GLOBAL NAVIGATION SATELLITE SYSTEMS, INERTIAL NAVIGATION, AND INTEGRATION 4/E 

Preface to the Fourth Edition xxv
Acknowledgments xxix
About the Authors xxx
Acronyms xxxi
About the Companion Website xxxix
1 Introduction 1
1.1 Navigation 1
1.1.1 Navigation-Related Technologies 1
1.1.2 Navigation Modes 2
1.2 GNSS Overview 3
1.2.1 GPS 4
1.2.2 Global Orbiting Navigation Satellite System (GLONASS) 6
1.2.3 Galileo 7
1.2.4 BeiDou 9
1.2.5 Regional Satellite Systems 10
1.3 Inertial Navigation Overview 10
1.3.1 History 11
1.3.2 Development Results 12
1.4 GNSS/INS Integration Overview 16
1.4.1 The Role of Kalman Filtering 16
1.4.2 Implementation 17
Problems 17
References 18
2 Fundamentals of Satellite Navigation Systems 21
2.1 Chapter Focus 21
2.2 Satellite Navigation Systems Considerations 21
2.2.1 Systems Other than GNSS 21
2.2.2 Comparison Criteria 22
2.3 Satellite Navigation 22
2.3.1 GNSS Orbits 23
2.3.2 Navigation Solution (Two-Dimensional Example) 25
2.3.3 User Solution and Dilution of Precision (DOP) 28
2.3.4 Example Calculation of DOPs 32
2.4 Time and GPS 33
2.4.1 Coordinated Universal Time (UTC) Generation 33
2.4.2 GPS System Time 33
2.4.3 Receiver Computation of UTC 34
2.5 Example: User Position Calculations with No Errors 35
2.5.1 User Position Calculations 35
2.5.2 User Velocity Calculations 37
Problems 39
References 41
3 Fundamentals of Inertial Navigation 43
3.1 Chapter Focus 43
3.2 Terminology 44
3.3 Inertial Sensor Technologies 50
3.3.1 Gyroscopes 50
3.3.2 Accelerometers 53
3.3.3 Sensor Errors 55
3.3.4 Inertial Sensor Assembly (ISA) Calibration 57
3.3.5 Carouseling and Indexing 60
3.4 Inertial Navigation Models 60
3.4.1 Geoid Models 61
3.4.2 Terrestrial Navigation Coordinates 61
3.4.3 Earth Rotation Model 63
3.4.4 Gravity Models 63
3.4.5 Attitude Models 68
3.5 Initializing the Navigation Solution 70
3.5.1 Initialization from an Earth-fixed Stationary State 70
3.5.2 Initialization on the Move 73
3.6 Propagating the Navigation Solution 73
3.6.1 Attitude Propagation 73
3.6.2 Position and Velocity Propagation 82
3.7 Testing and Evaluation 86
3.7.1 Laboratory Testing 86
3.7.2 Field Testing 86
3.7.3 Performance Qualification Testing 87
3.8 Summary 89
3.8.1 Further Reading 89
Problems 90
References 92
4 GNSS Signal Structure, Characteristics, and Information Utilization 93
4.1 Legacy GPS Signal Components, Purposes, and Properties 93
4.1.1 Signal Models for the Legacy GPS Signals 94
4.1.2 Navigation Data Format 98
4.1.3 GPS Satellite Position Calculations 102
4.1.4 C/A-Code and Its Properties 108
4.1.5 P(Y)-Code and Its Properties 115
4.1.6 L1 and L2 Carriers 116
4.1.7 Transmitted Power Levels 117
4.1.8 Free Space and Other Loss Factors 117
4.1.9 Received Signal Power 118
4.2 Modernization of GPS 118
4.2.1 Benefits from GPS Modernization 119
4.2.2 Elements of the Modernized GPS 120
4.2.3 L2 Civil Signal (L2C) 122
4.2.4 L5 Signal 123
4.2.5 M-Code 125
4.2.6 L1C Signal 126
4.2.7 GPS Satellite Blocks 128
4.2.8 GPS Ground Control Segment 129
4.3 GLONASS Signal Structure and Characteristics 129
4.3.1 Frequency Division Multiple Access (FDMA) Signals 130
4.3.2 CDMA Modernization 131
4.4 Galileo 132
4.4.1 Constellation and Levels of Services 132
4.4.2 Navigation Data and Signals 132
4.5 BeiDou 134
4.6 QZSS 135
4.7 IRNSS/NAVIC 138
Problems 138
References 141
5 GNSS Antenna Design and Analysis 145
5.1 Applications 145
5.2 GNSS Antenna Performance Characteristics 145
5.2.1 Size and Cost 145
5.2.2 Frequency and Bandwidth Coverage 146
