Global Positioning Systems, Inertial Navigation, and Integration

by Grewal, Mohinder S.; Weill, Lawrence R.; Andrews, Angus P.

• ISBN13: 9780470041901
• ISBN10: 0470041900
• Edition: 2nd
• Format: Hardcover
• Copyright: 2007-01-22
• Publisher: Wiley-Interscience

Summary

An updated guide to GNSS and INS, and solutions to real-world GPS/INS problems with Kalman filtering Written by recognized authorities in the field, this second edition of a landmark work provides engineers, computer scientists, and others with a working familiarity with the theory and contemporary applications of Global Navigation Satellite Systems (GNSS), Inertial Navigational Systems (INS), and Kalman filters. Throughout, the focus is on solving real-world problems, with an emphasis on the effective use of state-of-the-art integration techniques for those systems, especially the application of Kalman filtering. To that end, the authors explore the various subtleties, common failures, and inherent limitations of the theory as it applies to real-world situations, and provide numerous detailed application examples and practice problems, including GNSS-aided INS, modeling of gyros and accelerometers, and SBAS and GBAS. Drawing upon their many years of experience with GNSS, INS, and the Kalman filter, the authors present numerous design and implementation techniques not found in other professional references. This Second Edition has been updated to include: GNSS signal integrity with SBAS Mitigation of multipath, including results Ionospheric delay estimation with Kalman filters New MATLAB programs for satellite position determination using almanac and ephemeris data and ionospheric delay calculations from single and dual frequency data New algorithms for GEO with L1 /L5 frequencies and clock steering Implementation of mechanization equations in numerically stable algorithms To enhance comprehension of the subjects covered, the authors have included software in MATLAB, demonstrating the working of the GNSS, INS, and filter algorithms. In addition to showing the Kalman filter in action, the software also demonstrates various practical aspects of finite word length arithmetic and the need for alternative algorithms to preserve result accuracy.

Author Biography

MOHINDER S. GREWAL, PhD, PE, is Professor of Electrical Engineering in theCollege of Engineering and Computer Science at California State University, Fullerton.

LAWRENCE R. WEILL, PhD, is Professor Emeritus of Applied Mathematics in the College of Mathematics and Natural Sciences at California State University, Fullerton.

ANGUS P. ANDREWS, PhD, is Senior Scientist (Retired) at the Rockwell Science Center in Thousand Oaks, California.

