The definitive textbook and professional reference on Kalman
Filtering - fully updated, revised, and expanded
This book contains the latest developments in the implementation
and application of Kalman filtering. Authors Grewal and Andrews
draw upon their decades of experience to offer an in-depth
examination of the subtleties, common pitfalls, and limitations of
estimation theory as it applies to real-world situations. They
present many illustrative examples including adaptations for
nonlinear filtering, global navigation satellite systems, the error
modeling of gyros and accelerometers, inertial navigation systems,
and freeway traffic control.
Kalman Filtering: Theory and Practice Using MATLAB, Fourth
Edition is an ideal textbook in advanced undergraduate and
beginning graduate courses in stochastic processes and Kalman
filtering. It is also appropriate for self-instruction or review by
practicing engineers and scientists who want to learn more about
this important topic.
Autorentext
Mohinder S. Grewal, PhD, PE, is Professor of Electrical Engineering in the College of Engineering and Computer Science at California State University, Fullerton. He has more than forty years of experience in inertial navigation and control, and his mechanizations are currently used in commercial and military aircraft, surveillance satellites, missile and radar systems, freeway traffic control, and Global Navigation Satellite Systems.
Angus P. Andrews, PhD, is an MIT graduate with a PhD in mathematics from UCLA. His career in aerospace technology development spans more than 50 years, starting with navigation analysis for the Apollo moon missions, and including a dozen years in the analysis, design, development, and testing of inertial navigation systems. His discoveries included the orbital navigation method called unknown landmark tracking, alternative solutions for square root filters, and a model for bearing torques of electrostatic gyroscopes. Since retiring as a senior scientist from the Rockwell Science Center in 2000, he has continued consulting and instructing in sensor error modeling and analysis, and publishing articles and books on these subjects.
Klappentext
The definitive textbook and professional reference on Kalman Filtering fully updated, revised, and expanded
This book contains the latest developments in the implementation and application of Kalman filtering. Authors Grewal and Andrews draw upon their decades of experience to offer an in-depth examination of the subtleties, common pitfalls, and limitations of estimation theory as it applies to real-world situations. They present many illustrative examples including adaptations for nonlinear filtering, global navigation satellite systems, the error modeling of gyros and accelerometers, inertial navigation systems, and freeway traffic control.
Kalman Filtering: Theory and Practice Using MATLAB, Fourth Edition is an ideal textbook in advanced undergraduate and beginning graduate courses in stochastic processes and Kalman filtering. It is also appropriate for self-instruction or review by practicing engineers and scientists who want to learn more about this important topic.
Inhalt
Preface to the Fourth Edition ix
Acknowledgements xiii
List of Abbreviations xv
1 Introduction 1
1.1 Chapter Focus 1
1.2 On Kalman Filtering 1
1.3 On Optimal Estimation Methods 6
1.4 Common Notation 28
1.5 Summary 30
Problems 31
References 34
2 Linear Dynamic Systems 37
2.1 Chapter Focus 37
2.2 Deterministic Dynamic System Models 42
2.3 Continuous Linear Systems and their Solutions 47
2.4 Discrete Linear Systems and their Solutions 59
2.5 Observability of Linear Dynamic System Models 61
2.6 Summary 66
Problems 69
References 71
3 Probability and Expectancy 73
3.1 Chapter Focus 73
3.2 Foundations of Probability Theory 74
3.3 Expectancy 79
3.4 Least-Mean-Square Estimate (LMSE) 87
3.5 Transformations of Variates 93
3.6 The Matrix Trace in Statistics 102
3.7 Summary 106
Problems 107
References 110
4 Random Processes 111
4.1 Chapter Focus 111
4.2 Random Variables Processes and Sequences 112
4.3 Statistical Properties 114
4.4 Linear Random Process Models 124
4.5 Shaping Filters (SF) and State Augmentation 131
4.6 Mean and Covariance Propagation 135
4.7 Relationships Between Model Parameters 145
4.8 Orthogonality Principle 153
4.9 Summary 157
Problems 159
References 167
5 Linear Optimal Filters and Predictors 169
5.1 Chapter Focus 169
5.2 Kalman Filter 172
5.3 KalmanBucy Filter 197
5.4 Optimal Linear Predictors 200
5.5 Correlated Noise Sources 200
5.6 Relationships Between Kalman and Wiener Filters 201
5.7 Quadratic Loss Functions 202
5.8 Matrix Riccati Differential Equation 204
5.9 Matrix Riccati Equation in Discrete Time 219
5.10 Model Equations for Transformed State Variables 223
5.11 Sample Applications 224
5.12 Summary 228
Problems 232
References 235
6 Optimal Smoothers 239
6.1 Chapter Focus 239
6.2 Fixed-Interval Smoothing 244
6.3 Fixed-Lag Smoothing 256
6.4 Fixed-Point Smoothing 268
6.5 Summary 275
Problems 276
References 278
7 Implementation Methods 281
7.1 Chapter Focus 281
7.2 Computer Roundoff 283
7.3 Effects of Roundoff Errors on Kalman Filters 288
7.4 Factorization Methods for Square-Root Filtering 294
7.5 Square-Root and UD Filters 318
7.6 SigmaRho Filtering 330
7.7 Other Implementation Methods 346
7.8 Summary 358
Problems 360
References 363
8 Nonlinear Approximations 367
8.1 Chapter Focus 367
8.2 The Affine Kalman Filter 370
8.3 Linear Approximations of Nonlinear Models 372
8.4 Sample-and-Propagate Methods 398
8.5 Unscented Kalman Filters (UKF) 404
8.6 Truly Nonlinear Estimation 417
8.7 Summary 419
Problems 420
References 423
9 Practical Considerations 427
9.1 Chapter Focus 427
9.2 Diagnostic Statistics and Heuristics 428
9.3 Prefiltering and Data Rejection Methods 457
9.4 Stability of Kalman Filters 460
9.5 Suboptimal and Reduced-Order Filters 461
9.6 SchmidtKalman Filtering 471
9.7 Memory Throughput and Wordlength Requirements 478
9.8 Ways to Reduce Computational Requirements 486
9.9 Error Budgets and Sensitivity Analysis 491
9.10 Optimizing Measurement Selection Policies 495
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