Fundamentals of Inertial Navigation,Satellite-based Positioning and their Integration

Aboelmagd Noureldin •

Tashfeen B. Karamat • Jacques Georgy

Fundamentals of InertialNavigation, Satellite-basedPositioning and theirIntegration

123

Dr. Aboelmagd NoureldinDepartment of Electrical and Computer

EngineeringRoyal Military College of Canada/

Queen’s UniversityKingstonCanada

Tashfeen B. KaramatDepartment of Electrical

and Computer EngineeringQueen’s UniversityKingstonCanada

Jacques GeorgyTrusted Positioning Inc.CalgaryCanada

ISBN 978-3-642-30465-1 ISBN 978-3-642-30466-8 (eBook)DOI 10.1007/978-3-642-30466-8Springer Heidelberg New York Dordrecht London

Library of Congress Control Number: 2012945733

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Springer is part of Springer Science+Business Media (www.springer.com)

I dedicate this book to my mother and fatherfor their love and sacrifices and to my wifeand three sons, Abdelrahman, Yehia andTareq for their support, encouragement andpatience

Aboelmagd Noureldin

To my parents, Karamat and Safeena fortheir love, my brother Khaver for his kindpatronage after the early demise of myparents, my wife Shazia and my sons Fahaamand Saarim for their unwavering support

Tashfeen Karamat

To my wife Sarah for her great love andvaluable support, to my parents, Ford andLucie, for all their great love and its acts,continuous encouragement and supportthroughout my life, and to my sister Basmafor her love and encouragement

Jacques Georgy

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 General Classification of Positioning Techniques . . . . . . . . . . . 2

1.1.1 Techniques Using Relative Measurements(Known as DR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.2 Techniques Using Absolute Measurements(Known as Reference Based Systems) . . . . . . . . . . . . . . 2

1.1.3 Combined Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 GNSS-Based Positioning Techniques . . . . . . . . . . . . . . . . . . . . 5

1.2.1 Global Positioning System . . . . . . . . . . . . . . . . . . . . . . 61.3 Integration of GPS with Other Systems . . . . . . . . . . . . . . . . . . 8

1.3.1 GPS Augmentation Systems . . . . . . . . . . . . . . . . . . . . . 81.3.2 Local Wireless-Based Positioning Systems. . . . . . . . . . . 91.3.3 Vehicle Motion Sensors . . . . . . . . . . . . . . . . . . . . . . . . 111.3.4 Other Aiding Sensors . . . . . . . . . . . . . . . . . . . . . . . . . 121.3.5 Digital Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.4 Inertial Navigation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.5 Integrated INS/GPS Navigation . . . . . . . . . . . . . . . . . . . . . . . . 141.6 Types of INS/GPS Integration. . . . . . . . . . . . . . . . . . . . . . . . . 15

1.6.1 Loosely Coupled INS/GPS Integration. . . . . . . . . . . . . . 161.6.2 Tightly Coupled INS/GPS Integration . . . . . . . . . . . . . . 161.6.3 Ultra-Tightly or Deeply Coupled Integration . . . . . . . . . 16

1.7 INS/GPS Fusion Algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . 181.8 Summary of the Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2 Basic Navigational Mathematics, Reference Framesand the Earth’s Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.1 Basic Navigation Mathematical Techniques . . . . . . . . . . . . . . . 21

2.1.1 Vector Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.1.2 Vector Coordinate Transformation . . . . . . . . . . . . . . . . 22

vii

2.1.3 Angular Velocity Vectors. . . . . . . . . . . . . . . . . . . . . . . 232.1.4 Skew-Symmetric Matrix . . . . . . . . . . . . . . . . . . . . . . . 232.1.5 Basic Operations with Skew-Symmetric Matrices . . . . . . 242.1.6 Angular Velocity Coordinate Transformations . . . . . . . . 242.1.7 Least Squares Method . . . . . . . . . . . . . . . . . . . . . . . . . 252.1.8 Linearization of Non-Linear Equations . . . . . . . . . . . . . 26

