Chapter 1. Numerical Basics 1 --
Simple Vector Operations 1 --
Simple Matrix Operations 3 --
Numerical Integration of Differential Equations 13 --
Noise and Random Variables 19 --
Gaussian Noise Example 23 --
Calculating Standard Deviation 26 --
Simulating White Noise 30 --
State-Space Notation 33 --
Chapter 2. Method of Least Squares 41 --
Zeroth-Order or One-State Filter 42 --
First-Order or Two-State Filter 46 --
Second-Order or Three-State Least-Squares Filter 50 --
Experiments with Zeroth-Order or One-State Filter 59 --
Experiments with First-Order or Two-State Filter 64 --
Experiments with Second-Order or Three-State Filter 71 --
Comparison of Filters 78 --
Accelerometer Testing Example 80 --
Chapter 3. Recursive Least-Squares Filtering 91 --
Making Zeroth-Order Least-Squares Filter Recursive 91 --
Properties of Zeroth-Order or One-State Filter 93 --
Properties of First-Order or Two-State Filter 103 --
Properties of Second-Order or Three-State Filter 112 --
Chapter 4. Polynomial Kalman Filters 129 --
Derivation of Scalar Riccati Equations 131 --
Polynomial Kalman Filter (Zero Process Noise) 134 --
Comparing Zeroth-Order Recursive Least-Squares and Kalman Filters 136 --
Comparing First-Order Recursive Least-Squares and Kalman Filters 139 --
Comparing Second-Order Recursive Least-Squares and Kalman Filters 142 --
Comparing Different-Order Filters 148 --
Initial Covariance Matrix 151 --
Riccati Equations with Process Noise 155 --
Example of Kalman Filter Tracking a Falling Object 159 --
Revisiting Accelerometer Testing Example 171 --
Chapter 5. Kalman Filters in a Nonpolynomial World 183 --
Polynomial Kalman Filter and Sinusoidal Measurement 183 --
Sinusoidal Kalman Filter and Sinusoidal Measurement 194 --
Suspension System Example 203 --
Kalman Filter for Suspension System 207 --
Chapter 6. Continuous Polynomial Kalman Filter 219 --
Theoretical Equations 219 --
Zeroth-Order or One-State Continuous Polynomial Kalman Filter 221 --
First-Order or Two-State Continuous Polynomial Kalman Filter 227 --
Second-Order or Three-State Continuous Polynomial Kalman Filter 232 --
Transfer Function for Zeroth-Order Filter 238 --
Transfer Function for First-Order Filter 243 --
Transfer Function for Second-Order Filter 248 --
Chapter 7. Extended Kalman Filtering 257 --
Theoretical Equations 257 --
Drag Acting on Falling Object 259 --
First Attempt at Extended Kalman Filter 261 --
Second Attempt at Extended Kalman Filter 274 --
Third Attempt at Extended Kalman Filter 284 --
Chapter 8. Drag and Falling Object 293 --
Changing Filter States 309 --
Why Process Noise Is Required 311 --
Linear Polynomial Kalman Filter 320 --
Chapter 9. Cannon-Launched Projectile Tracking Problem 331 --
Extended Cartesian Kalman Filter 334 --
Polar Coordinate System 349 --
Extended Polar Kalman Filter 354 --
Using Linear Decoupled Polynomial Kalman Filters 367 --
Using Linear Coupled Polynomial Kalman Filters 376 --
Robustness Comparison of Extended and Linear Coupled Kalman Filters 385 --
Chapter 10. Tracking a Sine Wave 395 --
Extended Kalman Filter 395 --
Two-State Extended Kalman Filter with a Priori Information 408 --
Alternate Extended Kalman Filter for Sinusoidal Signal 417 --
Another Extended Kalman Filter for Sinusoidal Model 431 --
Chapter 11. Satellite Navigation 443 --
Problem with Perfect Range Measurements 443 --
Estimation Without Filtering 447 --
Linear Filtering of Range 453 --
Using Extended Kalman Filtering 455 --
Using Extended Kalman Filtering with One Satellite 465 --
Using Extended Kalman Filtering with Constant Velocity Receiver 474 --
Single Satellite with Constant Velocity Receiver 479 --
Using Extended Kalman Filtering with Variable Velocity Receiver 493 --
Variable Velocity Receiver and Single Satellite 505 --
Chapter 12. Biases 515 --
Estimating Satellite Bias with Known Receiver Location 519 --
Estimating Receiver Bias with Unknown Receiver Location and Two Satellites 525 --
Estimating Receiver Bias with Unknown Receiver Location and Three Satellites 533 --
Chapter 13. Linearized Kalman Filtering 549 --
Theoretical Equations 549 --
Falling Object Revisited 552 --
Developing a Linearized Kalman Filter 556 --
Cannon-Launched Projectile Revisited 569 --
Linearized Cartesian Kalman Filter 570 --
Chapter 14. Miscellaneous Topics 587 --
Sinusoidal Kalman Filter and Signal-to-Noise Ratio 587 --
When Only a Few Measurements Are Available 595 --
Detecting Filter Divergence in the Real World 606 --
Observability Example 618 --
Appendix Fundamentals of Kalman-Filtering Software 647 --
