priori estimate is

exceedingly inaccurate or (3) the filter update interval is too long, i.e. no estimate is

obtained for a long time. This feature helps the Kalman position estimator to recover

quickly.

6.3.2 Operational Considerations

Static positioning of several minutes under an open sky is used in the prototype

system to obtain the initial barometer and gyro measurement errors. It also gives the GPS

receiver tim adjuso et internas it t l receive timeS r clocGP . o Sinckt gyrea o sensee sth

rotatio e unitth f , no ther neea s o determini edt e initiath e l heading befor a headine g

constraint is applied. If the system is permanently attached to the vehicle, the last heading

ma e storedyb , thus eliminatin neee r redeterminingth dfo initian ga l heading each time.

However, this concep t vali thir no dfo s si t project since portabilit f primaro s yi y concern. therefors i t I e preferre r thifo ds syste mbegio t n operatio locatioa t na n wher elarga e

number of satellites are visible and to then drive into an urban area. 89

6.3.3 Real-Time Implementation

A real-time operatio t implementeno s nwa thir complexite dfo sth projeco t e du yt obtaininf o g differentia correctionS GP l urban si n areas. However t wouldifficule i , b t dno t

to modify the system for real-time operation. In land navigation applications, it is common

to update the position every second. With the current configuration, which includes five

two-stat eight-state on d ean e Kalman filters procese th , s tim approximatels ei y five epochs

per second using a 486DX- 100MHz IBM compatible computer. It takes less than 0.1

second obtaio st n GPS, baromete gyrd an ro data usin 386-20MHga compatiblM zIB e

computer e latencTh . f DGPo y S correction d transmittinan s g time shoul e alsb d o

considered, however, the operation of real-time system at 1 Hz may be feasible if 486DX-

100MHz or faster computer is employed.

6.3.4 Optimal Estimator Configuration

e systeTh m presented herein currently employs sensor information only when

either GPS-only position estimat t t sufficienaccuratrangeS no no GP s e i e r ar so o t et

comput esolutiona . Such syste mconsideres i d sub-optimal. This approac s takehwa n ni

this thesis in order to distinguish various sensor errors with GPS ones and to minimize the

position error induced by the sensor measurements. The system is considered theoretically

optimal whe observationl nal usee solutionr sar dfo timesl al t sa .

However arisine th , g proble optimae th f mo l syste mthas i sensof i t r measurements

are not as accurate as expected, they may deteriorate the position accuracy. Shown in 90 positioe th Figure ar n 4 errore6. s induce pooe th ry dheadinb g information durin none gth -

constraint positioning period. Position erroroptimae th f so l syste muce mar h higher than

sub-optimathose th f eo l (current) system smalles A . r weight (larger standard deviations )i

given to the heading measurement, the solutions become closer to ones of the current

system. Then, if good heading can be obtained during the non-constraint period, position

errors of the optimal system become considerably small as shown in Figure 6.5. Thus, it is

critical for an optimal system to determine the weight of sensor measurement during the

constraint-free period. Current error models are designed for the short-term constraint

positioning. They are based on the linear drift approximation and they cannot be used for

an extended period, e.g. longer than five minutes. Error models of higher order may be

needed for an optimal system.

Latitude Longitude

A -r

Heading error standard deviation Heading error standard deviation (deg) (deg) Figure 6.4. Position Error of Optimal Estimator with Poor Initial Heading 91 Latitude Longitude

Optimal

current Heading error standard deviation Heading error standard deviation (deg) (deg) Figure 6.5. Position Error of Optimal Estimator with Good Initial Heading 92 CHAPTER SEVEN

SYSTEM TESTING AND RESULTS

The sensor constraint portable GPS vehicle navigation system has been developed in previous chapters. The purpose of this chapter is to evaluate its performance. Generally, estimate systew s ne fro me m th coul e compareb d d with certain "reference" estimates given by a performance-proven precise navigation program. If the system could be operate idean a n dli environment, free from multipat witd han h excellent satellite coverage and geometry, we would be able to obtain a precise 3D reference trajectory using a DGPS navigation program such as FLYKIN™ (Lachapelle et al. 1996). However, this assumption does not hold in urban environments where ideal signal reception is not obtained.

DGPo Tw S field tests were r systecarriefo t mdou evaluationt a s e firswa Th t.

Springbank, Alberta, on June 29, 1996, in order to obtain clean, strong and sufficient GPS signal coverage. The reference trajectory was computed and an urban environment simulate rejectiny db g satellites belo wcertaia n cutoff angle secondowntowe n i Th .s dwa n

Calgary, Alberta Augusn o , t 17, 1996. Numerous building skywalkd san s preventee dth

GPS receiver from enjoying an optimal GPS coverage.

The data was processed in several manners. For this project, the unaided and barometric height constraint least squares solution e firsar s t presented. Then sensor constraint estimators (least squares and Kalman) are used to assess the improvement in terms of position accuracy and availability. 93 Urba1 7. n Environment Simulation

7.1.1 Route Description and Reference Trajectory

The first field test was carried out at Springbank, Alberta on June 29, 1996. The

system, describe n Chaptei d r s mounteTwowa a ,199 n i d6 Ford Thunderbirde Th .

reference statio locates nwa t controda l point 661-24.2 tese tTh . rout shows ei Figurn ni e directioa n i n s indicate ru na e rout7.1 s Th . ewa arrowy db Figurn i s e 7.1. Dats awa

collected every second. The location is very good for GPS positioning since there are few

obstructions along the test route. Most of the test route was in farmland except near

Calaway Park, where trees covered a portion of the sky. Sections A and B are marked in

Figurindicato t 1 e7. e sections magnifie laten i d r position plots numbee Th . f visiblo r e

satellite DOPd san showe sar Tabln i e Figur7.d 1an e 7.2.

A Reference Station Start / Stop L Springbank

Control Pointy,I* SectionA ...... *s 661-24.2 |« • '"^fcj^i: ———— ^^ " * " " * -200:- r^ —^ .....^. Y -400 • • ^ -60- 0 Section : B : "S -800 • | -100CL Trans-Canada Highwa y : * -1200- Calaway: 1% • -1400- Park : p -* -ifinn. 200 400 600 800 1000 Easting [m] Figur Tes1 e7. t Rout Simulatior efo n 94

Table 7.1. Satellite Coverag DOPd ean , Springbank, June 29,1996 Total Epochs # of Satellites GDOP NDOP EDOP VDOP (1-se6 35 c intervals) 5-8 1.7-5.8 0.7-2.3 0.6-1.4 1.3-4.1

10 30n r : ———— • 9 CO v. 25 J •& CD •-«• -Q ^CD f^ - 7 CD § 20- -^* <. : —— : : —— : :J ——, : : —— :: —— : - 6 CD

£ ir ^J ' *J \J co a. ^S 4 |io- *O CD CD CD -Q o 2 - 1 ^

n _ 1 I 1 1 I 1 1 1 1 1 1, 1 1 1 I 1 1 1 1 1 1 1 1 1 1... 1 L 1 1 \ 1 I 1 \ 1 1 I .1 -1 —— l—.J. -J,....J.,._ - n 573950 574000 574050 574100 574150 574200 574250 574300 574350 574400 TimeGPS [s]

Figure 7.2. Visible Satellites, Springbank, June 29,1996

e referencTh e trajector s obtainewa y d usin o NovAtetw g l GPSCard™ 951R receivers with FLYKIN™ double difference, carrier phase, float ambiguity solutions

(Lachapell t alee . 1996). With these receivers accurace th ,positio e th f yo n estimate given by this program is known to be decimetre level, whereas C NAV™ gives an estimate 3 accuracy at the metre level with carrier phase smoothed range observations (Cannon &

Lachapelle 1992). Therefore, disagreemene th t between thes o solutionsetw idean a n li , environment, should not exceed several metres. FLYKIN™ and C NAV™ solutions were 3 95 Table 7.2. Position Estimate Difference between SEMIKEV Cd ™3NAVan ™ Solutions, Springbank, June 29,1996 Latitude Longitude Height Mea] n[m -1.68 0.09 -0.57 Standard Deviation [m] 0.19 0.14 0.21 Max. Difference [m] -2.39 -0.60 -1.35 Min. Difference [m] -1.41 0.00 -0.18

compared to validate this assumption. The results are shown in Table 7.2. The double difference float ambiguity solution was employed for FLYKIN™ and the single difference carrier phase smoothed code solution chose Cr 3nfo NAV™ meaA . ne biath f 1.6n so i 7m latitude component is observed. However, the standard deviation of the position differences is 19 to 21cm. Since the desired accuracy of the sensor constraint positioning system is 10 metres DRMS, the reference trajectory obtained with FLYKIN™ is accurate enough to determine the accuracy of the system. For instance, standard deviations of approximatel metrey7 latitudn si longitudd ean e would yiel DRMda S metres0 erro1 f ro .