2.2 Coordinate Frames. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.2.1 Earth-Centered Inertial Frame. . . . . . . . . . . . . . . . . . . . 272.2.2 Earth-Centered Earth-Fixed Frame . . . . . . . . . . . . . . . . 282.2.3 Local-Level Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.2.4 Wander Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.2.5 Computational Frame . . . . . . . . . . . . . . . . . . . . . . . . . 312.2.6 Body Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.2.7 Orbital Coordinate System . . . . . . . . . . . . . . . . . . . . . . 32

2.3 Coordinate Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . 332.3.1 Euler Angles and Elementary Rotational Matrices. . . . . . 342.3.2 Transformation Between ECI and ECEF . . . . . . . . . . . . 382.3.3 Transformation Between LLF and ECEF . . . . . . . . . . . . 392.3.4 Transformation Between LLF and Wander Frame. . . . . . 402.3.5 Transformation Between ECEF and Wander Frame . . . . 412.3.6 Transformation Between Body Frame and LLF . . . . . . . 422.3.7 Transformation From Body Frame to ECEF

and ECI Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.3.8 Time Derivative of the Transformation Matrix . . . . . . . . 432.3.9 Time Derivative of the Position Vector

in the Inertial Frame . . . . . . . . . . . . . . . . . . . . . . . . . . 452.3.10 Time Derivative of the Velocity Vector in the Inertial

Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.4 The Geometry of the Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.4.1 Important Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . 472.4.2 Normal and Meridian Radii . . . . . . . . . . . . . . . . . . . . . 48

2.5 Types of Coordinates in the ECEF Frame . . . . . . . . . . . . . . . . 492.5.1 Rectangular Coordinates in the ECEF Frame . . . . . . . . . 492.5.2 Geodetic Coordinates in the ECEF Frame . . . . . . . . . . . 492.5.3 Conversion From Geodetic to Rectangular Coordinates

in the ECEF Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . 502.5.4 Conversion From Rectangular to Geodetic Coordinates

in the ECEF Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . 502.6 Earth Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

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3 Global Positioning System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.1 GPS Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.1.1 Pseudo-Ranges Measurements . . . . . . . . . . . . . . . . . . . 663.1.2 Carrier Phase Measurements. . . . . . . . . . . . . . . . . . . . . 673.1.3 Doppler Measurements . . . . . . . . . . . . . . . . . . . . . . . . 68

3.2 GPS Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693.2.1 Space Segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693.2.2 Control Segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693.2.3 User Segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.3 GPS Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713.3.1 Traditional GPS Signals. . . . . . . . . . . . . . . . . . . . . . . . 713.3.2 GPS Modernization . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

3.4 GPS Error Sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733.4.1 Satellite Clock Error . . . . . . . . . . . . . . . . . . . . . . . . . . 743.4.2 Receiver Clock Error. . . . . . . . . . . . . . . . . . . . . . . . . . 743.4.3 Ionosphere Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743.4.4 Tropospheric Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . 763.4.5 Multipath Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763.4.6 Satellite Orbital Errors. . . . . . . . . . . . . . . . . . . . . . . . . 763.4.7 Receiver Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773.4.8 User Equivalent Range Error . . . . . . . . . . . . . . . . . . . . 77

3.5 GPS Augmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773.5.1 Differential GPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793.5.2 Local Area DGPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793.5.3 Wide Area DGPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803.5.4 Assisted GPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

3.6 GPS Satellite Orbits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843.6.1 Kepler’s Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843.6.2 Keplerian Orbital Elements . . . . . . . . . . . . . . . . . . . . . 853.6.3 GPS Orbital Parameters . . . . . . . . . . . . . . . . . . . . . . . . 87

