KALMAN FILTERING with Real-Time Applications Charles K. Chui and Guanrong Chen PUBLISHER: Springer-Verlag 175 Fifth Ave., New York, NY 10010 phone:1-800-springer FAX:212-473-6272 ISBNs: 3-540-54013-X and 0-387-54013-X PRICEs: $39.50/$33.58 First edition, 1987; second edition, 1991; third edition 1998 Table of Contents --------------------- 1. Preliminaries --- 1 1.1 Matrix and Determinant Preliminaries --- 1 1.2 Probability Preliminaries --- 8 1.3 Least-Squares Preliminaries --- 15 Exercises --- 18 2. Kalman Filter: An Elementary Approach --- 20 2.1 The Model --- 20 2.2 Optimality Criterion --- 21 2.3 Prediction-Correction Formulation --- 23 2.4 Kalman Filtering Process --- 27 Exercises --- 29 3. Orthogonal Projection and Kalman Filter --- 33 3.1 Orthogonality Characterization of Optimal Estimates --- 33 3.2 Innovations Sequences --- 35 3.3 Minimum Variance Estimates --- 37 3.4 Kalman Filtering Equations --- 38 3.5 Real-Time Tracking --- 42 Exercises --- 45 4. Correlated System and Measurement Noise Processes --- 49 4.1 The Affine Model --- 49 4.2 Optimal Estimate Operators --- 51 4.3 Effect on Optimal Estimation with Additional Data --- 52 4.4 Derivation of Kalman Filtering Equations --- 55 4.5 Real-Time Applications --- 61 4.6 Linear Deterministic/Stochastic Systems -- 63 Exercises --- 65 5. Colored Noise --- 67 5.1 Outline of Procedure --- 67 5.2 Error Estimates --- 68 5.3 Kalman Filtering Process --- 70 5.4 White System Noise --- 73 5.5 Real-Time Applications --- 73 Exercises --- 75 6. Limiting Kalman Filter --- 77 6.1 Outline of Procedure --- 78 6.2 Preliminary Results --- 79 6.3 Geometric Convergence --- 88 6.4 Real-Time Applications --- 93 Exercises --- 95 7. Sequential and Square-Root Algorithms --- 97 7.1 Sequential Algorithm --- 97 7.2 Square-Root Algorithm --- 103 7.3 An Algorithm for Real-Time Applications --- 105 Exercises --- 107 8. Extended Kalman Filter and System Identification --- 108 8.1 Extended Kalman Filter --- 108 8.2 Satellite Orbit Estimation --- 111 8.3 Adaptive System Identification --- 113 8.4 An Example of Constant Parameter Identification --- 115 8.5 Modified Extended Kalman Filter --- 118 8.6 Time-Varying Parameter Identification --- 124 Exercises --- 129 9. Decoupling of Filtering Equations --- 131 9.1 Decoupling Formulas --- 131 9.2 Real-Time Tracking --- 134 9.3 The alpha-beta-gamma Tracker --- 136 9.4 An Example --- 139 Exercises --- 140
10.1 Interval Mathematics --- 143 10.2 Interval Kalman Filtering --- 154 10.3 Weighted-Average Interval Kalman Filtering --- 160 Exercises --- 162 11.
Wavelet Kalman Filtering --- 164
12. Notes --- 178 12.1 The Kalman Smoother --- 178 12.2 The alpha-beta-gamma-theta Tracker --- 180 12.3 Adaptive Kalman Filtering --- 182 12.4 Adaptive Kalman Filtering Approach to Wiener Filtering --- 184 12.5 The Kalman-Bucy Filter --- 185 12.6 Stochastic Optimal Control --- 186 12.7 Square-Root Filtering and Systolic Array Implementation --- 188 References --- 191 Answers and Hints to Exercises --- 197 Subject Index --- 1227 |
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