Global Navigation Satellite Systems, Inertial Navigation, and Integration

An updated guide to GNSS, and INS, and solutions to real–worldGNSS/INS problems with Kalman filtering

Written by recognized authorities in the field, this thirdedition of a landmark work provides engineers, computer scientists,and others with a working familiarity of the theory andcontemporary applications of Global Navigation Satellite Systems(GNSS), Inertial Navigational Systems, and Kalman filters.Throughout, the focus is on solving real–world problems, with anemphasis on the effective use of state–of–the–art integrationtechniques for those systems, especially the application of Kalmanfiltering. To that end, the authors explore the various subtleties,common failures, and inherent limitations of the theory as itapplies to real–world situations, and provide numerous detailedapplication examples and practice problems, including GNSS–aidedINS (tightly and loosely coupled), modeling of gyros andaccelerometers, and SBAS and GBAS.

Drawing upon their many years of experience with GNSS, INS, andthe Kalman filter, the authors present numerous design andimplementation techniques not found in other professionalreferences. The Third Edition includes:

Updates on the upgrades in existing GNSS and other systemscurrently under development Expanded coverage of basic principles of antenna design andpractical antenna design solutions Expanded coverage of basic principles of receiver design and anupdate of the foundations for code and carrier acquisition andtracking within a GNSS receiver Expanded coverage of inertial navigation, its history, itstechnology, and the mathematical models and methods used in itsimplementation Derivations of dynamic models for the propagation of inertialnavigation errors, including the effects of drifting sensorcompensation parameters Greatly expanded coverage of GNSS/INS integration, includingderivation of a unified GNSS/INS integration model, itsMATLAB® implementations, and performance evaluation undersimulated dynamic conditions

The companion website includes updated background material;additional MATLAB scripts for simulating GNSS–only and integratedGNSS/INS navigation; satellite position determination; calculationof ionosphere delays; and dilution of precision.

Preface xxvii

Acknowledgments xxxi

Acronyms and Abbreviations xxxiii

1 Introduction, 1

1.1 Navigation, 1

1.2 GNSS Overview, 4

1.3 Inertial Navigation Overview, 10

1.4 GNSS/INS Integration Overview, 30

Problems, 32

References, 32

2 Fundamentals of Satellite Navigation Systems, 35

2.1 Navigation Systems Considered, 35

2.2 Satellite Navigation, 36

2.3 Time and GPS, 46

2.4 Example: User Position Calculations with No Errors, 48

Problems, 51

References, 53

3 Fundamentals of Inertial Navigation, 54

3.1 Chapter Focus, 54

3.2 Basic Terminology, 55

3.3 Inertial Sensor Error Models, 59

3.4 Sensor Calibration and Compensation, 63

3.5 Earth Models, 68

3.6 Hardware Implementations, 77

3.7 Software Implementations, 83

3.8 INS Performance Standards, 101

3.9 Testing and Evaluation, 102

3.10 Summary, 103

Problems, 104

References, 106

4 GNSS Signal Structure, Characteristics, and InformationUtilization, 108

4.1 Legacy GPS Signal Components, Purposes, and Properties,109

4.2 Modernization of GPS, 132

4.3 GLONASS Signal Structure and Characteristics, 141

4.4 Galileo, 144

4.5 Compass/BD, 146

4.6 QZSS, 146

Problems, 148

References, 150

5 GNSS Antenna Design and Analysis, 152

5.1 Applications, 152

5.2 GNSS Antenna Performance Characteristics, 152

5.3 Computational Electromagnetic Models (CEMs) for GNSS AntennaDesign, 164

5.4 GNSS Antenna Technologies, 166

5.5 Principles of Adaptable Phased–Array Antennas, 180

5.6 Application Calibration/Compensation Considerations, 187

Problems, 189

References, 190

6 GNSS Receiver Design and Analysis, 193

6.1 Receiver Design Choices, 193

6.2 Receiver Architecture, 199

6.3 Signal Acquisition and Tracking, 204

6.4 Extraction of Information for User Solution, 223

6.5 Theoretical Considerations in Pseudorange, Carrier Phase,and Frequency Estimations, 231

6.6 High–Sensitivity A–GPS Systems, 235

6.7 Software–Defi ned Radio (SDR) Approach, 242

6.8 Pseudolite Considerations, 243

Problems, 244

References, 246

7 GNSS Data Errors, 250

7.1 Data Errors, 250

7.2 Ionospheric Propagation Errors, 251

7.3 Tropospheric Propagation Errors, 263

7.4 The Multipath Problem, 264

7.5 Methods of Multipath Mitigation, 266

7.6 Theoretical Limits for Multipath Mitigation, 283

7.7 Ephemeris Data Errors, 285

7.8 Onboard Clock Errors, 285

7.9 Receiver Clock Errors, 286

7.10 SA Errors, 288

7.11 Error Budgets, 288

Problems, 289

References, 291

8 Differential GNSS, 293

8.1 Introduction, 293

8.2 Descriptions of Local–Area Differential GNSS (LADGNSS),Wide–Area Differential GNSS (WADGNSS), and Space–Based AugmentationSystem (SBAS), 294

8.3 GEO with L1L5 Signals, 299

8.4 GUS Clock Steering Algorithm, 307

8.5 GEO Orbit Determination (OD), 310

8.6 Ground–Based Augmentation System (GBAS), 316

8.7 Measurement/Relative–Based DGNSS, 319

8.8 GNSS Precise Point Positioning Services and Products,323

Problems, 325

References, 326

9 GNSS and GEO Signal Integrity, 328

9.1 Introduction, 328

9.2 SBAS and GBAS Integrity Design, 332

Problems, 325

References, 326

10 Kalman Filtering, 350

10.1 Introduction, 350

10.2 Kalman Filter Correction Update, 354

10.3 Kalman Filter Prediction Update, 365

10.4 Summary of Kalman Filter Equations, 375

10.5 Accommodating Time–Correlated Noise, 377

10.6 Nonlinear and Adaptive Implementations, 384

10.7 Kalman Bucy Filter, 395

10.8 Host Vehicle Tracking Filters for GNSS, 397

10.9 Alternative Implementations, 413

10.10 Summary, 425

Problems, 426

References, 428

11 Inertial Navigation Error Analysis, 430

11.1 Chapter Focus, 430

11.2 Errors in the Navigation Solution, 432

11.3 Navigation Error Dynamics, 442

11.4 Inertial Sensor Noise, 459

11.5 Sensor Compensation Errors, 461

11.6 Software Sources, 467

11.7 Summary, 468

Problems, 470

References, 471

12 GNSS/INS Integration, 472

12.1 Chapter Focus, 472

12.2 GNSS/INS Integration Overview, 473

12.3 Unifi ed Model for GNSS/INS Integration, 479

12.4 Performance Analysis, 485

12.5 Other Integration Issues, 490

12.6 Summary, 492

Problem, 493

References, 494

Appendix A Software, 495

Appendix B Coordinate Systems and Transformations,500

Index 551

MOHINDER S. GREWAL, PhD, PE, is Professor of ElectricalEngineering in the College of Engineering and Computer Science atCalifornia State University, Fullerton.

ANGUS P. ANDREWS, PhD, was senior scientist (now retired)at the Rockwell Science Center in Thousand Oaks, California.

CHRIS G. BARTONE, PhD, PE, is Professor of ElectricalEngineering in the Russ College of Engineering and Technology,School of Electrical Engineering and Computer Science at OhioUniversity, Athens, Ohio.