Table of Contents

Preface to the Second Edition	p. xvii
Acknowledgments	p. xix
Acronyms	p. xxi
Introduction	p. 1
GNSS/INS Integration Overview	p. 1
GNSS Overview	p. 2
GPS	p. 2
GLONASS	p. 4
Galileo	p. 5
Differential and Augmented GPS	p. 7
Differential GPS (DGPS)	p. 7
Local-Area Differential GPS	p. 7
Wide-Area Differential GPS	p. 8
Wide-Area Augmentation System	p. 8
Space-Based Augmentation Systems (SBASs)	p. 8
Historical Background	p. 8
Wide-Area Augmentation System (WAAS)	p. 9
European Geostationary Navigation Overlay System (EGNOS)	p. 10
Japan's MTSAT Satellite-Based Augmentation System (MSAS)	p. 11
Canadian Wide-Area Augmentation System (CWAAS)	p. 12
China's Satellite Navigation Augmentation System (SNAS)	p. 12
Indian GPS and GEO Augmented Navigation System (GAGAN)	p. 12
Ground-Based Augmentation Systems (GBASs)	p. 12
Inmarsat Civil Navigation	p. 14
Satellite Overlay	p. 15
Future Satellite Systems	p. 15
Applications	p. 15
Aviation	p. 16
Spacecraft Guidance	p. 16
Maritime	p. 16
Land	p. 16
Geographic Information Systems (GISs), Mapping, and Agriculture	p. 16
Problems	p. 17
Fundamentals of Satellite and Inertial Navigation	p. 18
Navigation Systems Considered	p. 18
Systems Other than GNSS	p. 18
Comparison Criteria	p. 19
Fundamentals of Inertial Navigation	p. 19
Basic Concepts	p. 19
Inertial Navigation Systems	p. 21
Sensor Signal Processing	p. 28
Standalone INS Performance	p. 32
Satellite Navigation	p. 34
Satellite Orbits	p. 34
Navigation Solution (Two-Dimensional Example)	p. 34
Satellite Selection and Dilution of Precision	p. 39
Example Calculation of DOPs	p. 42
Time and GPS	p. 44
Coordinated Universal Time Generation	p. 44
GPS System Time	p. 44
Receiver Computation of UTC	p. 45
Example GPS Calculations with no Errors	p. 46
User Position Calculations	p. 46
User Velocity Calculations	p. 48
Problems	p. 49
Signal Characteristics and Information Extraction	p. 53
Mathematical Signal Waveform Models	p. 53
GPS Signal Components, Purposes, and Properties	p. 54
50-bps (bits per second) Data Stream	p. 54
GPS Satellite Position Calculations	p. 59
C/A-Code and Its Properties	p. 65
P-Code and Its Properties	p. 70
L[subscript 1] and L[subscript 2] Carriers	p. 71
Signal Power Levels	p. 72
Transmitted Power Levels	p. 72
Free-Space Loss Factor	p. 72
Atmospheric Loss Factor	p. 72
Antenna Gain and Minimum Received Signal Power	p. 73
Signal Acquisition and Tracking	p. 73
Determination of Visible Satellites	p. 73
Signal Doppler Estimation	p. 74
Search for Signal in Frequency and C/A-Code Phase	p. 74
Signal Detection and Confirmation	p. 78
Code Tracking Loop	p. 81
Carrier Phase Tracking Loops	p. 84
Bit Synchronization	p. 87
Data Bit Demodulation	p. 88
Extraction of Information for Navigation Solution	p. 88
Signal Transmission Time Information	p. 89
Ephemeris Data	p. 89
Pseudorange Measurements Using C/A-Code	p. 89
Pseudorange Measurements Using Carrier Phase	p. 91
Carrier Doppler Measurement	p. 92
Integrated Doppler Measurements	p. 93
Theoretical Considerations in Pseudorange and Frequency Estimation	p. 95
Theoretical versus Realizable Code-Based Pseudoranging Performance	p. 95
Theoretical Error Bounds for Carrier-Based Pseudoranging	p. 97
Theoretical Error Bounds for Frequency Measurement	p. 98
Modernization of GPS	p. 98
Deficiencies of the Current System	p. 99
Elements of the Modernized GPS	p. 100
Families of GPS Satellites	p. 103
Accuracy Improvements from Modernization	p. 104
Structure of the Modernized Signals	p. 104
Problems	p. 107
Receiver and Antenna Design	p. 111
Receiver Architecture	p. 111
Radiofrequency Stages (Front End)	p. 111
Frequency Downconversion and IF Amplification	p. 112
Digitization	p. 114
Baseband Signal Processing	p. 114
Receiver Design Choices	p. 116
Number of Channels and Sequencing Rate	p. 116
L[subscript 2] Capability	p. 118
Code Selections: C/A, P, or Codeless	p. 119
Access to SA Signals	p. 120
Differential Capability	p. 121
Pseudosatellite Compatibility	p. 123
Immunity to Pseudolite Signals	p. 128
Aiding Inputs	p. 128
High-Sensitivity-Assisted GPS Systems (Indoor Positioning)	p. 129
How Assisting Data Improves Receiver Performance	p. 130
Factors Affecting High-Sensitivity Receivers	p. 134
Antenna Design	p. 135
Physical Form Factors	p. 136
Circular Polarization of GPS Signals	p. 137
Principles of Phased-Array Antennas	p. 139
The Antenna Phase Center	p. 141
Problems	p. 142
Global Navigation Satellite System Data Errors	p. 144
Selective Availability Errors	p. 144