3.7 Ephemeris Data Processing. . . . . . . . . . . . . . . . . . . . . . . . . . . 883.7.1 Calculation of Satellite Clock Corrections . . . . . . . . . . . 883.7.2 Atmospheric Corrections . . . . . . . . . . . . . . . . . . . . . . . 903.7.3 Calculation of Satellite Position . . . . . . . . . . . . . . . . . . 943.7.4 Calculation of Satellite Velocity . . . . . . . . . . . . . . . . . . 96

3.8 Receiver Position and Velocity Estimation . . . . . . . . . . . . . . . . 973.8.1 Pseudo-Range Measurements . . . . . . . . . . . . . . . . . . . . 973.8.2 Position Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 983.8.3 Satellite Geometry and Dilution of Precision . . . . . . . . . 1013.8.4 Doppler Measurements . . . . . . . . . . . . . . . . . . . . . . . . 1053.8.5 Velocity Estimation from Doppler. . . . . . . . . . . . . . . . . 1063.8.6 Position and Velocity Estimation . . . . . . . . . . . . . . . . . 107

Contents ix

3.9 Carrier Phase Positioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1093.9.1 Relative Positioning and Linear Combinations

of GPS Observables . . . . . . . . . . . . . . . . . . . . . . . . . . 1103.9.2 Relative Positioning . . . . . . . . . . . . . . . . . . . . . . . . . . 1113.9.3 Linear Combinations of GPS Measurements. . . . . . . . . . 1113.9.4 Position Estimation from Carrier Phase Measurements . . . 117

3.10 Integer Ambiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1193.10.1 Integer Ambiguity Resolution . . . . . . . . . . . . . . . . . . . . 1203.10.2 Ambiguity Dilution of Precision . . . . . . . . . . . . . . . . . . 121

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

4 Inertial Navigation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1254.1 Principle of Inertial Navigation . . . . . . . . . . . . . . . . . . . . . . . . 1254.2 Physical Implementation of an INS . . . . . . . . . . . . . . . . . . . . . 1264.3 Inertial Measurement Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . 1274.4 Inertial Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

4.4.1 Accelerometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1294.4.2 Gyroscopes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

4.5 Basics of Inertial Navigation. . . . . . . . . . . . . . . . . . . . . . . . . . 1324.5.1 Navigation in One Dimension . . . . . . . . . . . . . . . . . . . 1334.5.2 Navigation in Two Dimensions. . . . . . . . . . . . . . . . . . . 133

4.6 Navigation in Three Dimensions . . . . . . . . . . . . . . . . . . . . . . . 1364.7 Overview of an Inertial Navigation System in 3D . . . . . . . . . . . 1374.8 Theoretical Measurements of the Inertial Sensor . . . . . . . . . . . . 137

4.8.1 Theoretical Measurements of a StationaryAccelerometer Triad . . . . . . . . . . . . . . . . . . . . . . . . . . 137

4.8.2 Theoretical Measurements of a Stationary Gyro Triad . . . 1394.8.3 Theoretical Measurements of a Moving Gyro Triad . . . . 141

4.9 Notes on Inertial Sensor Measurements . . . . . . . . . . . . . . . . . . 1454.10 Inertial Sensor Performance Characteristics . . . . . . . . . . . . . . . 1464.11 Inertial Sensor Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

4.11.1 Systematic Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1464.11.2 Random Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1494.11.3 Notes on Random Errors . . . . . . . . . . . . . . . . . . . . . . . 1514.11.4 Mathematical Models of Inertial Sensor Errors . . . . . . . . 152

4.12 Classification of Inertial Sensors . . . . . . . . . . . . . . . . . . . . . . . 1544.12.1 Gyroscope Technologies and their Applications . . . . . . . 1554.12.2 Accelerometer Technologies and their Applications . . . . 155

4.13 Calibration of Inertial Sensors. . . . . . . . . . . . . . . . . . . . . . . . . 1554.13.1 Six-Position Static Test . . . . . . . . . . . . . . . . . . . . . . . . 1564.13.2 Angle Rate Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

