Preface |
Acknowledgments |
General Information / 1: |
On Kalman Filtering / 1.1: |
On Estimation Methods / 1.2: |
On the Notation Used in This Book / 1.3: |
Summary / 1.4: |
Problems |
Linear Dynamic Systems / 2: |
Chapter Focus / 2.1: |
Dynamic Systems / 2.2: |
Continuous Linear Systems and Their Solutions / 2.3: |
Discrete Linear Systems and Their Solutions / 2.4: |
Observability of Linear Dynamic System Models / 2.5: |
Procedures for Computing Matrix Exponentials / 2.6: |
Random Processes and Stochastic Systems / 2.7: |
Probability and Random Variables / 3.1: |
Statistical Properties of Random Variables / 3.3: |
Statistical Properties of Random Processes / 3.4: |
Linear System Models of Random Processes and Sequences / 3.5: |
Shaping Filters and State Augmentation / 3.6: |
Covariance Propagation Equations / 3.7: |
Orthogonality Principle / 3.8: |
Linear Optimal Filters and Predictors / 3.9: |
Kalman Filter / 4.1: |
Kalman--Bucy Filter / 4.3: |
Optimal Linear Predictors / 4.4: |
Correlated Noise Sources / 4.5: |
Relationships between Kalman and Wiener Filters / 4.6: |
Quadratic Loss Functions / 4.7: |
Matrix Riccati Differential Equation / 4.8: |
Matrix Riccati Equation in Discrete Time / 4.9: |
Relationships between Continuous and Discrete Riccati Equations / 4.10: |
Model Equations for Transformed State Variables / 4.11: |
Application of Kalman Filters / 4.12: |
Smoothers / 4.13: |
Nonlinear Applications / 4.14: |
Problem Statement / 5.1: |
Linearization Methods / 5.3: |
Linearization about a Nominal Trajectory / 5.4: |
Linearization about the Estimated Trajectory / 5.5: |
Discrete Linearized and Extended Filtering / 5.6: |
Discrete Extended Kalman Filter / 5.7: |
Continuous Linearized and Extended Filters / 5.8: |
Biased Errors in Quadratic Measurements / 5.9: |
Application of Nonlinear Filters / 5.10: |
Implementation Methods / 5.11: |
Computer Roundoff / 6.1: |
Effects of Roundoff Errors on Kalman Filters / 6.3: |
Factorization Methods for Kalman Filtering / 6.4: |
Square-Root and UD Filters / 6.5: |
Other Alternative Implementation Methods / 6.6: |
Practical Considerations / 6.7: |
Detecting and Correcting Anomalous Behavior / 7.1: |
Prefiltering and Data Rejection Methods / 7.3: |
Stability of Kalman Filters / 7.4: |
Suboptimal and Reduced-Order Filters / 7.5: |
Schmidt--Kalman Filtering / 7.6: |
Memory, Throughput, and Wordlength Requirements / 7.7: |
Ways to Reduce Computational Requirements / 7.8: |
Error Budgets and Sensitivity Analysis / 7.9: |
Optimizing Measurement Selection Policies / 7.10: |
Application to Aided Inertial Navigation / 7.11: |
MATLAB Software / 7.12: |
Notice / A.1: |
General System Requirements / A.2: |
Diskette Directory Structure / A.3: |
MATLAB Software for Chapter 2 / A.4: |
MATLAB Software for Chapter 4 / A.5: |
MATLAB Software for Chapter 5 / A.6: |
MATLAB Software for Chapter 6 / A.7: |
MATLAB Software for Chapter 7 / A.8: |
Other Sources of Software / A.9: |
A Matrix Refresher / Appendix B: |
Matrix Forms / B.1: |
Matrix Operations / B.2: |
Block Matrix Formulas / B.3: |
Functions of Square Matrices / B.4: |
Norms / B.5: |
Cholesky Decomposition / B.6: |
Orthogonal Decompositions of Matrices / B.7: |
Quadratic Forms / B.8: |
Derivatives of Matrices / B.9: |
References |
Index |
Preface |
Acknowledgments |
General Information / 1: |
On Kalman Filtering / 1.1: |
On Estimation Methods / 1.2: |
On the Notation Used in This Book / 1.3: |