Time-Domain Description	p. 147
Collection of SA Data	p. 150
Ionospheric Propagation Errors	p. 151
Ionospheric Delay Model	p. 153
GNSS Ionospheric Algorithms	p. 155
Tropospheric Propagation Errors	p. 163
The Multipath Problem	p. 164
How Multipath Causes Ranging Errors	p. 165
Methods of Multipath Mitigation	p. 167
Spatial Processing Techniques	p. 167
Time-Domain Processing	p. 169
MMT Technology	p. 172
Performance of Time-Domain Methods	p. 182
Theoretical Limits for Multipath Mitigation	p. 184
Estimation-Theoretic Methods	p. 184
MMSE Estimator	p. 184
Multipath Modeling Errors	p. 184
Ephemeris Data Errors	p. 185
Onboard Clock Errors	p. 185
Receiver Clock Errors	p. 186
Error Budgets	p. 188
Differential GNSS	p. 188
PN Code Differential Measurements	p. 190
Carrier Phase Differential Measurements	p. 191
Positioning Using Double-Difference Measurements	p. 193
GPS Precise Point Positioning Services and Products	p. 194
Problems	p. 196
Differential GNSS	p. 199
Introduction	p. 199
Descriptions of LADGPS, WADGPS, and SBAS	p. 199
Local-Area Differential GPS (LADGPS)	p. 199
Wide-Area Differential GPS (WADGPS)	p. 200
Space-Based Augmentation Systems (SBAS)	p. 200
Ground-Based Augmentation System (GBAS)	p. 205
Local-Area Augmentation System (LAAS)	p. 205
Joint Precision Approach Landing System (JPALS)	p. 205
LORAN-C	p. 206
GEO Uplink Subsystem (GUS)	p. 206
Description of the GUS Algorithm	p. 207
In-Orbit Tests	p. 208
Ionospheric Delay Estimation	p. 209
Code-Carrier Frequency Coherence	p. 211
Carrier Frequency Stability	p. 212
GUS Clock Steering Algorithms	p. 213
Primary GUS Clock Steering Algorithm	p. 214
Backup GUS Clock Steering Algorithm	p. 215
Clock Steering Test Results Description	p. 216
GEO with L[subscript 1]/L[subscript 5] Signals	p. 217
GEO Uplink Subsystem Type 1 (GUST) Control Loop Overview	p. 220
New GUS Clock Steering Algorithm	p. 223
Receiver Clock Error Determination	p. 226
Clock Steering Control Law	p. 227
GEO Orbit Determination	p. 228
Orbit Determination Covariance Analysis	p. 230
Problems	p. 235
GNSS and GEO Signal Integrity	p. 236
Receiver Autonomous Integrity Monitoring (RAIM)	p. 236
Range Comparison Method of Lee [121]	p. 237
Least-Squares Method [151]	p. 237
Parity Method [182, 183]	p. 238
SBAS and GBAS Integrity Design	p. 238
SBAS Error Sources and Integrity Threats	p. 240
GNSS-Associated Errors	p. 240
GEO-Associated Errors	p. 243
Receiver and Measurement Processing Errors	p. 243
Estimation Errors	p. 245
Integrity-Bound Associated Errors	p. 245
GEO Uplink Errors	p. 246
Mitigation of Integrity Threats	p. 247
SBAS example	p. 253
Conclusions	p. 254
GPS Integrity Channel (GIC)	p. 254
Kalman Filtering	p. 255
Introduction	p. 255
What Is a Kalman Filter?	p. 255
How It Works	p. 256
Kalman Gain	p. 257
Approaches to Deriving the Kalman Gain	p. 258
Gaussian Probability Density Functions	p. 259
Properties of Likelihood Functions	p. 260
Solving for Combined Information Matrix	p. 262
Solving for Combined Argmax	p. 263
Noisy Measurement Likelihoods	p. 263
Gaussian Maximum-Likelihood Estimate	p. 265
Kalman Gain Matrix for Maximum-Likelihood Estimation	p. 267
Estimate Correction Using Kalman Gain	p. 267
Covariance Correction for Measurements	p. 267
Prediction	p. 268
Stochastic Systems in Continuous Time	p. 268
Stochastic Systems in Discrete Time	p. 273
State Space Models for Discrete Time	p. 274
Dynamic Disturbance Noise Distribution Matrices	p. 275
Predictor Equations	p. 276
Summary of Kalman Filter Equations	p. 277
Essential Equations	p. 277
Common Terminology	p. 277
Data Flow Diagrams	p. 278
Accommodating Time-Correlated Noise	p. 279
Correlated Noise Models	p. 279
Empirical Sensor Noise Modeling	p. 282
State Vector Augmentation	p. 283
Nonlinear and Adaptive Implementations	p. 285
Nonlinear Dynamics	p. 285
Nonlinear Sensors	p. 286
Linearized Kalman Filter	p. 286
Extended Kalman Filtering	p. 287
Adaptive Kalman Filtering	p. 288
Kalman-Bucy Filter	p. 290
Implementation Equations	p. 290
Kalman-Bucy Filter Parameters	p. 291
GPS Receiver Examples	p. 291
Satellite Models	p. 291
Measurement Model	p. 292
Coordinates	p. 293
Measurement Sensitivity Matrix	p. 293
Implementation Results	p. 294
Other Kalman Filter Improvements	p. 302
Schmidt-Kalman Suboptimal Filtering	p. 302
Serial Measurement Processing	p. 305
Improving Numerical Stability	p. 305
Kalman Filter Monitoring	p. 309
Problems	p. 313
Inertial Navigation Systems	p. 316
Inertial Sensor Technologies	p. 316