Parameters used for computations are listed in Table 7.3 (error models) and Tables

7.4 to 7.6 (Kalman filters). Equations (4.12) to (4.15) are used to compute GPS measurement variances. Equations (3.19 d (4.16 an e )use r barometriar )fo d c height measurement variances. Equations (3.20), (3.21 (4.17d an )e use r gyrar ) dfo o heading measurement variances. These measurement variances are employed in the augmented position estimato obtaio rt n constrained solutions parameter f same o t Th .e se usee r sar dfo both simulations and downtown testing. These values are selected such that the solutions fro Kalmae mth n estimato comparable rar thoso et e fro lease mth t squares. Thus, solutions 96 Table 7.3. Parameters Use Erron di r Models

Barometric height offset error efc m 1.0

Barometric height drift rate efc m/s 0.01667

Gyro heading rate offset error sg rad/s 0.05

2 Gyro drift error eg rad/s 0.01

Initial heading error ee rad tan'O.O/v) wher velocits i vehiclee v th f yo e

GPS code measurement error ap m 2.0 range carrieS GP r phase measurement errom r ae 0.02

GPS ephemeris error a6p + a6dr m 6.0

Table 7.4. Parameters Use Kalman di n Position Estimator Description Latitude Longitude Height Clock offset Time correlation P 1/s 1.0 1.0 1.0 1.0 Spectral density, position q m2/s 400.0 400.0 400.0 400.0 Spectral density, rate q m2/s3 100.0 100.0 4.0 4.0

from both estimators shoul e similab d r unless other factor alter one's solutions from

another. 97 Table 7.5. Parameters Used in Kalman Barometer Measurement and Correction Filters Description Barometer measurement Barometer correction Time correlation p 1/s 1/5 1/30 Spectral density q m2/s3 1.0 1.0 Measurement error r m 1.0 1.0

Table 7.6. Parameters Used in Kalman Gyro Measurement, Correction and Heading Filters

Description Gyro measurement Gyro correction Heading Time correlatios 1/ nP 1.0 1.0 1/3 Spectral density q rad2/s3 25.0 1.0 9.0 Measurement error r rad 1.0 0.5 1.0

7.1.2 Virtual Wall Concept

A conventional satellite rejection routine setsingle son e cutoff angl rejectd ean l sal satellites below this cutoff angle. Suc hsatellita e rejection routine doe t ideallsno y simulate an urban environment. In an urban environment, weak satellite geometry is frequently observed in terms of the cross-track satellite geometry, the direction perpendicular to the vehicle trajectory e virtuaTh . l wall concep s introducei t thin i d s project. This routine computes a cutoff angle based on simulated obstructions along the street, parallel to the vehicle trajectory. Figure 7.3 illustrates the virtual wall concept. 98

East

Figure 7.3. Virtual Wall Concept

Given a cross-track cutoff angle acr, the relation between the distance to the walls perpendicula trajectore th o rt heighwalle e yth th f d dso tCTs han i

h tan(occr) = (7.1) 1CT 99

Assuming dCT is a constant, the height of the walls may be computed as

h = ten(cnCT)'dCT. (7.2)

Given a vehicle's heading at /, , 0,. , and the azimuth of a satellite &k , the relative azimuth

satellita f o e with respec vehicle'e th o t s headin obtainee b gy j kma s da

Then distance th , e fro vehicle wallme th th t thiso a et s relative azimuth gives di k y nb

Finally, the cutoff angle of a satellite a^ may be computed as

a, = tan"1 --. (7.5)

elevatioe th f I satellita f no less ei s than a^, this satellite informatioe t useth r no dfo s n i

position computation. This algorithm simulate urbae sth n area well. However realitn i , t yi 100 t likelisno y thawile on lt encounte continuoua r s arra buildingf yo same th t esa heightt I .

woul desirable db chango et distance eth e fro obstructioe mth heighs it d thao e s tnan th t

algorithm could create more realistic situation.

7.1.3 Simulation Results

A cross-trac degree0 6 kd cutof an applies si tes e 5 4 fth t , anglo datdt 30 f aeo using

virtuae th l wall satellite rejection angle algorithm described above. This correspondso t

wall height f 5.77so , 10. 17.3d 0an 2 metres assumin gcross-traca k distanc wale f th o l o et

dCT -10.0 m. To simulate intersections where better satellite coverage is expected and

the vehicle is often brought to a stop, the satellite rejection algorithm is disabled when the

vehicle speed is less than 10 metres per second. The unaided least squares, barometric

height constraint least squares, height and gyro heading constraint least squares and height

and heading constraint Kalman filter solutions are compared.

Figures 7.4 shows the visible satellites using the virtual wall concept at cross-track degree0 6 d cutofan s 5 wit4 f , degreh0 angle 30 f o se vehicle azimuth (heading north-

degree0 south9 d )an s vehicle azimuth (east-west). Dotted figure e lineth n si s indicate eth

cutoff thresholds generated by the algorithm. There are sufficient satellites when the cross-

track cutoff angldegrees0 3 s ei . Three satellite wead san k geometr observee yar d when

the cutoff angle is 45 and 60 degrees and the vehicle trajectory is east-west. Two satellites

are visible when the cutoff angle is 60 degrees and the vehicle trajectory is north-south.

Note that some satellites close to the threshold line may not be observed at a particular

instance sinc threshole eth d angl functioa vehicls e i th f no e headin satellitd gan e azimuth. 101

Cutoff Angle = 30°, Azimuth = 0° Cutoff Angle = 30°, Azimuth - 90°

Cutoff Angl 45°e= , Azimut ° 0 h= Cutoff Angl 45°e= , Azimut° 90 h=

Cutoff Angl 60°e= , Azimut ° 0 h= Cutoff Angl 60°e= , Azimut° 90 h= Figure 7.4. Visible Satellites with Virtual Wall Concept, Springbank, June 29,1996

The numbe satellitesf o r , dilutio precisiof no rangd nan e residual monitoree sar o dt r mor o determin S solutionf e theso eGP on ee e f qualit I th th .eexceed f o ye th s 102 predetermined threshold value, the barometric height and / or heading constraint are used improvo t positionine eth g accuracy threshole Th . d value listee sar Tabln di e 7.7. There

may be a more effective strategy to properly determine whether the GPS estimate is

acceptable. This topic is left for future investigation.

Table 7.7. Threshold Value Acceptablr sfo EstimatS eGP e

Number of Satellites >4 HDOP = [NDOP2 + EDOP2]172 Range Residuals (magnitude) <5.0 metres

30 -,j _ ;- 10 9 to v. 25 0) 8 »*^> -Q Q) - — n n H . f r-f; • 7 "CD 1 20 CO 6 Q) 8^: 1c : | j jy M| I i i b ^ O j§ 10 - ^ ^ ^) 3 d5 CD 2 "c CO 5n ^^""^ ^? 1 ^

n . , 1 !.! I ,i J 1 I * ,!1 , 1 , . 1k 4. .1.....J. _J_ . i 1, J ———— 1 • ,i ————— I , 1 , ————— 1 ————— , ———— L i. l..,,,.J ———— . ———— I .n 573950 574000 574050 574100 574150 574200 574250 574300 574350 574400 TimeS ] GF [s

Figure 7.5. Visible Satellites, Springbank, June 29,1996. (30° Cross-Track Cutoff Angle) 103

573950 574000 574050 574100 574150 574200 574250 574300 574350 574400 TimeS ] GP [s

Figure 7.6. DOPs, Springbank, June 29,1996. (30° Cross-Track Cutoff Angle, Unaided Least Squares)

7.1.3.1 Cross-Track Cutoff Angle of 30 Degrees

e cross-tracAth t k cutoff 0 degreesangl3 f o e receive th , r could observa e sufficient number of GPS satellites all the time to compute position estimates. The number of observed satellites was four or more for the entire test as shown in Figure 7.5. In Figure

7.6, one sees, however, that poor satellite geometry developed at the end of the session.

This occurred when the test vehicle was in Section A of Figure 7.1. It manifests itself as an unreasonably high NDOP. At that time the observed satellites, PRN 2, 5, 7 and 9, are almos positio 2D sho t7.8 linew the Figuren and up. dplot 7.7 s using unaided least square forware th r reversd sfo dan e segmen run e seee th f .sOn o t from Figur tha8 e e7. th t position estimates stray northerly and southerly from the reference trajectory (dotted line) by about two metres and there is a discontinuity due to a satellite constellation change. 104

-400

-600

•S -800

-1000

-1200

-1400

-1600 200 400 600 800 1000 Easting [m]

Figure 7.7. 2D Position, Springbank, June 29,1996. (30° Cross-Track Cutoff Angle, Unaided Least Squares)

200 0 60 400 800 1000 Easting [m]

Figure 7.8 PositionD .2 , Sectio , SpringbanknA , June 29,1996. (30° Cross-Track Cutoff Angle, Unaided Least Squares) 105 Table 7.8. Position Estimate Difference Between Reference Trajectory and Unaided Least Squares Solutions, Springbank, June 29,1996. (30° Cross-Track Cutoff Angle) Latitude Longitude Height Mea] n[m -2.02 -0.44 -0.51 Standard Deviatio] n[m 1.46 0.61 0.37 Max. Difference [m] 3.44 1.57 1.58 Min. Difference [m] 0.05 0.00 0.00 Position Availability 100 %/356 epochs

60

20-: £~"*-2S74pO fc O 574050—' 374100 574150 574200 574250 574300 57435C 574400 -40 -60 GPS Time [s]

20

O 574DOO 57405& 57435C 574400 •J -20± GPS Time [s]

574150 ^574^00^-67^250 574300^ 574350,— 574400

GPS Time [s]

Figure 7.9. Unaided Least Squares Position Errors, Springbank, June 29,1996. (30° Cross-Track Cutoff Angle) 106 Figure 7.9 shows the differences between the reference trajectory and the unaided least squares solutions with 2a error envelopes. 2a estimated error envelope obtainee sar d from Cgcovariance th , e matrix associated with position estimates lease th tr squaresFo . ,

Cg may be computed by (Krakiwsky 1990)

CJ=[ATC;'A]~' (7.6) where

A design matrix from equations (4.7) to (4.9),

C^1 weight matrix from equation (4.10).

