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,
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
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
2023-09-15 18:26:06
43.47MB
清晰版
1