Fundamentals of Kalman Filtering:: A Practical Approach

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This is a practical guide to building Kalman filters that shows how the filtering equations can be applied to real-life problems. Numerous examples are presented in detail, showing the many ways in which Kalman filters can be designed. Computer code written in FORTRAN, MATLAB[registered], and True BASIC accompanies all of the examples so that the interested reader can verify concepts and explore issues beyond the scope of the text. In certain instances, the authors intentionally introduce mistakes to the initial filter designs to show the reader what happens when the filter is not working properly. The text carefully sets up a problem before the Kalman filter is actually formulated, to give the reader an intuitive feel for the problem being addressed. Because real problems are seldom presented as differential equations, and usually do not have unique solutions, the authors illustrate several different filtering approaches. Readers will gain experience in software and performance tradeoffs for determining the best filtering approach. The material that has been added to this edition is in response to questions and feedback from readers. The third edition has three new chapters on unusual topics related to Kalman filtering and other filtering techniques based on the method of least squares. Chapter 17 presents a type of filter known as the fixed or finite memory filter, which only remembers a finite number of measurements from the past. Chapter 18 shows how the chain rule from calculus can be used for filter initialization or to avoid filtering altogether. A realistic three-dimensional GPS example is used to illustrate the chain-rule method for filter initialization. Finally, Chapter 19 shows how a bank of linear sine-wave Kalman filters, each one tuned to a different sine-wave frequency, can be used to estimate the actual frequency of noisy sinusoidal measurements and obtain estimates of the states of the sine wave when the measurement noise is low.

Author(s): Paul Zarchan, Howard Musoff, Frank K. Lu
Series: Progress in Astronautics and Aeronautics (Volume 232)
Edition: 3
Publisher: AIAA (American Institute of Aeronautics & Astronautics)
Year: 2009

Language: English
Pages: 852
Tags: Финансово-экономические дисциплины;Эконометрика;

Cover......Page 1
Title......Page 2
Copyright......Page 5
Foreword......Page 10
Table of Contents......Page 12
Preface......Page 18
Introduction......Page 20
Acknowledgments......Page 28
Numerical Basics......Page 30
Method of Least Squares......Page 70
Recursive Least-Squares Filtering
......Page 120
Polynomial Kalman Filters......Page 158
Kalman Filters in a Nonpolynomial World......Page 212
Continuous Polynomial Kalman Filter......Page 248
Extended Kalman Filtering......Page 286
Drag and Falling Object......Page 322
Cannon-Launched Projectile Tracking Problem......Page 360
Tracking a Sine Wave......Page 424
Satellite Navigation
......Page 472
Biases......Page 544
Linearized Kalman Filtering......Page 578
Miscellaneous Topics......Page 616
Fading-Memory Filter......Page 676
Assorted Techniques for Improving Kalman-Filter Performance......Page 706
Fixed-Memory Filters......Page 752
Chain-Rule and Least-Squares Filtering......Page 782
Filter Bank Approach to Tracking a Sine Wave......Page 814
Appendix A: Fundamentals of Kalman-Filtering Software......Page 840
Appendix B: Key Formula and Concept Summary......Page 856
Index......Page 864
Supporting Materials......Page 882