For the Kalman filter, Cg may be obtained from the covariance matrix associated with updated estimates P^. of equation (5.9). The 2a error corresponds to the 95% probability region in 2-D, therefore 95% of errors should be within the envelope.

As seen in Figure 7.9, the differences between the reference trajectory and unaided least squares solutions are within the envelopes. The size of envelopes roughly corresponds to that of DOPs comparing Figures 7.6 and 7.9. The position estimator expects large position displacements when large DOP observede sar noticee On . s thae th t latitud longitudd ean e position estimate t maintaino o sd n consistencd en e stard th an t y a of the session. This agrees with the poor DOPs seen in Figure 7.6. The accuracy of the position estimates is still reasonable as summarized in Table 7.8. The DRMS is approximately 2.6m. 107

Height constraint least squares solutions are then examined. Although four or more satellites were observe entire th r ed fo session e algorithth , m employe e heighdth t constraint when the HDOP computed with GPS data only was greater than 10. Figure

7.10 show DOPe sth s wit heighe hth t constraint DOPe Th significantle . sar y decreased, especially the VDOP. One property of height constraint positioning is that with height information, the VDOP is always small, close to 1.0. The additional information also contribute improven a o st d NDO EDOd Pan explaines Pa Tann di g (1996) resulta s A . , the GDOP is reduced to about 12, from a maximum of over 25 as shown in Figure 7.6.

Figures 7.11 and 7.12 are 2D position plots with height constraint least squares positioning. Estimates are not superior to those of unaided least squares. They seem to be

30T

25 - c; .O .£ 20 -- O

+ 5 s1 ^ O

,3 10 3 5 --

573950 574000 574050 574100 574150 574200 574250 574300 574350 574400 TimeS ] GP [s

Figure 7.10. DOPs, Springbank, June 29,1996. (30° Cross-Track Cutoff Angle, Height Constraint Least Squares) 108

Table 7.9. Position Estimate Difference Between Reference Trajectory and Height Constraint Least Squares Solutions, Springbank, June 29,1996. (30° Cross-Track Cutoff Angle) Latitude Longitude Height Mean [m] -1.38 -0.17 -0.67 Standard Deviation [m] 2.87 1.15 0.49 Max. Difference [m] 9.35 4.05 2.37 Min. Difference [m] 0.07 0.00 0.00 Position Availability 100% 7356 epochs

wea wanderingd kan . Comparing Figure 7.1 Figuro 2t e 7.8 seee ,on s thasolutione th t f so

Figure 7.12 deviate more than e thosinferioth f Figur o eo t re e du 7.8 e b . Thiy ma s barometric height accuracy to the GPS height. The height error in Figure 7.13 is larger than tha Figurn i t e 7.9. Figure 7.13 show difference sth e betwee reference nth e trajectory and the height constraint least squares solutions with 2a estimated error envelopese Th . difference withie ar s envelopese nth . These envelope significantle sar y smaller than those of unaided least squares (Figure 7.9) due to the improved redundancy. Since the sensor error models take cumulative errors into account as shown in equations (3.19) to (3.21), the estimated position errors should grow accordingly whe constrainte nth e appliedsar .

As a consequence, estimated height errors are gradually increased at the beginning and end of the session as seen in Figure 7.13. As shown in Table 7.9, the latitude and longitude errors reach 9.35 and 4.05 metres, respectively. The DRMS is approximately 3.4 metres. 109

-200

-400 "81 W I* -800

-1000

-1200

-1400 -

-1600 200 400 600 800 1000 Easting [m]

Figure 7.11. 2D Position, Springbank, June 29,1996. (30° Cross-Track Cutoff Angle, Height Constraint Least Squares)

0 30 0 20 100 0 60 0 50 0 40 0 90 100 00 80 0 70 Easting[m]

Figure 7.12 PositionD 2 . , Sectio , SpringbanknA , June 29,1996. (30° Cross-Track Cutoff Angle, Height Constraint Least Squares) Height Difference Longitude , Difference [m] 3 cr5c*

^4 wh-i W 'w cf5* ^^2^ o . n2 8 8 o•^ 790 Oa S o- ss. 3o n!*r ?CM O s I I " CD CD 5? 3?

3> vo »g Ill Both height and heading constraints are used next. The observations, sensor measurements and constraint positioning periods of least squares are identical to those of the Kalman filter. As a consequence, the DOPs are also identical. Figure 7.14 shows the

DOP plot with height and heading constraint positioning. One notices that the GDOP is further reduce satellit e abouo dt Th . 8 te geometr effectivels yi y enhance heighy db d an t heading constraints.

e leasTh t squares estimato s firsi r t employed. Figures 7.1 D d 7.152 an e 6ar positio ne heigh th plotd headin f an o ts g constraint least squares solutionso Tw . discontinuities are observed. These are caused by the GPS-only position updates. Errors at these points are mainly due to the sensor heading error, which grows in a quadratic fashion. The sensor heading error, which affects the horizontal position accuracy, may be seen more obviously in Figure 7.17. Latitude error grows rapidly towards the end of the trajectory, althoug maximue hth m error standard san d deviations show Tabln ni e 7.1e 0ar still well within the requirements. The resultant DRMS is approximately 2.8 metres.

Table 7.10. Position Estimate Difference Between Reference Trajectord yan Heigh Headind tan g Constraint Least Squares Solutions, Springbank, June 29,1996. (30° Cross-Track Cutoff Angle) Latitude Longitude Height Mean [m] -1.87 -0.35 -0.67 Standard Deviation [m] 1.91 0.77 0.48 Max. Differenc] [m e 5.89 2.39 2.35 Min. Differenc] [m e 0.08 0.00 0.00 Position Availability 100 %/356 epochs 112

30T

25 c: .o .<2 20 -- O

15 -- O oc: 10 Q

573950 574000 574050 574100 574150 574200 574250 574300 574350 574400 GPS Time [s] Figure 7.14. DOPs, Springbank, June 29,1996. (30° Cross-Track Cutoff Angle, Heigh Headind tan g Constraint Least Square Kalmad san n Filter)

Figure 7.17 shows the difference between the reference trajectory and the height

and heading constraint least squares solutions with 2a error envelopes. Error envelopes in

Figure 7.17 are reduced as compared to the use of the height constraint positioning in

Figure 7.13 positiol Al . n error withie sar erroe nth r envelopes erroe Th . r envelope growth e sessioth f o s e causeerroi n th d ry en b d increas e e heighth th d headint a n i an et g

constraints as a function of time. Thus, the sensor error models described in Chapter

Three tak actuae eth l errors into account very well.

The Kalman filter estimator was also used. Figures 7.18 and 7.19 show 2D

position heighe plot th headind f an o st g constrain Kalmae Th t n filter solutions. Kalman

filter solutions do not show a position discontinuity. This smoothness is a significant 113 advantage of Kalman filters. As shown in Table 7.11, the accuracy and standard deviation e botar h superio e leas o thost th e rsmoothe tf th o esquare o t e ddu s solutionse Th .

maximum latitud longitudd ean e error 4.1 e 1.4d sar 5an 2 metres, respectively DRMe Th . S

is approximately 2.6 metres. The difference between the reference trajectory and the

height and heading constraint Kalman filter solutions with 2a estimated error envelopes

are shown in Figure 7.20. The errors are mostly within error envelopes, indicating the

filte workins i r g properly erroe Th .r envelope similae sar thoso t r e generate lease th ty db

squares solutions.

The accuracy of constraint positioning largely depends on the quality of calibration

and operation time. Prolonged sensor constraint positioning shoul avoidee db d since eth

sensor errors are cumulative.