5.2.3 Radiation Pattern Characteristics 147
5.2.4 Antenna Polarization and Axial Ratio 149
5.2.5 Directivity, Efficiency, and Gain of a GNSS Antenna 152
5.2.6 Antenna Impedance, Standing Wave Ratio, and Return Loss 153
5.2.7 Antenna Bandwidth 154
5.2.8 Antenna Noise Figure 155
5.3 Computational Electromagnetic Models (CEMs) for GNSS Antenna Design 157
5.4 GNSS Antenna Technologies 159
5.4.1 Dipole-Based GNSS Antennas 159
5.4.2 GNSS Patch Antennas 160
5.4.3 Survey-Grade/Reference GNSS Antennas 169
5.5 Principles of Adaptable Phased-Array Antennas 173
5.5.1 Digital Beamforming Adaptive Antenna Array Formulations 176
5.5.2 STAP 179
5.5.3 SFAP 179
5.5.4 Configurations of Adaptable Phased-Array Antennas 179
5.5.5 Relative Merits of Adaptable Phased-Array Antennas 180
5.6 Application Calibration/Compensation Considerations 181
Problems 183
References 184
6 GNSS Receiver Design and Analysis 189
6.1 Receiver Design Choices 189
6.1.1 Global Navigation Satellite System (GNSS) Application to Be Supported 189
6.1.2 Single or Multifrequency Support 189
6.1.3 Number of Channels 191
6.1.4 Code Selections 191
6.1.5 Differential Capability 192
6.1.6 Aiding Inputs 194
6.2 Receiver Architecture 195
6.2.1 Radio Frequency (RF) Front End 195
6.2.2 Frequency Down-Conversion and IF Amplification 197
6.2.2.1 SNR 198
6.2.3 Analog-to-Digital Conversion and Automatic Gain Control 199
6.2.4 Baseband Signal Processing 200
6.3 Signal Acquisition and Tracking 200
6.3.1 Hypothesize About the User Location 201
6.3.2 Hypothesize About Which GNSS Satellites Are Visible 201
6.3.3 Signal Doppler Estimation 202
6.3.4 Search for Signal in Frequency and Code Phase 202
6.3.5 Signal Detection and Confirmation 207
6.3.6 Code Tracking Loop 210
6.3.7 Carrier Phase Tracking Loops 215
6.3.8 Bit Synchronization 219
6.3.9 Data Bit Demodulation 219
6.4 Extraction of Information for User Solution 220
6.4.1 Signal Transmission Time Information 220
6.4.2 Ephemeris Data for Satellite Position and Velocity 221
6.4.3 Pseudorange Measurements Formulation Using Code Phase 221
6.4.4 Measurements Using Carrier Phase 223
6.4.5 Carrier Doppler Measurement 225
6.4.6 Integrated Doppler Measurements 226
6.5 Theoretical Considerations in Pseudorange, Carrier Phase, and Frequency Estimations 228
6.5.1 Theoretical Error Bounds for Code Phase Measurement 229
6.5.2 Theoretical Error Bounds for Carrier Phase Measurements 230
6.5.3 Theoretical Error Bounds for Frequency Measurement 231
6.6 High-Sensitivity A-GPS Systems 232
6.6.1 How Assisting Data Improves Receiver Performance 233
6.6.2 Factors Affecting High-Sensitivity Receivers 237
6.7 Software-Defined Radio (SDR) Approach 239
6.8 Pseudolite Considerations 240
Problems 242
References 244
7 GNSS Measurement Errors 249
7.1 Source of GNSS Measurement Errors 249
7.2 Ionospheric Propagation Errors 249
7.2.1 Ionospheric Delay Model 251
7.2.2 GNSS SBAS Ionospheric Algorithms 253
7.3 Tropospheric Propagation Errors 262
7.4 The Multipath Problem 263
7.4.1 How Multipath Causes Ranging Errors 264
7.5 Methods of Multipath Mitigation 266
7.5.1 Spatial Processing Techniques 266
7.5.2 Time-Domain Processing 269
7.5.3 Multipath Mitigation Technology (MMT) 271
7.5.4 Performance of Time-Domain Methods 281
7.6 Theoretical Limits for Multipath Mitigation 283
7.6.1 Estimation-Theoretic Methods 283
7.6.2 Minimum Mean-Squared Error (MMSE) Estimator 284
7.6.3 Multipath Modeling Errors 284
7.7 Ephemeris Data Errors 285
7.8 Onboard Clock Errors 285
7.9 Receiver Clock Errors 286
7.10 Error Budgets 287
