Preface |
Introduction |
Acknowledgments |
Numerical Basics / Chapter 1: |
Simple Vector Operations |
Simple Matrix Operations |
Numerical Integration of Differential Equations |
Noise and Random Variables |
Gaussian Noise Example |
Calculating Standard Deviation |
White Noise |
Simulating White Noise |
State-Space Notation |
Fundamental Matrix |
Summary |
References |
Method of Least Squares / Chapter 2: |
Overview |
Zeroth-Order or One-State Filter |
First-Order or Two-State Filter |
Second-Order or Three-State Least-Squares Filter |
Third-Order System |
Experiments with Zeroth-Order or One-State Filter |
Experiments with First-Order or Two-State Filter |
Experiments with Second-Order or Three-State Filter |
Comparison of Filters |
Accelerometer Testing Example |
Recursive Least-Squares Filtering / Chapter 3: |
Making Zeroth-Order Least-Squares Filter Recursive |
Properties of Zeroth-Order or One-State Filter |
Properties of First-Order or Two-State Filter |
Properties of Second-Order or Three-State Filter |
Polynomial Kalman Filters / Chapter 4: |
General Equations |
Derivation of Scalar Riccati Equations |
Polynomial Kalman Filter (Zero Process Noise) |
Comparing Zeroth-Order Recursive Least-Squares and Kalman Filters |
Comparing First-Order Recursive Least-Squares and Kalman Filters |
Comparing Second-Order Recursive Least-Squares and Kalman Filters |
Comparing Different-Order Filters |
Initial Covariance Matrix |
Riccati Equations with Process Noise |
Example of Kalman Filter Tracking a Falling Object |
Revisiting Accelerometer Testing Example |
Kalman Filters in a Nonpolynomial World / Chapter 5: |
Polynomial Kalman Filter and Sinusoidal Measurement |
Sinusoidal Kalman Filter and Sinusoidal Measurement |
Suspension System Example |
Kalman Filter for Suspension System |
Continuous Polynomial Kalman Filter / Chapter 6: |
Theoretical Equations |
Zeroth-Order or One-State Continuous Polynomial Kalman Filter |
First-Order or Two-State Continuous Polynomial Kalman Filter |
Second-Order or Three-State Continuous Polynomial Kalman Filter |
Transfer Function for Zeroth-Order Filter |
Transfer Function for First-Order Filter |
Transfer Function for Second-Order Filter |
Filter Comparison |
Extended Kalman Filtering / Chapter 7: |
Drag Acting on Falling Object |
First Attempt at Extended Kalman Filter |
Second Attempt at Extended Kalman Filter |
Third Attempt at Extended Kalman Filter |
Drag and Falling Object / Chapter 8: |
Problem Setup |
Changing Filter States |
Why Process Noise Is Required |
Linear Polynomial Kalman Filter |
Cannon-Launched Projectile Tracking Problem / Chapter 9: |
Problem Statement |
Extended Cartesian Kalman Filter |
Polar Coordinate System |
Extended Polar Kalman Filter |
Using Linear Decoupled Polynomial Kalman Filters |
Using Linear Coupled Polynomial Kalman Filters |
Robustness Comparison of Extended and Linear Coupled Kalman Filters |
Reference |
Tracking a Sine Wave / Chapter 10: |
Extended Kalman Filter |
Two-State Extended Kalman Filter with a Priori Information |
Alternate Extended Kalman Filter for Sinusoidal Signal |
Another Extended Kalman Filter for Sinusoidal Model |
Satellite Navigation / Chapter 11: |
Problem with Perfect Range Measurements |
Estimation Without Filtering |
Linear Filtering of Range |
Using Extended Kalman Filtering |
Using Extended Kalman Filtering with One Satellite |
Using Extended Kalman Filtering with Constant Velocity Receiver |
Single Satellite with Constant Velocity Receiver |
Using Extended Kalman Filtering with Variable Velocity Receiver |
Variable Velocity Receiver and Single Satellite |
Biases / Chapter 12: |
Influence of Bias |
Estimating Satellite Bias with Known Receiver Location |
Estimating Receiver Bias with Unknown Receiver Location and Two Satellites |
Estimating Receiver Bias with Unknown Receiver Location and Three Satellites |
Linearized Kalman Filtering / Chapter 13: |
Falling Object Revisited |
Developing a Linearized Kalman Filter |
Cannon-Launched Projectile Revisited |
Linearized Cartesian Kalman Filter |
Miscellaneous Topics / Chapter 14: |
Sinusoidal Kalman Filter and Signal-to-Noise Ratio |
When Only a Few Measurements Are Available |
Detecting Filter Divergence in the Real World |
Observability Example |
Aiding |
Fading-Memory Filter / Chapter 15: |
Fading-Memory-Filter Structure and Properties |
Radar Tracking Problem |
Assorted Techniques for Improving Kalman-Filter Performance / Chapter 16: |
Increasing Data Rate |
Adding a Second Measurement |
Batch Processing |
Adaptive Filtering-Multiple Filters |
Adaptive Filtering-Single Filter with Variable Process Noise |
Fundamentals of Kalman-Filtering Software / Appendix A: |
Software Details |
MATLAB |
True BASIC |
Key Formula and Concept Summary / Appendix B: |
Overview of Kalman-Filter Operation Principles |
Kalman-Filter Gains and the Riccati Equations |
Kalman-Filter Gain Logic |
Matrix Inverse |
Numerical Integration |
Postprocessing Formulas |
Simulating Pseudo White Noise |
Method of Least-Squares Summary |
Fading-Memory Filter Summary |
Index |
Supporting Materials |