Table 7.11. Position Estimate Difference Between Reference Trajectord yan Height and Heading Constraint Kalman Filter Solutions, Springbank, June 29,1996. (30° Cross-Track Cutoff Angle) Latitude Longitude Height Mean [m] -2.11 -0.45 -0.67 Standard Deviation [m] 1.33 0.58 0.51 Max. Differenc] [m e 4.15 1.42 2.42 Min. Difference [m] 0.00 0.00 0.00 Position Availability 100 %/356 epochs 114

-200

-400

-600

5 -800

-1000

-1200

-1400 -

-1600 200 400 600 800 1000 Easting[m]

Figure Position7.15D 2 . , Springbank, June 29,1996. (30° Cross-Track Cutoff Angle, Heigh Headind an t g Constraint Least Squares)

-100 200 400 600 800 1000 Easting [m]

Figure Position7.16D 2 . , Sectio Springbank, nA , June 29,1996. (30° Cross-Track Cutoff Angle, Height and Heading Constraint Least Squares) Height Difference Longitude , Difference[m]

M

n.2 s 8a "-5'

3 ng I I e ••• CD CD 5? 116

-1400

-1600 200 400 600 800 1000 Easting [m]

Figure 7.18PositionD 2 . , Springbank, June 29,1996. (30° Cross-Track Cutoff Angle, Height and Heading Constraint Kalman Filter)

-100 0 90 100 0 80 0 70 0 60 0 50 0 40 0 30 0 20 0 10 0 Easting [m]

Figure 7.19. 2D Position, Section A, Springbank, June 29,1996. (30° Cross-Track Cutoff Angle, Heigh Headind an t g Constraint Kalman Filter) TO Height Difference Longitude Latitude Difference = 3 [m] , Difference[m] ^5 C) Cjj ^5 ^D CD c5 iMMtnn&Ml,M,!,,,,!,,,,| O w 2 TO*

. %2 O 3 -Q8 . O TO =' £ O" 3 f p TO H s n O (D a?s§ >*W o 3 5 8-Srl ^H 2' I CD <&

3? - >5 s ^> I, TO ?N as T **

o S-* o* 9 118 7.1.3.2 Cross-Track Cutoff Angl Degree5 4 f eo s

cross-trace Ath t k cutoff degrees5 angl4 f eo receivee th , longeo n r r observea sufficient numbe f satelliteo r entir e th r es fo operation . Durin periodso gtw numbee th , f o r observed satellites drops to three for about 40 to 50 seconds as seen in Figure 7.21. The visible satellites during this outag . There9 perioalsd e ear an oPR e 7 shord ar , N 2 t outage period e middle sessionth th DOPn e f i so e Th . s during these outage periods become infinit sees a e Figur n ni e 7.22. Note that Figur efollowine 7.2th d a plotP 2 an e gDO sus logarithmic vertical scale. Figures 7.2 7.2d 3an 4 show thae outagth t e periods cause blank position si n estimates. Figure , positio25 n difference plot with 2a error envelopes, shows that the position displacements stay within the envelopes when solutions are available. The standard deviations are 0.35 to 0.78 metres and the maximum errors are

1.1 3.4o 2t 4 metre shows sa Tabln i e 7.12 DRMe Th . abouSs i t 2.9m. Note that although the standard deviations in Table 7.12 are small, position availability is reduced to 73.9% of time or 263 out of 356 epochs.

Table 7.12. Position Estimate Difference Between Reference Trajectord yan Unaided Least Squares Solutions, Springbank, June 29,1996. (45° Cross-Track Cutoff Angle) Latitude Longitude Height Mean [m] -2.65 -0.64 -0.55 Standard Deviation [m] 0.78 0.46 0.35 Max. Difference [m] 3.44 1.12 1.51 Min. Differenc] [m e 0.30 0.00 0.00 Position Availability 73.9% 7263 epochs Satellite PRN Number -»• -» ro ro co Dilution of Precision O Ol o 01 o 01 o

9Q U-l e o 8 n a 3

3 §' oro. 3* CD ^« (TOO" Cl as e -t f* Ss?" w3' > g re °[1 5" v2, 6H S aCs ON 8 •n VO ON o -»• to Ol O) -«J 00 <£> -» O Number Visibleof Satellites 120

-200

-400

•g- -600 "*^d O> •S -800 i -1000

-1200

-1400

-1600 200 400 600 800 1000 Easting[m]

Figur ePosition D 7.232 . , Springbank, June 29,1996. (45° Cross-Track Cutoff Angle, Unaided Least Squares)

-10 -I—— -20 -L __ fen

-OVJ • ""•-. --.~P EC* -40*rU - : D 0) "-- - -, .S -50 - no, « msP | -60 - v¥ 1 -70- "? an ? -yu 9 -100 -:————————— () 2()0 4(30 6()0 8C)0 10 Easting[m]

Figur ePosition D 7.242 . , Sectio , SpringbanknA , June 29,1996. (45° Cross-Track Cutoff Angle, Unaided Least Squares) oro e Difference Longitude Latitude Difference , Difference[m] , , M o cn] o 01 o 8 ^^ o g 8 d I . . . . I M

0-g 3 S Ol ws -t 5! O O 1 * 3' I I |l CD CD CD 3? -t ~h 9 >?*

^i 6 TO Jl

VO ON 122 Next, height constraint least square uses si r computation dfo . Satellites PR7 N2,

and 9 form a weak geometry at the beginning and end of the session. Consequently, very

large DOP observee sar s seeda Figur n ni e 7.26DOPe Th . slon o durintw g e outaggth e

periods which correspond to Section A grow at a very rapid rate. NDOP is larger than

EDOP during these periods since the satellites are aligned roughly in an east-west

direction. This satellite constellation is typically seen in urban environments due to

buildings along the road (Hayashi 1996). NDOP and GDOP exceed 100.

Figure spositio D 2 7.2 e d 7.27th nan e 8plotsar . Poor satellite geometrs i y

reflected in the horizontal position errors seen in these figures. The differences between referencthe e trajector heighyand t constraint solutions with 2a error envelope showsare n

in Figure 7.29 envelopee Th . latitudf so longitudd ean vere ear y large durin constraine gth t

positioning period suggesting a poor geometry which results in a poor horizontal

positioning accuracy. The maximum position error reaches 41.1 metres in latitude and

16.7 metres in longitude as shown in Table 7.13. The DRMS is approximately 9.6 metres.

Latitude and longitude solutions oscillate at larger magnitudes than those with a cross-

track cutoff angle of 30° as seen in Figure 7.29. This is probably caused by a poorer

horizontal satellite geometry heighe Th . t erro withis ri reasonablna e level maximue Th . m

heigh te VDO 7 metreth erro2. d s s approximatelPi i ran s y 1.0e heighTh . t constraint

maintains the height error within an acceptable level, however, it may not improve the

horizontal position accuracy significantly. There is one epoch when the solution did not

converge. The position availability is 99.7% of time or 355 out of 356 epochs. 123

1000 -r

c: 100 .o

o 10 -: c ,0

Q 1 -

0.1 573950 574000 574050 574100 574150 574200 574250 574300 574350 574400 TimeGPS [s] Figure 7.26. DOPs, Springbank, June 29,1996. (45° Cross-Track Cutoff Angle, Height Constraint Least Squares)

Table 7.13. Position Estimate Difference Between Reference Trajectory and Height Constraint Least Squares Solutions, Springbank, June 29,1996. (45° Cross-Track Cutoff Angle) Latitude Longitude Height Mea] n[m -1.20 -0.11 -0.68 Standard Deviatio] n[m 8.85 3.63 0.65 Max. Difference [m] 41.12 16.67 2.69 Min. Difference [m] 0.09 0.00 0.00 Position Availability 99.7 % / 355 epochs 124

200

0

-200

-400

I i -1000

-1200

200 0 60 400 800 1000 Easting [m]

Figure 7.27. 2D Position, Springbank, June 29,1996. (45° Cross-Track Cutoff Angle, Height Constraint Least Squares)

0 100 200 300 400 500 600 700 800 900 1000 Easting [m]

Figure 7.28. 2D Position, Section A, Springbank, June 29,1996. (45° Cross-Track Cutoff Angle, Height Constraint Least Squares) Difference Longitude Latitude Difference [m] Difference [m] o 01 o 88 8 8 Q8 o 8 OTQ S |.M.I,MJfe,l,ll.,,|l,l.|l,l,|

VO = . 2 ,—s t4*n. c/3 cfqsr* nl. o •t 9 O 2 TO S

O O g CO I1 I I K» CD CD CD 57 126 Heading constraint is then applied in addition to height constraint. Both the least

squares and Kalman filter solutions are examined. Figure 7.30 shows the effectiveness of

adding the heading constraint. The NDOP and GDOP are now reduced to approximately

10. Comparing Figure 7.30 with Figure 7.26, the heading constraint improves the NDOP

s wel a s EDOPa l e headinTh . g constraint effectively improve e horizontath s l satellite

geometry.