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 Augmentation System (SBAS) 294
8.2.1 LADGNSS 294
8.2.2 WADGNSS 294
8.2.3 SBAS 294
8.3 GEO with L1L5 Signals 299
8.3.1 GEO Uplink Subsystem (GUS) Control Loop Overview 302
8.4 GUS Clock Steering Algorithm 307
8.4.1 Receiver Clock Error Determination 309
8.4.2 Clock Steering Control Law 311
8.5 GEO Orbit Determination (OD) 312
8.5.1 OD Covariance Analysis 313
8.6 Ground-Based Augmentation System (GBAS) 318
8.6.1 Local-Area Augmentation System (LAAS) 318
8.6.2 Joint Precision Approach and Landing System (ALS) 318
8.6.3 Enhanced Long-Range Navigation (eLORAN) 319
8.7 Measurement/Relative-Based DGNSS 320
8.7.1 Code Differential Measurements 320
8.7.2 Carrier Phase Differential Measurements 322
8.7.3 Positioning Using Double-Difference Measurements 324
8.8 GNSS Precise Point Positioning Services and Products 325
8.8.1 The International GNSS Service (IGS) 325
8.8.2 Continuously Operating Reference Stations (CORSs) 326
8.8.3 GPS Inferred Positioning System (GIPSY) and Orbit Analysis Simulation Software (OASIS) 326
8.8.4 Scripps Coordinate Update Tool (SCOUT) 327
8.8.5 The Online Positioning User Service (OPUS) 327
8.8.6 Australia’s Online GPS Processing System (AUPOS) 328
8.8.7 National Resources Canada (NRCan) 328
Problems 328
References 328
9 GNSS and GEO Signal Integrity 331
9.1 Introduction 331
9.1.1 Range Comparison Method 332
9.1.2 Least-Squares Method 332
9.1.3 Parity Method 334
9.2 SBAS and GBAS Integrity Design 334
9.2.1 SBAS Error Sources and Integrity Threats 336
9.2.2 GNSS-Associated Errors 337
9.2.3 GEO-Associated Errors 339
9.2.4 Receiver and Measurement Processing Errors 340
9.2.5 Estimation Errors 341
9.2.6 Integrity-Bound Associated Errors 342
9.2.7 GEO Uplink Errors 343
9.2.8 Mitigation of Integrity Threats 344
9.3 SBAS Example 349
9.4 Summary 351
9.5 Future: GIC 351
Problems 352
References 352
10 Kalman Filtering 355
10.1 Chapter Focus 355
10.2 Frequently Asked Questions 356
10.3 Notation 360
10.3.1 Real Vectors and Matrices 360
10.3.2 Probability Essentials 363
10.3.3 Discrete Time Notation 365
10.4 Kalman Filter Genesis 366
10.4.1 Measurement Update (Corrector) 366
10.4.2 Time Update (Predictor) 373
10.4.3 Basic Kalman Filter Equations 378
10.4.4 The Time-Invariant Case 378
10.4.5 Observability and Stability Issues 378
10.5 Alternative Implementations 380
10.5.1 Implementation Issues 380
10.5.2 Conventional Implementation Improvements 381
10.5.3 James E. Potter (1937–2005) and Square Root Filtering 383
10.5.4 Square Root Matrix Manipulation Methods 384
10.5.5 Alternative Square Root Filter Implementations 386
10.6 Nonlinear Approximations 388
10.6.1 Linear Approximation Errors 389
10.6.2 Adaptive Kalman Filtering 392
10.6.3 Taylor–Maclauren Series Approximations 392
10.6.4 Trajectory Perturbation Modeling 393
10.6.5 Structured Sampling Methods 394
10.7 Diagnostics and Monitoring 397
10.7.1 Covariance Matrix Diagnostics 397
10.7.2 Innovations Monitoring 398
10.8 GNSS-Only Navigation 401
10.8.1 GNSS Dynamic Models 402
10.8.2 GNSS Measurement Models 406
10.9 Summary 410
Problems 412
References 414
11 Inertial Navigation Error Analysis 419
11.1 Chapter Focus 419
11.2 Errors in the Navigation Solution 420
11.2.1 Navigation Error Variables 421
11.2.2 Coordinates Used for INS Error Analysis 421
11.2.3 Model Variables and Parameters 421
11.2.4 Dynamic Coupling Mechanisms 427
11.3 Navigation Error Dynamics 430
11.3.1 Error Dynamics Due to Velocity Integration 431