4.14 Importance of Calibration of Inertial Sensors . . . . . . . . . . . . . . 1594.14.1 Case-I: Bias Error in an Accelerometer . . . . . . . . . . . . . 1614.14.2 Case-II: Bias Error in the Gyroscope. . . . . . . . . . . . . . . 161

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4.15 Initialization and Alignment of Inertial Sensors. . . . . . . . . . . . . 1624.15.1 Position and Velocity Initialization . . . . . . . . . . . . . . . . 1624.15.2 Attitude Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

5 Inertial Navigation System Modeling . . . . . . . . . . . . . . . . . . . . . . 1675.1 Dynamic Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1675.2 Kinematic Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

5.2.1 Rigid Body Motion Modeling. . . . . . . . . . . . . . . . . . . . 1695.2.2 Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

5.3 INS Mechanization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1705.3.1 INS Mechanization in an Inertial Frame of Reference . . . 1715.3.2 INS Mechanization in ECEF Frame . . . . . . . . . . . . . . . 1725.3.3 INS Mechanization in the Local-Level Frame . . . . . . . . 1745.3.4 INS Mechanization in Wander Frame . . . . . . . . . . . . . . 180

5.4 Parameterization of the Rotation Matrix . . . . . . . . . . . . . . . . . . 1835.4.1 Solution to Transformation Matrix . . . . . . . . . . . . . . . . 1845.4.2 Quaternions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1865.4.3 Solutions of the Quaternion Equation . . . . . . . . . . . . . . 1885.4.4 Advantages of Quaternion . . . . . . . . . . . . . . . . . . . . . . 189

5.5 Step by Step Computation of Navigation Parametersin the l-Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1905.5.1 Raw Measurement Data . . . . . . . . . . . . . . . . . . . . . . . . 1935.5.2 Correction of the Measurement Data . . . . . . . . . . . . . . . 1945.5.3 Calculation and Updating of Rotation Matrix . . . . . . . . . 1945.5.4 Attitude Computation . . . . . . . . . . . . . . . . . . . . . . . . . 1965.5.5 Velocity Computation . . . . . . . . . . . . . . . . . . . . . . . . . 1975.5.6 Position Computation . . . . . . . . . . . . . . . . . . . . . . . . . 198

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

6 Modeling INS Errors by Linear State Equations . . . . . . . . . . . . . . 2016.1 Local-Level Frame Error State Equations . . . . . . . . . . . . . . . . . 202

6.1.1 Position Errors for Local-Level Frame. . . . . . . . . . . . . . 2036.1.2 Velocity Errors for Local-Level Frame . . . . . . . . . . . . . 2056.1.3 Attitude Errors for Local-Level Frame. . . . . . . . . . . . . . 2116.1.4 Inertial Sensor Error States. . . . . . . . . . . . . . . . . . . . . . 2166.1.5 Summary of Local-Level Frame Error State Equations . . . 217

6.2 Schuler Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2196.2.1 Error Model Along the East Channel. . . . . . . . . . . . . . . 2196.2.2 Error Model Along the North Channel . . . . . . . . . . . . . 2216.2.3 Understanding the Error Behavior of the Inertial

System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

Contents xi

7 Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2257.1 Discrete-Time KF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

7.1.1 KF Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2287.2 KF Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

7.2.1 Time Update or Prediction . . . . . . . . . . . . . . . . . . . . . . 2307.2.2 Measurement Update or Correction . . . . . . . . . . . . . . . . 230

7.3 KF Algorithm Steps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2337.4 Non-Linear Kalman Filtering . . . . . . . . . . . . . . . . . . . . . . . . . 235

7.4.1 Linearized KF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2357.4.2 Extended KF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236

7.5 KF Divergence Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2367.5.1 Addition of Fictitious Noise to the KF Process Model. . . 2367.5.2 Schmidt Epsilon Technique . . . . . . . . . . . . . . . . . . . . . 2377.5.3 Finite Memory Filtering. . . . . . . . . . . . . . . . . . . . . . . . 2377.5.4 Fading Memory Filtering . . . . . . . . . . . . . . . . . . . . . . . 238

