Kalman filtering theory

A. V Balakrishnan091157526X, 9780911575262

This is a textbook intended for a one-quarter (or one-semester, depending on the pace) course at the graduate level in Engineering. The prerequisites are Elementary State-Space theory and Elementary (second-order Gaussian) Stochastic Process theory. As a textbook, it does not not purport to be a compendium of all known work on the subject. Neither is it a ”trade book.” Rather it attempts a logically sequenced set of topics of proven pedagogical value, emphasizing theory while not devoid of practical utility. The organization is based on experience gained over a period of ten years of class room teaching. It develops those aspects of Kalman Filtering lore which can be given a firm mathematical basis, avoiding the industry syndrome manifest in professional short courses: ”Here is the recipe. Use it, it will ”work”!”

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Table of contents :
Cover ……Page 1
Series ……Page 2
Title page ……Page 3
Date-line ……Page 4
ABOUT THE AUTHOR ……Page 5
ERRATA ……Page 6
Series title ……Page 8
CONTENTS ……Page 9
PREFACE ……Page 11
NOTATION ……Page 13
CHAPTER 1. REVIEW OF LINEAR SYSTEM THEORY ……Page 15
CHAPTER 2. REVIEW OF SIGNAL THEORY ……Page 27
CHAPTER 3. STATISTICAL ESTIMATION THEORY ……Page 48
3.1. Parameter estimation: the Cramer-Rao bound; the principle of maximum likelihood ……Page 49
3.2. Bayesian theory of estimation: optimal mean square estimates and conditional expectation ……Page 60
3.3. Gaussian distributions: conditional density; unconditional maximum likelihood; mutual information ……Page 63
3.4. Gram-Schmidt orthogonalization and covariance matrix factorization ……Page 73
3.5. Estimation of signal parameters in additive noise ……Page 78
3.6. Performance degradation due to parameter uncertainty ……Page 86
CHAPTER 4. THE KALMAN FILTER ……Page 90
4.1. Basic theory ……Page 91
4.2. Kalman filter; steady state theory ……Page 114
4.3. Steady state theory: frequency domain analysis ……Page 147
4.4. On-line estimation of system parameters ……Page 163
4.5. (Kalman) smoother filter ……Page 185
4.6. Kalman filter: correlated signal and noise ……Page 198
4.7. Kalman filter for colored (observation) noise ……Page 207
4.8. Example ……Page 214
CHAPTER 5. LIKELIHOOD RATIOS: GAUSSIAN SIGNALS IN GAUSSIAN NOISE ……Page 225
BIBLIOGRAPHY ……Page 233
INDEX ……Page 235