The position accuracy is also improved. Figures 7.31 and 7.32 are 2D position

plots with heigh headind an t g constraint least squares solutione Th . consistente sar e Th .

standard deviations have improved to 1.79 metres in latitude and 0.84 metres in longitude

sees a Tabln ni e 7.14 DRMe Th . approximatels Si metres2 y3. longitudA . e erro f 4.8o r 6

metres in the middle of the session is seen in Figure 7.33. This error exceeds the 2o error rangS GP ecausee e b error envelopth y y db ma s whicd t modeledean no s hi . Since thers ei

less redundanc solutionn yi urban si n environments, these solutions become vulnerablo et

range errors. epocThere on s hei whe solutioe t convergenth no d ndi . Consequentlye th ,

position availability with height and heading constraint least squares is 99.7% of time or

epochs6 35 f o 35.t 5ou

Table 7.14. Position Estimate Difference Between Reference Trajectord yan Heigh Headind tan g Constraint Least Squares Solutions, Springbank, June 29,1996. (45° Cross-Track Cutoff Angle) Latitude Longitude Height Mean [m] -2.39 -0.61 -0.68 Standard Deviation [m] 1.79 0.84 0.64 Max. Differenc] [m e 6.88 4.86 2.67 Min. Difference [m] 0.08 0.00 0.00 Position Availability 99.7 %/355 epochs 127

1000 T

c: 100 .o .w 0

s^ 10 O c: .Q

1 -:

0.1 573950 574000 574050 574100 574150 574200 574250 574300 574350 574400 GPS Time [s] Figure 7.30. DOPs, Springbank, June 29,1996. (45° Cross-Track Cutoff Angle, Height and Heading Constraint Least Squares and Kalman Filter)

Figures 7.3 7.3d 4an 5 sho positioD w2 n plot f heigho s headind an t g constraint

Kalman filter solutions. Kalman filter solutions are smoother than least squares solutions due to the filtering process. The differences between the reference trajectory and height and heading constraint solutions with 2a error envelope showe sar Figurn i e 7.36. Errors are within the envelopes except for the longitude error in the middle of the session. The error envelopes produced by the least squares and Kalman solutions are comparable. Table

7.15 shows larger position displacements compared to Table 7.14. The latitude and longitude maximum position displacements of Kalman filter solutions are 7.31 and 11.11 metres, respectively, while those of least squares solutions are 6.88 and 4.86 metres. This may be caused by the Kalman filter mechanism, which does not have a divergence state as 124. ^8 vs discussed in Chapter Six. It appears that the Kalman filter produces solutions even with extremely poor measurements. The range residual checking algorithm did not warn of contaminated range measurements. More stringent error detection routines may be required. Position availability for height and heading constraint Kalman filter positioning is

DRMe 100%Th .approximatels Si metres2 y3. . Position availabilit ° cross-trac45 a t ya k cutoff angl summarizes ei Tabln di e 7.16.

Table 7.15. Position Estimate Difference Between Reference Trajectord yan Height and Heading Constraint Kalman Filter Solutions, Springbank, June 29,1996. (45° Cross-Track Cutoff Angle) Latitude Longitude Height Mea] n[m -2.47 -0.68 -0.70 Standard Deviatio] n[m 1.63 1.05 0.63 Max. Difference [m] 7.31 11.11 2.67 Min. Differenc] e[m 0.00 0.00 0.00 Position Availability epoch6 35 10 / 0s %

Table 7.16. Position Estimate Availability, Springbank, June 29,1996. (45° Cross-Track Cutoff Angle) Estimation Mode Position Estimate Availability DRMS Unaided Least Squares 263 epochs 773. 9% 2.9m Height Constraint Least Squares 355 epochs 799.7% 9.6m Sensor Constraint Least Squares 355 epochs 7 99.7% 3.2m Sensor Constraint Kalman 3 56 epochs 7 100% 3.2m 129

QBQEU EDOOOQOQJ3C HftP-fflflBO -200

-400

•g- -600

5 -800

i -1000

-1200

-1400

-1600 200 400 600 800 1000 Easting [m]

Figure Position 7.31D 2 . , Springbank, June 29,1996. (45° Cross-Track Cutoff Angle, Heigh Headind an t g Constraint Least Squares)

-100 200 400 600 800 1000 Easting[m]

Figure 7.32. 2D Position, Section A, Springbank, June 29,1996. (45° Cross-Track Cutoff Angle, Height and Heading Constraint Least Squares) orq He/gfA)f Difference Longitude Latitude Difference c , Difference [m] o i . i . 1 1 . 1 1 1 . 1 1 1 . .. . . i

W 2. TO* *"tsr- as a n

g O O - 0=~ e 2a- I I £ iff CD CD CD o \o *+

IP aCs

O S W i 131

-1600 0 60 400 800 1000 Easting [m]

Figure 7.34. 2D Position, Springbank, June 29,1996. (45° Cross-Track Cutoff Angle, Height and Heading Constraint Kalman Filter)

-90 -100 0 60 200 0 40 800 1000 Easting [m]

Figure 7.35 PositionD 2 . , Sectio Springbank, nA , June 29,1996. (45° Cross-Track Cutoff Angle, Height and Heading Constraint Kalman Filter) TO Difference Longitude Latitude Difference 3 [m] , Difference [m] , , .[m] oO> No) T+qIj o -o» toO CoO

M QTQ p+ as a O 2. 330. O QTQ -• fO an?" cSw 2H *o s•

> ,.v o HBL* L? 9 'O 9 TO, OS g ^ 9 ^

U) to 133 7.1.3.3 Cross-Track Cutoff Angle of 60 Degrees

Many satellite ° cross-tracrejectee 60 sar a t da k cutoff angle. Figure 7.37 shows visible th e satellite° cross-trac60 a t a s k cutoff angle numbee Th . f visiblo r e satellites i s

three in Section A and one to two in Section B. Unaided least squares barely works in this

case. Figure 7.38 shows the DOPs and Figures 7.39 and 7.40 show the 2D position plots

for the unaided least squares solutions. Position determination is nearly impossible at a 60°

cross-track cutoff angle. Figure 7.41 shows the differences between the reference

trajectore unaideth d dan y solutions with 2a error envelopes. When solutione ar s

available, they seem goo s seeda Tabln ni e 7.1Figurd 7an e 7.41 e DRMTh . s abouSi t

2.0m. However positioe th , n availabilit onlepochss y6 i 35 y f 34.8o .4 %timf 12 o r eo

ou - - IU

^mim mim mmmfm 9 to v. 25 Q) i -Q '- r [~. n i • j.^ ~ n 7 'CD § 20- CO - 6 :Q ^ 15 5 CL 4 •^ 10 - *O Q) £CD -Q ; .' : •' '..'..''.i •. :•; : ' '. ! : ; 2 C CO 5- ^^ 1 •' ', •' :.'•.':' : ^ i >^^^ i '. ! ^ i U iii U LJ LJ LJ 1 ^

n - i < j i 1 i i I I i i i j i I I 1 1 i i j i 1 i I I I 1 i i i I 1 I i J, , i 1 i j I I n 573950 574000 574050 574100 574150 574200 574250 574300 574350 574400 TimeGPS [s] Figure 7.37. Visible Satellites, Springbank, June 29,1996. (60° Cross-Track Cutoff Angle) 134

Table 7.17. Position Estimate Difference Between Reference Trajectord yan Unaided Least Squares Solutions, Springbank, June 29,1996. (60° Cross-Track Cutoff Angle) Latitude Longitude Height Mean [m] -1.86 0.04 -0.59 Standard Deviation [m] 0.52 0.33 0.54 Max. Difference [m] 1.28 0.84 1.17 Min. Difference [m] 0.02 0.00 0.00 Position Availability 34.*5 %/ 124 epochs

1000

100 -: I 10 -: c; .O

1 -:

0.1 573950 574000 574050 574100 574150 574200 574250 574300 574350 574400 GPS Time [s] Figure 7.38. DOPs, Springbank, June 29,1996. (60° Cross-Track Cutoff Angle, Unaided Least Squares) 135

-200

-400

-600

-1000

-1200

-1400

-1600 200 400 600 800 1000 Easting [m]

Figure 7.39. PositionD 2 , Springbank, June 29,1996. (60° Cross-Track Cutoff Angle, Unaided Least Squares)

-90 -100 200 400 600 800 1000 Easting [m]

Figure 1AQ. 2D Position, Section A, Springbank, June 29,1996. (60° Cross-Track Cutoff Angle, Unaided Least Squares) TO C Height Difference Longitude Latitude Difference , Difference [m] ± [m] o enSJ] o en o I,,

o. o. ^ i o *+ 0 n- gC/3 o ^

O g o I

> " S 5 g

9 TaO1 S —f

vo ON

U) C7N 137 Height constraint least squares positioning is evaluated next. Figure 7.42 is the

DOP plot for height constraint least squares. Since the visible satellites in Section A are

identical to those for a 45° cross-track cutoff angle, we see the DOPs growing rapidly as

see Figurn ni e 7.26. NDO GDOd Pan P occasionally excee noticy o dma etw e 100 On .

outage periods caused by insufficient GPS observations.

