Global Positioning Systems, Inertial Navigation, and Integration / Edition 1

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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 L[subscript 1]/L[subscript 5] 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 toshowing 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.

About the Author:
Mohinder S. Grewal, PhD, PE, is Professor of Electrical Engineering in the College of Engineering and Computer Science at California State University, Fullerton

About the Author:
Lawrence R. Weill, PhD, is Professor Emeritus of Applied Mathematics in the College of Mathematics and Natural Sciences at California State University, Fullerton

About the Author:
Angus P. Andrews, PhD, is Senior Scientist (Retired) at the Rockwell Science Center in Thousand Oaks, California

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Editorial Reviews

From the Publisher
"This work is a necessary update and is recommended for academic technology collections." (E-STREAMS, September 2007)
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Product Details

  • ISBN-13: 9780471350323
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 1/28/2001
  • Edition description: Older Edition
  • Edition number: 1
  • Pages: 416
  • Product dimensions: 6.54 (w) x 9.61 (h) x 1.08 (d)

Meet the Author

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.

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Table of Contents

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