Early Gyroscopes	p. 316
Early Accelerometers	p. 320
Feedback Control Technology	p. 323
Rotating Coriolis Multisensors	p. 326
Laser Technology and Lightwave Gyroscopes	p. 328
Vibratory Coriolis Gyroscopes (VCGs)	p. 329
MEMS Technology	p. 331
Inertial Systems Technologies	p. 332
Early Requirements	p. 332
Computer Technology	p. 332
Early Strapdown Systems	p. 333
INS and GNSS	p. 334
Inertial Sensor Models	p. 335
Zero-Mean Random Errors	p. 336
Systematic Errors	p. 337
Other Calibration Parameters	p. 340
Calibration Parameter Instability	p. 341
Auxilliary Sensors	p. 342
System Implementation Models	p. 343
One-Dimensional Example	p. 343
Initialization and Alignment	p. 344
Earth Models	p. 347
Gimbal Attitude Implementations	p. 355
Strapdown Attitude Implementations	p. 357
Navigation Computer and Software Requirements	p. 363
System-Level Error Models	p. 364
Error Sources	p. 365
Navigation Error Propagation	p. 367
Sensor Error Propagation	p. 373
Examples	p. 377
Problems	p. 381
GNSS/INS Integration	p. 382
Background	p. 382
Sensor Integration	p. 382
The Influence of Host Vehicle Trajectories on Performance	p. 383
Loosely and Tightly Coupled Integration	p. 384
Antenna/ISA Offset Correction	p. 385
Effects of Host Vehicle Dynamics	p. 387
Vehicle Tracking Filters	p. 388
Specialized Host Vehicle Tracking Filters	p. 390
Vehicle Tracking Filter Comparison	p. 402
Loosely Coupled Integration	p. 404
Overall Approach	p. 404
GNSS Error Models	p. 404
Receiver Position Error Model	p. 407
INS Error Models	p. 408
Tightly Coupled Integration	p. 413
Using GNSS for INS Vertical Channel Stabilization	p. 413
Using INS Accelerations to Aid GNSS Signal Tracking	p. 414
Using GNSS Pseudoranges	p. 414
Real-Time INS Recalibration	p. 415
Future Developments	p. 423
Software	p. 425
Software Sources	p. 425
Software for Chapter 3	p. 426
Satellite Position Determination Using Ephemeris Data	p. 426
Satellite Position Determination Using Almanac Data for All Satellites	p. 426
Software for Chapter 5	p. 426
Ionospheric Delays	p. 426
Software for Chapter 8	p. 426
Software for Chapter 9	p. 427
Software for Chapter 10	p. 428
Vectors and Matrices	p. 429
Scalars	p. 429
Vectors	p. 430
Vector Notation	p. 430
Unit Vectors	p. 430
Subvectors	p. 430
Transpose of a Vector	p. 431
Vector Inner Product	p. 431
Orthogonal Vectors	p. 431
Magnitude of a Vector	p. 431
Unit Vectors and Orthonormal Vectors	p. 431
Vector Norms	p. 432
Vector Cross-Product	p. 432
Right-Handed Coordinate Systems	p. 433
Vector Outer Product	p. 433
Matrices	p. 433
Matrix Notation	p. 433
Special Matrix Forms	p. 434
Matrix Operations	p. 436
Matrix Transposition	p. 436
Subscripted Matrix Expressions	p. 437
Multiplication of Matrices by Scalars	p. 437
Addition and Multiplication of Matrices	p. 437
Powers of Square Matrices	p. 438
Matrix Inversion	p. 438
Generalized Matrix Inversion	p. 438
Orthogonal Matrices	p. 439
Block Matrix Formulas	p. 439
Submatrices, Partitioned Matrices, and Blocks	p. 439
Rank and Linear Dependence	p. 440
Conformable Block Operations	p. 441
Block Matrix Inversion Formula	p. 441
Inversion Formulas for Matrix Expressions	p. 441
Functions of Square Matrices	p. 442
Determinants and Characteristic Values	p. 442
The Matrix Trace	p. 444
Algebraic Functions of Matrices	p. 444
Analytic Functions of Matrices	p. 444
Similarity Transformations and Analytic Functions	p. 446
Norms	p. 447
Normed Linear Spaces	p. 447
Matrix Norms	p. 447
Factorizations and Decompositions	p. 449
Cholesky Decomposition	p. 449
QR Decomposition (Triangularization)	p. 451
Singular-Value Decomposition	p. 451
Eigenvalue-Eigenvector Decompositions of Symmetric Matrices	p. 452
Quadratic Forms	p. 452
Symmetric Decomposition of Quadratic Forms	p. 453
Derivatives of Matrices	p. 453
Derivatives of Matrix-Valued Functions	p. 453
Gradients of Quadratic Forms	p. 455
Coordinate Transformations	p. 456
Notation	p. 456
Inertial Reference Directions	p. 458
Vernal Equinox	p. 458
Polar Axis of Earth	p. 459
Coordinate Systems	p. 460
Cartesian and Polar Coordinates	p. 460
Celestial Coordinates	p. 461
Satellite Orbit Coordinates	p. 461
ECI Coordinates	p. 463
ECEF Coordinates	p. 463
LTP Coordinates	p. 470
RPY Coordinates	p. 473
Vehicle Attitude Euler Angles	p. 473
GPS Coordinates	p. 475
Coordinate Transformation Models	p. 477
Euler Angles	p. 477
Rotation Vectors	p. 478
Direction Cosines Matrix	p. 493
Quaternions	p. 497
References	p. 502
Index	p. 517
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