Figures 7.43 and 7.44 are 2D position plots. Height constraint least squares

solutions for a 60° cross-track cutoff angle behave similar to those for a 45° cross-track

cutoff angle excep Section i t . TherenB positioo n , obtaineds ni . Figure 7.45 showe sth

differences between the reference trajectory and the height constraint solutions with 2a

error envelopes. The algorithm expects a large horizontal position error when the height

constraint is activated and widen the error envelopes accordingly. This error is largely due

to a very poor horizontal satellite geometry. The horizontal position accuracy of height

constraint least square s pooi s s seea r Tabln i n e 7.1Figurd 8an e 7.45e standarTh . d

deviation latitudf so longitudd ean 15.7e 6.0d ear 63an metres, while maximum errore sar

42.35 and 16.62 metres, respectively. The DRMS is approximately 17.5 metres. One may

notice larger latitude and longitude standard deviations in Table 7.18 compared to Table

7.13. This is due to a poor GPS coverage. Position availability is 58.2% of time or 207 out epochs6 35 f o . Therefore, height constraint improves position availabilit 23.4%y yb , from

34.8 %58.2%o t , althoug accurace hth t satisfactoryno s yi . 138

1000

c: .o 100 55 O . o c .o

573950 574000 574050 574100 574150 574200 574250 574300 574350 574400 TimeGPS [s] Figure 7.42. DOPs, Springbank, June 29,1996. (60° Cross-Track Cutoff Angle, Height Constraint Least Squares)

Table 7.18. Position Estimate Difference Between Reference Trajectory and Height Constraint Least Squares Solutions, Springbank, June 29,1996. (60° Cross-Track Cutoff Angle) Latitude Longitude Height Mean [m] 4.13 2.11 -0.93 Standard Deviatio] n[m 15.73 6.06 0.82 Max. Differenc] e[m 42.35 16.62 2.38 Min. Difference [m] 0.07 0.13 0.00 Position Availability 58.2 % / 207 epochs 139

-200

-400

.5 -800 € * -1000

-1200

-1400

-1600 200 400 600 800 1000 Easting [m]

Figure 7.43 PositionD 2 . , Springbank, Jun , 1996e29 . (60° Cross-Track Cutoff Angle, Height Constraint Least Squares)

200 400 600 800 1000 Easting [m]

Figure 7.44. 2D Position, Section A, Springbank, June 29,1996. (60° Cross-Track Cutoff Angle, Height Constraint Least Squares) Difference Longitude Latitude Difference [m] , Difference [m] 8 8JQ o S 8 8 8 8 o 3 88 era . i.... i |MI.|II.&M|M,I|I,M|I.M|

11 1! 2. en I ON

Sectio . HeadinnB g constraint require previousa s positio computo nt e eTh dkd . d§ an previous position is treated as a constant, and the heading is evaluated from this point. If the vehicle turns during an outage period, as shown in Figure 7.46, the sensor heading may give a false constraint to the current position estimate. Therefore, the algorithm must include logic which shuts dow headinnthe g constrain previouthe if t s positio missednis .

This logic is implemented to avoid a false heading constraint after an outage period. One may notice from Figure 7.37 thanumbee th t f visiblo r e satellite t soma s e dropeon o st locations. The heading constraint is then shut down and is not used until good GPS coverage is obtained.

The position propagation using the last vehicle velocity and gyro heading during the outage period was examined but was not accurate enough to meet the requirement.

"True" position after outage v. period

Positions during ___ outage period f Vehicle heading after outage period

Last position "Constrained" update position estimate

Figure 7.46. False Heading Constraint 142 vehicle th o t e e accelerationThidu s si decelerationd san relativela r sfo y short perion di

urban areas.

DOPs of height and heading constraint least squares and Kalman filtering are

shown in Figure 7.47. GDOP and NDOP are reduced to approximately 10 during the

constraint period. Figures positio7.4D 2 7.4d 8e an 9ar n plot f heigho s d headinan t g

constraint least squares solutions. Ther outage ear e period Section differencee si Th . nB s

betwee e referencth n e trajector e heigh th d headin d an t an y g constraint least squares

solutions with 2a error envelope showe sar Figurn ni e 7.50 standare Th . d deviationf so

latitude and longitude are 2.21 and 0.83 metres and the maximum errors are 5.83 and 2.51

metres, respectively, as shown in Table 7.19. The DRMS is approximately 2.9 metres.

Position availabilit epochs6 35 f o . t 58.2s yi ou 7 % timf 20 o r eo

1000 T

C 100 .0 <75 G

o 10 -: c: .P

0.1 I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I 573950 574000 574050 574100 574150 574200 574250 574300 574350 574400 GPS Time [s]

Figure 7.47. DOPs, Springbank, June 29,1996. (60° Cross-Track Cutoff Angle, Height and Heading Constraint Least Squares and Kalman Filter) 143

numimm.a • IBL JHUHIII IHFIEI

-200

-400

-600

-800

-1000

-1200

-1400

-1600 200 400 600 800 1000 Easting [m]

Figure 7.48 PositionD .2 , Springbank, June 29,1996. (60° Cross-Track Cutoff Angle, Heigh Headind an t g Constraint Least Squares)

-100 200 400 600 800 1000 Easting [m]

Figure 7.49. 2D Position, Section A, Springbank, June 29,1996. (60° Cross-Track Cutoff Angle, Heigh Headind an t g Constraint Least Squares) TeO Height Difference Longitude Latitude Difference Difference[m] , , fm] g p

2W TO* c* as ^ s ON & 0(7)^ 0 -a PM ** ft n i—. ^9 a- s » TO

o c-3 Mi ^5Te " 5- <-»• ?S 3 o S-v o S>^> 3

9 vo do ON <-K

O w9 i 145 Table 7.19. Position Estimate Difference Between Reference Trajectord yan Heigh Headind tan g Constraint Least Squares Solutions, Springbank, June 29,1996. (60° Cross-Track Cutoff Angle) Latitude Longitude Height Mea] n[m -1.62 -0.22 -0.93 Standard Deviatio] n[m 2.21 0.83 0.81 Max. Differenc] [m e 5.83 2.51 2.23 Min. Difference [m] 0.00 0.01 0.00 Position Availability 58.2 % / 207 epochs

Figures 7.51 and 7.52 are 2D position plots of height and heading constraint

Kalman filter solutions. As seen in Table 7.20, the standard deviations of latitude and

longitud e 1.8 0.8ear d 5an 2 maximu e metreth d an s m error e 6.7 2.8d ar s 5an 2 metres,

respectively DRMe Th . approximatels Si metres7 y2. . Figure 7.53 show differencee sth s

between the reference trajectory and the height and heading constraint Kalman filter

solutions with 2a error envelopes. Position displacements are mostly within the envelopes.

In general, the solutions at a 60° cross-track cutoff angle are similar to those at a 45°

cross-track cutof favailabilite anglth t ebu significantls yi y reduced. Position availabilits yi same th thas ea f heigh o t headind an t g constraint least squares solutions, 7 58,220 r %o

out of 356 epochs. A summary of position availability is given in Table 7.21. 146

u 1 JUi™f

I1 -600- c son-

5 -innn -I

-19OO - -1400 - ^ 1fiOO - 0 200 400 600 800 1000 Easting [m]

Figure 7.51. 2D Position, Springbank, June 29,1996. (60° Cross-Track Cutoff Angle, Heigh Headind an t g Constraint Kalman Filter)

-100 200 400 600 800 1000 Easting [m]

Figure 7.52 PositionD 2 . , Sectio , SpringbanknA , June 29,1996. (60° Cross-Track Cutoff Angle, Height and Heading Constraint Kalman Filter) orci Height Difference Longitude Latitude Difference e , Difference [m] [m] , , en o Qj o en o en

InnliiiJfeMilMiilMMliinl

2. cf3* 3-

01

O 2. S 330. 2

3 ^ 148

Table 7.20. Position Estimate Difference Between Reference Trajectord yan Heigh Headind tan g Constraint Kalman Filter Solutions, Springbank, June 29,1996. (60° Cross-Track Cutoff Angle) Latitude Longitude Height Mean [m] -1.83 -0.30 -0.94 Standard Deviatio] n[m 1.85 0.82 0.81 Max. Differenc] [m e 6.75 2.82 2.67 Min. Differenc] [m e 0.07 0.00 0.01 Position Availability 58.2 % / 207 epochs

Table 7.21. Position Estimate Availability, Springbank, June 29,1996. (60° Cross-Track Cutoff Angle) Estimation Mode Position Estimate Availability DRMS Unaided Least Squares 124 epochs 734.8% 2.0m Height Constraint Least Squares 207 epochs 758.2% 17.5m Sensor Constraint Least Squares 207 epochs 7 58.2% 2.9m Sensor Constraint Kalman 207 epochs 7 58.2% 2.7m 149 7.2 Downtown Calgary Field Test

7.2.1 Objectives and Strategies

objective Th downtowe th f eo n testin observo t s gi e system behavio actuan a n i r l and signal masking environment. Major weaknesse e systeth thaf e mo s ar t requirei t a s minimum of two satellites in an appropriate geometry for computation and a previous positio s alwayi n s requiree headinth r fo dg constraint. Since Calgar a skywal s ha y k network called +15, there are occasions when all satellite signals are temporarily blocked b yskywalka . Althoug ideae hth l solution woul integrato t e dpositioninb R D ea g devicn ei the absence of GPS, it was not allowed for this project since portability was a primary requirement. Instead, the algorithm was modified to compensate for this weakness. This revised logic is based on an assumption that the vehicle does not turn during an outage period. Although this assumption initially sounds unreasonable expecn ca e tw , betteS rGP coverage at intersections and intersections are mostly connected by straight roads in downtown Calgary makiny B . g suc assumptionn a h n stilca l e activatw , e headinth e g constraint with a position estimate before the outage period and provide more positioning solutions. Note that this kind of assumption should only be made for relatively short periods since the program may become unstable and solutions may diverge. This testing is only intended to show the potential of the system in a harsh environment.