7.6 Explanatory Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2387.6.1 A Simple Navigation Example . . . . . . . . . . . . . . . . . . . 2387.6.2 Zero Velocity Update . . . . . . . . . . . . . . . . . . . . . . . . . 2397.6.3 Coordinate Update . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244

8 INS/GPS Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2478.1 Error Feedback Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

8.1.1 Open-Loop INS/GPS Architecture. . . . . . . . . . . . . . . . . 2498.1.2 Closed-Loop INS/GPS Architecture. . . . . . . . . . . . . . . . 249

8.2 Types of Integration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2498.2.1 Loosely Coupled INS/GPS Integration. . . . . . . . . . . . . . 2508.2.2 Tightly Coupled INS/GPS Integration . . . . . . . . . . . . . . 2518.2.3 Ultra-Tight INS/GPS Integration . . . . . . . . . . . . . . . . . . 252

8.3 Dynamic Error Model of INS Equations. . . . . . . . . . . . . . . . . . 2528.4 Models for Loosely Coupled INS/GPS Integration. . . . . . . . . . . 255

8.4.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2558.4.2 Measurement Model . . . . . . . . . . . . . . . . . . . . . . . . . . 2578.4.3 The Overall Implementation Block Diagram

of the Loosely Coupled INS/GPS Integration . . . . . . . . . 2598.5 Modeling Tightly Coupled INS/GPS Integration . . . . . . . . . . . . 259

8.5.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2608.5.2 Measurement Model . . . . . . . . . . . . . . . . . . . . . . . . . . 2628.5.3 The Overall Measurements Model. . . . . . . . . . . . . . . . . 269

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

xii Contents

9 Three-Dimensional Reduced Inertial Sensor System/GPSIntegration for Land-Based Vehicles . . . . . . . . . . . . . . . . . . . . . . . 2739.1 Performance Analysis of 3D Positioning Utilizing a MEMS

Grade Full IMU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2739.2 The Proposed Techniques for Overcoming MEMS

Grade IMU Shortcomings for Land-Based Vehicles. . . . . . . . . . 2749.3 Three-Dimensional Reduced Inertial Sensor System . . . . . . . . . 276

9.3.1 Overview of 3D RISS . . . . . . . . . . . . . . . . . . . . . . . . . 2769.3.2 Advantages of 3D RISS for Wheel-Based Land

Vehicles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2779.3.3 Derivation of the 3D RISS Motion Equations. . . . . . . . . 2809.3.4 Overview of 3D RISS Motion Model . . . . . . . . . . . . . . 285

9.4 KF for Loosely Coupled 3D RISS/GPS Integration . . . . . . . . . . 2869.4.1 The Linearized Error Model for 3D RISS . . . . . . . . . . . 2879.4.2 Measurement Model for Updating 3D RISS . . . . . . . . . . 289

9.5 KF for Tightly Coupled 3D RISS/GPS Integration . . . . . . . . . . 2909.5.1 Augmenting the System Model. . . . . . . . . . . . . . . . . . . 2909.5.2 Raw GPS Measurement Model for Updating 3D RISS . . . 290

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

10 Two Case Studies: Full IMU/GPS and 3D RISS/GPSIntegration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29710.1 Navigation Equipment Used for the Experiments . . . . . . . . . . . 297

10.1.1 Partial GPS Outage Criterion . . . . . . . . . . . . . . . . . . . . 29910.2 Performance of Tightly Coupled Algorithm with

Full IMU/GPS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30010.2.1 Analysis of Selected GPS Outages . . . . . . . . . . . . . . . . 303

10.3 Performance of Tightly Coupled Algorithmfor 3D RISS/GPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30710.3.1 Analysis of Selected GPS Outages . . . . . . . . . . . . . . . . 309

