Kalman filtering : theory and practice using MATLAB

✍ Scribed by Mohinder S Grewal; Angus P Andrews

• Publisher: Wiley
• Year: 2001
• Tongue: English
• Category: Library

✦ Table of Contents

Content: 1.1 On Kalman Filtering 1 --
1.2 On Estimation Methods 5 --
1.3 On the Notation Used in This Book 20 --
2 Linear Dynamic Systems 25 --
2.1 Chapter Focus 25 --
2.2 Dynamic Systems 26 --
2.3 Continuous Linear Systems and Their Solutions 30 --
2.4 Discrete Linear Systems and Their Solutions 41 --
2.5 Observability of Linear Dynamic System Models 42 --
2.6 Procedures for Computing Matrix Exponentials 48 --
3 Random Processes and Stochastic Systems 56 --
3.1 Chapter Focus 56 --
3.2 Probability and Random Variables 58 --
3.3 Statistical Properties of Random Variables 66 --
3.4 Statistical Properties of Random Processes 68 --
3.5 Linear System Models of Random Processes and Sequences 76 --
3.6 Shaping Filters and State Augmentation 84 --
3.7 Covariance Propagation Equations 88 --
3.8 Orthogonality Principle 97 --
4 Linear Optimal Filters and Predictors 114 --
4.1 Chapter Focus 114 --
4.2 Kalman Filter 116 --
4.3 Kalman--Bucy Filter 126 --
4.4 Optimal Linear Predictors 128 --
4.5 Correlated Noise Sources 129 --
4.6 Relationships between Kalman and Wiener Filters 130 --
4.7 Quadratic Loss Functions 131 --
4.8 Matrix Riccati Differential Equation 133 --
4.9 Matrix Riccati Equation in Discrete Time 148 --
4.10 Relationships between Continuous and Discrete Riccati Equations 153 --
4.11 Model Equations for Transformed State Variables 154 --
4.12 Application of Kalman Filters 155 --
4.13 Smoothers 160 --
5 Nonlinear Applications 169 --
5.1 Chapter Focus 169 --
5.2 Problem Statement 170 --
5.3 Linearization Methods 171 --
5.4 Linearization about a Nominal Trajectory 171 --
5.5 Linearization about the Estimated Trajectory 175 --
5.6 Discrete Linearized and Extended Filtering 176 --
5.7 Discrete Extended Kalman Filter 178 --
5.8 Continuous Linearized and Extended Filters 181 --
5.9 Biased Errors in Quadratic Measurements 182 --
5.10 Application of Nonlinear Filters 184 --
6 Implementation Methods 202 --
6.2 Computer Roundoff 204 --
6.3 Effects of Roundoff Errors on Kalman Filters 209 --
6.4 Factorization Methods for Kalman Filtering 216 --
6.5 Square-Root and UD Filters 238 --
6.6 Other Alternative Implementation Methods 252 --
7.2 Detecting and Correcting Anomalous Behavior 271 --
7.3 Prefiltering and Data Rejection Methods 294 --
7.4 Stability of Kalman Filters 298 --
7.5 Suboptimal and Reduced-Order Filters 299 --
7.6 Schmidt--Kalman Filtering 309 --
7.7 Memory, Throughput, and Wordlength Requirements 316 --
7.8 Ways to Reduce Computational Requirements 326 --
7.9 Error Budgets and Sensitivity Analysis 332 --
7.10 Optimizing Measurement Selection Policies 336 --
7.11 Application to Aided Inertial Navigation 342 --
Appendix A MATLAB Software 350 --
A.2 General System Requirements 350 --
A.3 Diskette Directory Structure 351 --
A.9 Other Sources of Software 353 --
Appendix B A Matrix Refresher 355 --
B.1 Matrix Forms 355 --
B.2 Matrix Operations 359 --
B.3 Block Matrix Formulas 363 --
B.4 Functions of Square Matrices 366 --
B.5 Norms 370 --
B.6 Cholesky Decomposition 373 --
B.7 Orthogonal Decompositions of Matrices 375 --
B.8 Quadratic Forms 377 --
B.9 Derivatives of Matrices 379.