Bullock (1995) examined the GPS signal availability in downtown Calgary and the position availability was between 58 % and 83 % (Bullock 1995). Thus, the GPS signal availability in downtown Calgary varies depending on the route selected, time of 150 operation , e rangetcTh . e error detection logi e s criticasensoi cth o t rl constraint

navigation system since it relies on "good" GPS update to calibrate and initialize the

sensor measurements detectioo Tw . n routine implementee ar s e systemth n di . Firste th ,

solution without constraint computes si d eac range hth timd e ean residual comparee sar d

to a predetermined threshold value. The residual threshold is optimized for best results.

Second horizontae th , verticad an l l acceleration monitoree sar warnina d dan gives gi f ni acceleratioe th n exceed expecten sa d number determined fro vehicle mth e dynamics. These

threshold value followingivee e sar th n i g sections.

7.2.2 Route Description

The field test was conducted in downtown Calgary on August 17, 1996. The test

rout shows ei Figurn ni e 7.54systee Th s mounte. mwa a 199 n di 6 Pontiac Sunfiree Th .

reference statio Engineerine s locaterooth e f th nwa o f n do g Complex buildine Th t ga

Universit f Calgaryo y . Dats collectewa a d every second e distancTh . e betweee th n

reference rovee statioth d r vehiclnan ee locatio ranger Th . fa s ni dkm betwee7 d an n4

from ideal for GPS positioning since there are numerous multi-storey buildings, +15

skywalks, reflective glass surface heavd an s y traffic. There were also several occasions

whe e tesnth t vehicl s surroundewa e largy b d e busse trucksd an s , blocking additional

satellite signals.

Ther railroaa s ei d betwee 10td an h h avenuesatellitne 9t th d san e visibilit fairls yi y avenueh goo9t n do . However, 10-store higher yo r hotel buildingd san s alon avenuh g9t e

could be major multipath sources. Such is the case around 3rd avenue and 5th street as 151

Figure 7.54. Test Route, Downtown Calgary, August 17,1996

well. The buildings there use mirrored windows to reflect sunlight. These windows also reflect GPS signals quite efficiently. 4th and 8th avenues are in the downtown core where satellite visibilit s extremeli y y poor. Road width ranges from approximatel5 1 o t 0 1 y metres. Most roads have four lanes.

satellite Th e visibility plo gives i t Figurn ni e 7.55 numbee Th . f visiblo r e satellites changes rapidly because of the dynamic environment and temporary satellite blockage. noticOny ema e from Figure 7.55 tha sectiono t thertw e ear s whe numbee nth f satellitero s is always less than four. Ther s alsi e onumbea f instanceo r s when onle signaon y s i l 152

30 T 8

7 V* 25-W CD CD -Q e 75 "CD 20 - 5

15-- 4 ;g

iio 1 CD CD 2 - co

585400 585600 585800 586000 586200 586400 GPS Time [s]

Figure 7.55. Visible Satellites, Downtown Calgary, August 17,1996

available. Therefore unlikels i t i , y thawoule on t d receive continuous solutions froe mth

sensor constraint GPS navigation system, which requires two signals for computation.

7.2.3 Test Results

7.2.3.1 Unaide ResultS dGP s

Figure 7.56 shows DOPs for the unaided least squares solutions. The GDOP

ranges between 15 and 30 when available. For reference, the 2D positions are plotted on shows a route p th Figurn ni ema e 7.57. Note that thi sneithes i rout p ema r accuratr eno

precise. The route map is used here to measure the consistency of the positioning

solutions. One may conclude from Figure 7.57 that unaided GPS positioning is simply not 153 sufficient for urban land navigation applications. Solutions are obtained only on the edge of downtown. This result agrees with the satellite visibility plot, Figure 7.55, in which there are two long GPS signal outage periods. The first outage period starts near 9th

avenuestreeh d avenu endd 7t 3r secone t an d t sa avenu d Th ean starte . 3r don d t sa e an centre street and ends at llth street. Position availability is 35.1% or 351 out of 1001 epochs.

1000 T

o 100 .55 0 OGDOP AHDOP 10 -: 0 CO otf DVDOP c IP EO .o E ° 9^AA

0.1 -1—\—•- 585400 585600 585800 586000 586200 586400 TimeGPS [s]

Figure 7.56. DOPs, Downtown Calgary, August 17,1996. (Unaided Least Squares) 154

-3000

Figure 7.57. 2D Position, Downtown Calgary, August 17,1996. (Unaided Least Squares)

7.2.3.2 Height and Heading Constraint GPS Results

DOPe Th heighr sfo headind an t g constraint positionin showe gar Figurn ni e 7.58.

Compared to the DOP plot of unaided least squares, Figure 7.56, an improvement

is immediately seen. The DOPs for the least squares and Kalman filter are identical

since they shar same eth e algorith datd man a set. Whe heighe nth t constrains i t

applied e VDOth , s i alwayP s approximately 1.0e satellitTh . e geometrs i y

outlierP sufficientlDO Figury n si an e ye se enhance 7.58t no .o d tha n de i w t 155

1000 -F

.§ 10°

10 -: c I.0 3

0.1 585400 585600 585800 586000 586200 586400 TimeGPS [s]

Figure 7.58. DOPs, Downtown Calgary, August 17,1996. (Heigh Headind tan g Constraint Least Square Kalmad san n Filter)

e leasTh t squares positioning mod firss ei t examined. Threshold values user dfo computation are summarized in Table 7.22. The horizontal acceleration is taken from the maximum acceleration of 0-60 mph of the test vehicle, a Pontiac Sunfire. Since the test vehicl s driveewa n gently acceleratioe th , n shoul t exceedno threshole dth d withouS GP t range errors. The vertical acceleration is less than the horizontal considering the vehicle's dynamics. The NovAtel GPSCard™ gives good range measurements and the range threshold used is therefore very tight. The threshold of 1.5 metres, which provided the best result s respectabli , e considerin a gnois y range measurement, frequent satellite constellation changeharse th hd multipatsan h environment threshole th f I . larges di r than this number s mori t i ,e likely thae algorithth t m will introduce range errors inte oth 156 solution. If it is smaller, the algorithm will keep activating sensor constraints without

adequate initializations and calibrations. For the best performance, both extremes should avoidede b .

Table 7.22. GPS Range Error Detection Thresholds, Downtown Calgary, August 17,1996. (Height and Heading Constraint Least Squares) Target Threshold Horizontal Acceleration 4m/s2 Vertical Acceleration 1.5m/s2 Range Residual 1.5m

Figure 7.59. 2D Position, Downtown Calgary, August 17,1996. (Height and Heading Constraint Least Squares) 157 Figure 7.59 shows the effect of height and heading constraint. We have a good

number of positioning solutions throughout the session. It is expected that we would not

obtain continuous solutions becaus limitatioe th f eo two-satellitf no e positioning. Indeed,

solution e downtowth t continuousn i no s e ar n . Ther e numerouar e s blanks between

revisee estimatesth o t d e algorithmDu . stile ar l able w ,maintai o et headine nth g constraint

afte outagn a r e period. Positio nf 100 o availabilit 1t ou epochs 5 69 69.4 s yi r o . %Ther s ei

e sectioavenuh 8t on n no e where heading constraint provides false information. This i s

headino t likel e ydu g initializatio nsolutioS witGP ha n which contain undetectabln a s e

multipath magnitude. The implemented error detection routine was not sufficient enough

to find all range errors. The range residuals may not be suitable for the error threshold

sinc t eredundan therno e ear t solution urban si n environment feweo t e rsdu observations.

Another multipath error detection strateg desirable b superioe y th yr ma efo r performance.