11.3.2 Error Dynamics Due to Gravity Miscalculations 432
11.3.3 Error Dynamics Due to Coriolis Acceleration 433
11.3.4 Error Dynamics Due to Centrifugal Acceleration 434
11.3.5 Error Dynamics Due to Earthrate Leveling 435
11.3.6 Error Dynamics Due to Velocity Leveling 436
11.3.7 Error Dynamics Due to Acceleration and IMU Alignment Errors 437
11.3.8 Composite Model from All Effects 438
11.3.9 Vertical Navigation Instability 439
11.3.10 Schuler Oscillations 444
11.3.11 Core Model Validation and Tuning 445
11.4 Inertial Sensor Noise Propagation 447
11.4.1 1∕f Noise 447
11.4.2 White Noise 447
11.4.3 Horizontal CEP Rate Versus Sensor Noise 449
11.5 Sensor Compensation Errors 450
11.5.1 Sensor Compensation Error Models 450
11.5.2 Carouseling and Indexing 456
11.6 Chapter Summary 456
11.6.1 Further Reading 457
Problems 458
References 459
12 GNSS/INS Integration 461
12.1 Chapter Focus 461
12.2 New Application Opportunities 462
12.2.1 Integration Advantages 462
12.2.2 Enabling New Capabilities 463
12.2.3 Economic Factors 464
12.3 Integrated Navigation Models 468
12.3.1 Common Navigation Models 468
12.3.2 GNSS Error Models 470
12.3.3 INS Error Models 473
12.3.4 GNSS/INS Error Model 474
12.4 Performance Analysis 476
12.4.1 The Influence of Trajectories 476
12.4.2 Performance Metrics 477
12.4.3 Dynamic Simulation Model 479
12.4.4 Sample Results 480
12.5 Summary 485
Problems 486
References 487
Appendix A Software 489
A.1 Software Sources 489
A.2 Software for Chapter 2 490
A.3 Software for Chapter 3 490
A.4 Software for Chapter 4 490
A.5 Software for Chapter 7 491
A.6 Software for Chapter 10 491
A.7 Software for Chapter 11 492
A.8 Software for Chapter 12 493
A.9 Software for Appendix B 494
A.10 Software for Appendix C 494
A.11 GPS Almanac/Ephemeris Data Sources 495
Appendix B Coordinate Systems and Transformations 497
B.1 Coordinate Transformation Matrices 497
B.1.1 Notation 497
B.1.2 Definitions 498
B.1.3 Unit Coordinate Vectors 498
B.1.4 Direction Cosines 499
B.1.5 Composition of Coordinate Transformations 500
B.2 Inertial Reference Directions 500
B.2.1 Earth’s Polar Axis and the Equatorial Plane 500
B.2.2 The Ecliptic and the Vernal Equinox 500
B.2.3 Earth-Centered Inertial (ECI) Coordinates 501
B.3 Application-dependent Coordinate Systems 501
B.3.1 Cartesian and Polar Coordinates 501
B.3.2 Celestial Coordinates 502
B.3.3 Satellite Orbit Coordinates 503
B.3.4 Earth-Centered Inertial (ECI) Coordinates 504
B.3.5 Earth-Centered, Earth-Fixed (ECEF) Coordinates 505
B.3.6 Ellipsoidal Radius of Curvature 512
B.3.7 Local Tangent Plane (LTP) Coordinates 513
B.3.8 Roll–Pitch–Yaw (RPY) Coordinates 516
B.3.9 Vehicle Attitude Euler Angles 516
B.3.10 GPS Coordinates 518
B.4 Coordinate Transformation Models 520
B.4.1 Euler Angles 521
B.4.2 Rotation Vectors 522
B.4.3 Direction Cosines Matrix 538
B.4.4 Quaternions 542
B.5 Newtonian Mechanics in Rotating Coordinates 547
B.5.1 Rotating Coordinates 547
B.5.2 Time Derivatives of Matrix Products 548
B.5.3 Solving for Centrifugal and Coriolis Accelerations 548
Appendix C PDF Ambiguity Errors in Nonlinear Kalman Filtering 551
C.1 Objective 551
C.2 Methodology 552
C.2.1 Computing Expected Values 552
C.2.2 Representative Sample of PDFs 553
C.2.3 Parametric Class of Nonlinear Transformations Used 556
C.2.4 Ambiguity Errors in Nonlinearly Transformed Means and Variances 558
C.3 Results 558
C.3.1 Nonlinearly Transformed Means 558
C.3.2 Nonlinearly Transformed Variances 559
C.4 Mitigating Application-specific Ambiguity Errors 563
References 564
Index 565