Preface |
Acknowledgments |
List of Abbreviations |
General Information / 1: |
On Kalman Filtering / 1.1: |
On Optimal 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 System Models / 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: |
Random Processes and Stochastic Systems / 2.6: |
Probability and Random Variables (RVs) / 3.1: |
Statistical Properties of RVs / 3.3: |
Statistical Properties of Random Processes (RPs) / 3.4: |
Linear RP Models / 3.5: |
Shaping Filters and State Augmentation / 3.6: |
Mean and Covariance Propagation / 3.7: |
Relationships Between Model Parameters / 3.8: |
Orthogonality Principle / 3.9: |
Linear Optimal Filters and Predictors / 3.10: |
Kalman Filter / 4.1: |
Kalman-Bucy Filter / 4.3: |
Optimal Linear Predictors / 4.4: |
Correlated Noise Sources / 4.5: |
Relationships Between Kalman-Bucy and Wiener Filters / 4.6: |
Quadratic Loss Functions / 4.7: |
Matrix Riccati Differential Equation / 4.8: |
Matrix Riccati Equation In Discrete Time / 4.9: |
Model Equations for Transformed State Variables / 4.10: |
Application of Kalman Filters / 4.11: |
Optimal Smoothers / 4.12: |
Fixed-Interval Smoothing / 5.1: |
Fixed-Lag Smoothing / 5.3: |
Fixed-Point Smoothing / 5.4: |
Implementation Methods / 5.5: |
Computer Roundoff / 6.1: |
Effects of Roundoff Errors on Kalman Filters / 6.3: |
Factorization Methods for Square-Root Filtering / 6.4: |
Square-Root and UD Filters / 6.5: |
Other Implementation Methods / 6.6: |
Nonlinear Filtering / 6.7: |
Quasilinear Filtering / 7.1: |
Sampling Methods for Nonlinear Filtering / 7.3: |
Practical Considerations / 7.4: |
Detecting and Correcting Anomalous Behavior / 8.1: |
Prefiltering and Data Rejection Methods / 8.3: |
Stability of Kalman Filters / 8.4: |
Suboptimal and Reduced-Order Filters / 8.5: |
Schmidt-Kalman Filtering / 8.6: |
Memory, Throughput, and Wordlength Requirements / 8.7: |
Ways to Reduce Computational Requirements / 8.8: |
Error Budgets and Sensitivity Analysis / 8.9: |
Optimizing Measurement Selection Policies / 8.10: |
Innovations Analysis / 8.11: |
Applications to Navigation / 8.12: |
Host Vehicle Dynamics / 9.1: |
Inertial Navigation Systems (INS) / 9.3: |
Global Navigation Satellite Systems (GNSS) / 9.4: |
Kalman Filters for GNSS / 9.5: |
Loosely Coupled GNSS/INS Integration / 9.6: |
Tightly Coupled GNSS/INS Integration / 9.7: |
MATLAB Software / 9.8: |
Notice / A.1: |
General System Requirements / A.2: |
CD Directory Structure / A.3: |
MATLAB Software for Chapter 2 / A.4: |
MATLAB Software for Chapter 3 / A.5: |
MATLAB Software for Chapter 4 / A.6: |
MATLAB Software for Chapter 5 / A.7: |
MATLAB Software for Chapter 6 / A.8: |
MATLAB Software for Chapter 7 / A.9: |
MATLAB Software for Chapter 8 / A.10: |
MATLAB Software for Chapter 9 / A.11: |
Other Sources of Software / A.12: |
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: |
Bibliography |
Index |
Preface |
Acknowledgments |
List of Abbreviations |
General Information / 1: |
On Kalman Filtering / 1.1: |
On Optimal Estimation Methods / 1.2: |