Fundamentals of Kalman Filtering:: A Practical Approach 232

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.

In 2008 the National Academy of Engineering awarded Rudolf Kalman the Charles Stark Draper Prize—the engineering equivalent of the Nobel Prize ($500,000 cash award)—for the development and dissemination of the optimal digital technique (known as the Kalman Filter) that is pervasively used to control a vast array of consumer, health, commercial, and defense products.

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®, 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.

MATLAB is a registered trademark of The MathWorks, Inc.

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