Kalman Filtering: Theory and Practice Using MATLAB®, Third Edition

Cover Page......Page 1
Title: KALMAN FILTERING Theory and Practice Using MATLAB......Page 3
ISBN 0470173661......Page 4
3 Random Processes and Stochastic Systems......Page 5
7 Nonlinear Filtering......Page 6
Appendix A MATLAB Software......Page 7
Bibliography, Index......Page 8
PREFACE......Page 9
ACKNOWLEDGMENTS......Page 12
LIST OF ABBREVIATIONS......Page 13
1.1 ON KALMAN FILTERING......Page 15
1.2 ON OPTIMAL ESTIMATION METHODS......Page 19
1.3 ON THE NOTATION USED IN THIS BOOK......Page 37
1.4 SUMMARY......Page 39
PROBLEMS......Page 40
2.1 CHAPTER FOCUS......Page 45
2.2 DYNAMIC SYSTEM MODELS......Page 50
2.3 CONTINUOUS LINEAR SYSTEMS AND THEIR SOLUTIONS......Page 54
2.4 DISCRETE LINEAR SYSTEMS AND THEIR SOLUTIONS......Page 67
2.5 OBSERVABILITY OF LINEAR DYNAMIC SYSTEM MODELS......Page 69
2.6 SUMMARY......Page 75
PROBLEMS......Page 78
3.1 CHAPTER FOCUS......Page 81
3.2 PROBABILITY AND RANDOM VARIABLES (RVs)......Page 84
3.3 STATISTICAL PROPERTIES OF RVs......Page 92
3.4 STATISTICAL PROPERTIES OF RANDOM PROCESSES (RPs)......Page 94
3.5 LINEAR RP MODELS......Page 102
3.6 SHAPING FILTERS AND STATE AUGMENTATION......Page 109
3.7 MEAN AND COVARIANCE PROPAGATION......Page 113
3.8 RELATIONSHIPS BETWEEN MODEL PARAMETERS......Page 119
3.9 ORTHOGONALITY PRINCIPLE......Page 128
3.10 SUMMARY......Page 132
PROBLEMS......Page 135
4.1 CHAPTER FOCUS......Page 145
4.2 KALMAN FILTER......Page 147
4.3 KALMAN–BUCY FILTER......Page 158
4.4 OPTIMAL LINEAR PREDICTORS......Page 160
4.5 CORRELATED NOISE SOURCES......Page 161
4.6 RELATIONSHIPS BETWEEN KALMAN–BUCY AND WIENER FILTERS......Page 162
4.7 QUADRATIC LOSS FUNCTIONS......Page 163
4.8 MATRIX RICCATI DIFFERENTIAL EQUATION......Page 165
4.9 MATRIX RICCATI EQUATION IN DISCRETE TIME......Page 179
4.10 MODEL EQUATIONS FOR TRANSFORMED STATE VARIABLES......Page 184
4.11 APPLICATION OF KALMAN FILTERS......Page 186
4.12 SUMMARY......Page 191
PROBLEMS......Page 193
5.1 CHAPTER FOCUS......Page 197
5.2 FIXED-INTERVAL SMOOTHING......Page 203
5.3 FIXED-LAG SMOOTHING......Page 214
5.4 FIXED-POINT SMOOTHING......Page 227
5.5 SUMMARY......Page 234
PROBLEMS......Page 235
6.1 CHAPTER FOCUS......Page 239
6.2 COMPUTER ROUNDOFF......Page 241
6.3 EFFECTS OF ROUNDOFF ERRORS ON KALMAN FILTERS......Page 246
6.4 FACTORIZATION METHODS FOR SQUARE-ROOT FILTERING......Page 252
6.5 SQUARE-ROOT AND UD FILTERS......Page 275
6.6 OTHER IMPLEMENTATION METHODS......Page 289
6.7 SUMMARY......Page 302
PROBLEMS......Page 303
7.1 CHAPTER FOCUS......Page 307
7.2 QUASILINEAR FILTERING......Page 310
7.3 SAMPLING METHODS FOR NONLINEAR FILTERING......Page 344
7.4 SUMMARY......Page 359
PROBLEMS......Page 364
8.1 CHAPTER FOCUS......Page 369
8.2 DETECTING AND CORRECTING ANOMALOUS BEHAVIOR......Page 370
8.3 PREFILTERING AND DATA REJECTION METHODS......Page 393
8.4 STABILITY OF KALMAN FILTERS......Page 396
8.5 SUBOPTIMAL AND REDUCED-ORDER FILTERS......Page 397
8.6 SCHMIDT–KALMAN FILTERING......Page 407
8.7 MEMORY, THROUGHPUT, AND WORDLENGTH REQUIREMENTS......Page 417
8.8 WAYS TO REDUCE COMPUTATIONAL REQUIREMENTS......Page 423
8.9 ERROR BUDGETS AND SENSITIVITY ANALYSIS......Page 428
8.10 OPTIMIZING MEASUREMENT SELECTION POLICIES......Page 433
8.11 INNOVATIONS ANALYSIS......Page 438
8.12 SUMMARY......Page 439
PROBLEMS......Page 440
9.1 CHAPTER FOCUS......Page 441
9.2 HOST VEHICLE DYNAMICS......Page 445
9.3 INERTIAL NAVIGATION SYSTEMS (INS)......Page 449
9.4 GLOBAL NAVIGATION SATELLITE SYSTEMS (GNSS)......Page 479
9.5 KALMAN FILTERS FOR GNSS......Page 484
9.6 LOOSELY COUPLED GNSS/INS INTEGRATION......Page 502
9.7 TIGHTLY COUPLED GNSS/INS INTEGRATION......Page 505
9.8 SUMMARY......Page 521
PROBLEMS......Page 522
A.2 GENERAL SYSTEM REQUIREMENTS......Page 525
A.6 MATLAB SOFTWARE FOR CHAPTER 4......Page 526
A.8 MATLAB SOFTWARE FOR CHAPTER 6......Page 527
A.9 MATLAB SOFTWARE FOR CHAPTER 7......Page 528
A.11 MATLAB SOFTWARE FOR CHAPTER 9......Page 529
A.12 OTHER SOURCES OF SOFTWARE A.12.1 MATLAB Controls Toolbox......Page 530
A.12.4 GNSS and Inertial Navigation Software......Page 531
B.1 MATRIX FORMS......Page 533
B.2 MATRIX OPERATIONS......Page 537
B.3 BLOCK MATRIX FORMULAS......Page 541
B.4 FUNCTIONS OF SQUARE MATRICES......Page 545
B.5 NORMS......Page 552
B.6 CHOLESKY DECOMPOSITION......Page 555
B.7 ORTHOGONAL DECOMPOSITIONS OF MATRICES......Page 557
B.8 QUADRATIC FORMS......Page 559
B.9 DERIVATIVES OF MATRICES......Page 560
BIBLIOGRAPHY......Page 563
INDEX (with page links)......Page 579