Kalmae Th n filter positioning mod thes ei n employed. This 8-state Kalman position

filter userangS sGP e measurement sensod san r measurement updater sfo advantagn A . e

Kalmae th f o n filte thas i r t givei t smootsa h trajectory. This property greatly helps when

satellite th e constellation changes. However Kalmaa , n filter solution contain responssa e

delay due to the filtering process. The range residual threshold must be increased,

otherwise the algorithm would keep activating the sensor constraint without proper

initialization e thresholTh . d numbe 3 metre f o r s gav e besth e t performanc r thifo es

particular data set with the Kalman filter. This compromise will increase the possibility

that undetectable multipath may degrade the position accuracy. Threshold values are

summarized in Table 7.23. 158

Table 7.23. GPS Range Error Detection Thresholds, Downtown Calgary, August 17,1996. (Height and Heading Constraint Kalman Filter) Target Threshold Horizontal Acceleration 4m/s2 Vertical Acceleration 1.5m/s2 Range Residual 3.0m

-3000

Figure 7.60. 2D Position, Downtown Calgary, August 17, 1996. (Height and Heading Constraint Kalman Filter) 159 Figure 7.60 positio showD 2 e sth n plo f heigho t headind an t g constraint Kalman filter solutions s gooa s Figurt resule da no Th lesa .s i et o st 7.5 stringene 9du t range residual threshold and thus inferior error control. The Kalman filter tends to break down whe nfalsa e constrain introduces i t d (i.e. whe initializatioe nth calibratiod nan t donno es ni properly). Note that this filter alread huga s eyha horizontal spectral densitm0 /s40 f yo 2 3 plus adaptive logic which only increases this number filtee Th .r would break dowa f ni larger spectral density is used. As expected, the multipath-induced heading error is larger than tha f leaso t t squareavenueh 8t n additionn so I . e solutionh th ,9t d 3rdn an o s h ,6t avenues are not as consistent as those in Figure 7.59. Another multipath detection logic, which rang e doe th t rel n esno yo residuals , woul necessare db improvo yt accurace eth f yo the Kalman filter solutions. The Kalman filter produces slightly more position solutions than the least squares does, 70.4% or 705 out of 1001 epochs. This may be due to the lack of divergence state in the Kalman filter as discussed in the simulation section. Position availability is summarized in Table 7.24.

Table 7.24. Position Estimate Availability, Downtown Calgary, August 17,1996 Positioning Mode Position Availability (total 1001 epochs) Unaided Least Squares 351 epochs 735.1% Height and Heading Constraint Least Squares 695 epoch s69.4/ % Heigh Headind an t g Constraint Kalman Filter 705 epoch s/ 70.4 % 160 Figure 7.61 give verticaa s le positio vieth f wo n solutions e unaideTh . d least squares solutions apparently contain errors o multipatht . e Thesdu ee b .error y ma s

Althoug e heigh th hd headin an t g constraint least squares solution e mucar s h more consistent, they also have spike-like errors. These spikes may be caused by in-vehicle pressure disturbances, which occur during acceleratio d decelerationnan . This effecs i t inevitable sinc vehiclea e repeat stop-and-ge sth o maneuve urban a n i rn area. Heighd an t heading constraint Kalman filter solutions are less consistent than those of least squares because of the inferior error detection threshold.

1080 -r

1060

Sensor ConstrainS L t UnaideS dL Sensor Constraint Kalman 940 585400 585500 585600 585700 585800 585900 586000 586100 586200 586300 586400 586500 TimeGPS [s]

Figure 7.61. Vertical Position, Downtown Calgary, August 17,1996 161 CHAPTER EIGHT

CONCLUSION RECOMMENDATIOND SAN S

8.1 Conclusions

The height and heading constraint navigation system developed herein significantly improve possibilite sth navigatio S GP f yo urban ni n environments casee th r s testedFo . t i , improve e positioninth s whil% g35 e availabilito t mostl 4 2 yy b ymaintainin e th g positioning accuracy within 10 metres DRMS. The barometer and gyro information enhance the satellite geometry. In the process, they can also constrain the vertical and horizontal positioning estimate minimizo st erroe eth r cause poosignay S db GP r l quality.

Sinc e accurac th ee senso th f o yr constraint solution degrades with time e systeth , m requires periodical sensor data initialization and calibration with good GPS data for the best results.

e urbaTh n canyon simulations usin e virtuagth l wall concep e examinear t o t d evaluate the performance of the height and heading constraint navigation system. The virtual wall concep proves i t usefue b o simulatno t t l urbae eth n environment concepe Th . t successfully creates the weak satellite geometry which is often seen in the urban areas

(Hayashi 1996) fule l Th . availabilit signalS GP f syo provide precissa e reference trajectory whic uses hi asseso dt accurace th sconstrainee th f yo d solutions s showi t I . n thae th t sensor measurements improv DOPe th e s significantly heighe Th . t constraint navigation metho e suitablb t dr urba no fo e alon y n ma elan d navigation. This technique enablea s three-satellite positioning, however, three satellites form poor horizontal satellite geometry 162 more t degradelikeli d yan s position accuracy pooe Th .r horizontal geometr causes yi y db obstructions which mask satellite signals on each side of the vehicle. The heading constraint introduce additionan sa l horizontal constrain solutione th o t . This enhancee sth horizontal geometrical strength r thesFo . e simulations, heigh d headinan t g constraint navigation improves position availability by 26% for a cross-track cutoff angle of 45 degrees and 24% for 60 degrees. In this test, errors induced by employing height and heading constraint t degradno o sd e accuracy beyonmetre0 1 e dsth DRMS whice th s hi requiremen thir fo ts project.

lease Th t squares solutions become discontinuous whe satellite nth e constellation change s wel a ss durin a l g transitions betwee e sensonth r constrain e unaideth d an dt solutions. The Kalman filter solutions are smooth and more consistent due to the filtering process. The overall performance of least squares and the Kalman filter are comparable.

However erroe th , r detection logic used herei Kalmar nfo n filter coul t detecd no rang e th t e erro effectivels a r tha s leasr a y fo t t squares. Thicauses swa largey db r range residualf so

Kalman filter which forced to use a larger error detection threshold. As a consequence, the

Kalman filter solutions seem more affecte y rangb d e errors thae leasth n t squares solutions.

Actual downtown testing revealed some limitations. The position availability of the unaided least square 35.1s si timf %o thin ei s test ,worse whicb y eh ma tha positioe nth n availabilit downtown yi n Calgary conducted othery b s (Bullock 1995). This poor result ma causee harse yb th y hdb test route environment . r froThifa ms si sufficien r urbafo t n navigation applications. The position availability is improved to approximately 70% of 163 time with heigh headind an t g constraints. Stringen rangS GP te error detection logis ci needed contaminatee sincsignalS b y eGP ma s multipathy db erroe Th . r detection logic implemented is not sufficient. Thus, there are still some undetectable GPS range errors which giv a false e initial heading determination e heigh d Th headin. an t g constraint positioning solution consistene sar includint bu t g vertical position "spikes". The likele yar y due to in-vehicle pressure disturbances.

The Kalman filter solution has a delay because of the filtering process. The delay appear large a rang S s a s GP re residual. This force erroe th s r detection lese logib so ct stringent than tha leasf o t t square orden si adequatelo rt y calibrat sensoe eth r information.

Consequently, the Kalman filter positioning solutions are not as good as those of least squares. However, they still trac tese kth t route fairly well, considerin extremele gth y poor

GPS signal reception and harsh multipath environment in downtown.

8.2 Recommendations

Some weaknesse systee th f mso have been pointed out. Probably biggese th , s i t that the system requires a minimum of two visible satellites to update the solution. This is majoa r drawback sinc l satelliteeal frequentle sar y blocke downtown di n Calgare th y yb

+15 skywalk network. Ideally, continuous positioning is desirable for the heading constraint which utilizes a previous position as a starting point. The revised algorithm, which is based on the assumption that intersections are connected by straight roads, would not work welcita n yi l where intersection connectee sar curvesy db authoe Th . r strongly recommends that the system be combined with a distance sensor such as an odometer or 164 accelerometer. The distance sensor can be incorporated into the constraint algorithm as a

distance constraint or used to complete DR positioning with a gyro. Another possibility is

to use an on-board precise clock. If the clock is stable enough, the receiver clock offset

ma estimatee yb certaia r dfo n period. This will enable one-satellite positioning.

Another weakness of the system is that it requires periodical sensor data

initializatio d calibrationan n . This shoul e performeb d d with health S solutionsGP y .

However determinatioe th , solutionqualitS e th GP f nf o y o extremels si y difficul lessa n i t-

than-perfect environment since there is far less redundancy. The error detection logic

implemented, which relies on the range residual, DOP and vehicle dynamics, may not be

sufficient. There are still undetected range errors causing sensor initialization and

calibration errors. Another error detection strategy, which detects range errors more

effectively, is highly recommended.

concepe Th f sensoo t r constrain utilizee b y numeroun dma i t s applications it d san

algorith s mquiti e simple. However e shoulon , d give great attentio e sensoth o t nr

characteristics accurace Th . f sensoyo r constraint positionin s directlgi y proportionao t l accurace th sensorse th f yo . Therefore, quality monitorin controd gan f sensoo l r daty ama requirede b sensore Th . s use thin di s project have been teste controllea n di d environment

(factory laboratory) before shipment specificatione Th . e sensorth e f givee o sth ar s y nb

manufacturer. Other tests are needed on-site to determine the short and long term stability,

relation betwee e uninth t temperatur outputd an e , etc. Som f theso e e propertiey ma s

change as the unit ages. It is therefore highly recommended that these properties be

routinely checked to ensure optimal performance. 165 This system has been developed using NovAtel GPSCard™ receivers but the algorithm itself is totally independent of the GPS receiver used. Although the data logging program is tightly integrated with NovAtel commands, adaptation to any other receiver would not be difficult. The navigation program is designed to accept any

C NAV™/FLYKIN ™dataw ra forma , S barometeGP t gyrd an ro filese adjustmenTh . t 3 ma done yb changiny eb g filtering parameter errod san r detection thresholds. 166 REFERENCES

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