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

Contents xiii

Abbreviations

1D One dimension2D Two dimension3D Three dimensionADOP Ambiguity DOPAFM Ambiguity function methodA-GPS Assisted GPSAI Artificial intelligenceAOA Angle of arrivalAR Ambiguity resolutionAR AutoregressiveARNS Aeronautical radio navigation servicesARW Angle random walkBD-1 Beidou-1BD-2 Beidou-2BOC Binary offset carrierBPSK Binary phase shifted keyCASC China aerospace science and technologyCAST China academy of space technologyCDMA Code division multiple accessCNSS Compass navigation satellite systemCORS Continuously operating reference stationCTP Conventional terrestrial poleCUPT Coordinate updateCWAAS Canadian wide area augmentation systemDCM Direction cosine matricesDD Double differenceDGPS Differential GPSDLL Delay-lock loopsDOP Dilution of precisionDR Dead-reckoning

xv

DTG Dynamically tuned gyroscopesDVB-T Digital video broadcasting - terrestrialECEF Earth-centered earth-fixedECI Earth-centered inertialEGNOS European geostationary navigation overlay serviceEKF Extended Kalman filterENU East North UpEOTD Enhanced observed time differenceESA European space agencyFAA Federal aviation administrationFASF Fast ambiguity search filterFOC Full operational capabilityFOG Fiber optic gyroscopesGAGAN Geo-augmented navigation systemGBAS Ground-based augmentation systemsGDOP Geometric dilution of precisionGDPS Global differential GPSGLONASS Global navigation satellite systemGM Gauss-MarkovGNSS Global navigation satellite systemsGPS Global positioning systemGRAS Ground-based regional augmentation systemGRS Geographic reference systemGSM Global system of mobileHDOP Horizontal dilution of precisionHOT Higher order termsHRG Hemispherical resonant gyroscopesIA Integer ambiguityIFOG Interferometric fiber-optic gyroscopesIGS International GNSS serviceIMU Inertial measurement unitINS Inertial navigation systemIOC Initial operational capabilityIRNSS Indian regional navigational satellite systemISA Inertial sensor assemblyISDB Integrated services digital broadcastingKF Kalman filterLAAS Local area augmentation systemLADGPS Local area DGPSLAMBDA Least-squares ambiguity decorrelation adjustmentLIDAR Light detection and rangingLKF Linearized Kalman filterLLF Local-level frame

xvi Abbreviations

LOS Line of sightLSAST Least-squares ambiguity search techniqueMBOC Multiplexed binary offset carrierMCS Master control stationMEMS Micro-electro-mechanical systemMSAS Multifunction transport satellite (MTSAT) satellite augmentation

systemMTSAT Multifunction transport satelliteNED North East DownNGA National geospatial-intelligence agencyNGDGPS Nationwide differential GPS systemNTSC National television system committeeOTDOA Observed time difference of arrivalPDOP Position dilution of precisionPF Particle filterPLL Phase-lock loopsPPS Precise positioning servicePRN Pseudo random noiseQZSS Quasi-zenith satellite systemRAAN Right ascension of the ascending nodeRF Radio frequencyRISS Reduced inertial sensor systemRLG Ring laser gyroscopesRMS Root mean squareRNSS Radio navigation satellite servicesRS Reference stationRSD Receiver single differenceSA Selective availabilitySBAS Space-based augmentation systemsSECAM Séquentiel couleur à mémoireSNAS Satellite navigation augmentation systemSPAN Synchronized position attitude navigationSPS Standard positioning serviceSSD Satellite single differenceSTM State transition matrixTD Triple differenceTDOA Time difference of arrivalTDOP Time dilution of precisionTEC Total electron contentTOA Time of arrivalTTFF Time-to-first-fixTV TelevisionUERE User equivalent range error

Abbreviations xvii

U-TDOA Uplink time difference of arrivalUWB Ultra-wide bandVBA Vibrating beam accelerometersVRW Velocity random walkWAAS Wide-area augmentation systemWADGPS Wide area DGPSWGS World geodetic systemWLAN Wireless local area networksZUPT Zero velocity update

xviii Abbreviations