- Browse
- » Fundamentals of Kalman filtering: a practical approach
Fundamentals of Kalman filtering: a practical approach
Author
Publisher
Varies, see individual formats and editions
Publication Date
Varies, see individual formats and editions
Language
English
More Details
Contributors
ISBN
9781563474552
9781624102776
9781563476945
9781624102776
9781563476945
Description
Loading Description...
Table of Contents
From the Book - Regular Print - Second edition.
Numerical basics
Method of least squares
Recursive least-quares filtering
Polynomial Kalman filters
Kalman filters in a nonpolynomial world
Continuous polynomial Kalman filter
Extended Kalman filtering
Drag and falling object
Cannon-launched projectile tracking problem
Tracking a sine wave
Satellite navigation
Biases
Linearized Kalman filtering
Miscellaneous topics
Fading-memory filter
Assorted techniques for improving Kalman-filter performance
Fundamentals of Kalman-filtering software
Key formula and concept summary.
From the Book - Regular Print
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 --
White Noise 28 --
Simulating White Noise 30 --
State-Space Notation 33 --
Fundamental Matrix 34 --
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 --
Third-Order System 56 --
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 --
General Equations 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 --
Filter Comparison 251 --
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 --
Problem Setup 293 --
Changing Filter States 309 --
Why Process Noise Is Required 311 --
Linear Polynomial Kalman Filter 320 --
Chapter 9. Cannon-Launched Projectile Tracking Problem 331 --
Problem Statement 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 --
Influence of Bias 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 --
Aiding 629 --
Appendix Fundamentals of Kalman-Filtering Software 647 --
Software Details 647 --
MATLAB 648 --
True BASIC 654.
Excerpt
Loading Excerpt...
Author Notes
Loading Author Notes...
Reviews from GoodReads
Loading GoodReads Reviews.
Staff View
Loading Staff View.