Kalman Filtering

Auteur

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.

Texte du rabat

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.

Résumé
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.

Contenu

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 Kalman Bucy 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 Schmidt Kalman 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 9.11 Summary, 501 Problems, 501 References, 502 10 Applications to Navigation 503 10.1 Chapter Focus, 503 10.2 Navigation Overview, 504 10.3 Global Navigation Satellite Systems (GNSS), 510 10.4 Inertial Navigation Systems (INS), 544 10.5 GNSS/INS Integration, 578 10.6 Summary, 588 Problems, 590 References, 591 Appendix A Software 593 A.1 Appendix Focus, 593 A.2 Chapter 1 Software, 594 A.3 Chapter 2 Software, 594 A.4 Chapter 3 Software, 595 A.5 Chapter 4 Software, 595 A.6 Chapter 5 Software, 596 A.7 Chapter 6 Software, 596 A.8 Chapter 7 Software, 597 A.9 Chapter 8 Software, 598 A.10 Chapter 9 Software, 599 A.11 Chapter 10 Software, 599 A.12 Other Software Sources, 601 References, 603 Index 605