Cover -- Title -- Copyright -- Table of Contents -- Preface -- Introduction -- Acknowledgments -- Chapter 1. Numerical Basics -- Introduction -- 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 -- Chapter 2. Method of Least Squares -- Introduction -- 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 -- Summary -- References -- Chapter 3. Recursive Least-Squares Filtering -- Introduction -- 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 -- Summary -- References -- Chapter 4. Polynomial Kalman Filters -- Introduction -- 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 -- Summary -- References -- Chapter 5. Kalman Filters in a Nonpolynomial World -- Introduction.

Polynomial Kalman Filter and Sinusoidal Measurement -- Sinusoidal Kalman Filter and Sinusoidal Measurement -- Suspension System Example -- Kalman Filter for Suspension System -- Summary -- References -- Chapter 6. Continuous Polynomial Kalman Filter -- Introduction -- 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 -- Summary -- References -- Chapter 7. Extended Kalman Filtering -- Introduction -- Theoretical Equations -- Drag Acting on Falling Object -- First Attempt at Extended Kalman Filters -- Second Attempt at Extended Kalman Filter -- Third Attempt at Extended Kalman Filter -- Summary -- References -- Chapter 8. Drag and Falling Object -- Introduction -- Problem Setup -- Changing Filter States -- Why Process Noise Is Required -- Linear Polynomial Kalman Filter -- Summary -- References -- Chapter 9. Cannon-Launched Projectile Tracking Problem -- Introduction -- 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 -- Summary -- Reference -- Chapter 10. Tracking a Sine Wave -- Introduction -- 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 -- Summary -- References -- Chapter 11. Satellite Navigation -- Introduction.

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 -- Summary -- References -- Chapter 12. Biases -- Introduction -- 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 -- Summary -- Reference -- Chapter 13. Linearized Kalman Filtering -- Introduction -- Theoretical Equations -- Falling Object Revisited -- Developing a Linearized Kalman Filter -- Cannon-Launched Projectile Revisited -- Linearized Cartesian Kalman Filter -- Summary -- References -- Chapter 14. Miscellaneous Topics -- Introduction -- 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 -- Summary -- References -- Chapter 15. Fading-Memory Filter -- Introduction -- Fading-Memory-Filter Structure and Properties -- Radar Tracking Problem -- Summary -- References -- Chapter 16. Assorted Techniques for Improving Kalman-Filter Performance -- Introduction -- Increasing Data Rate -- Adding a Second Measurement -- Batch Processing -- Adaptive Filtering-Multiple Filters -- Adaptive Filtering-Single Filter with Variable Process Noise -- Summary -- Appendix A Fundamentals of Kalman-Filtering Software -- Software Details -- MATLAB(sup[®]) -- True BASIC -- Reference -- Appendix B Key Formula and Concept Summary.

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 -- Fundamental Matrix -- Method of Least-Squares Summary -- Fading-Memory Filter Summary -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- L -- M -- N -- O -- P -- R -- S -- T -- U -- V -- W -- X -- Z.