Kalman Filtering Theory

Excerpt from the Preface: 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 Stochastic Process theory. As a textbook, it does 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. It develops those aspects of Kalman Filtering lore which can be given a firm mathematical basis. The first two capters cover review material on State-Space theory and Signal (Random Process) theory – necessary but not sufficient for the sequel. The third chapter deals with Statistical Estimation theory, the mathematical framework on which Kalman Filtering rests. The main chapter is the fourth chapter dealing with the subject matter per se. The book concludes with a chapter on Likelihood Ratios in which the Kalman filter formulation plays and essential role. We only consider discrete-time models throughout, since all Kalman filter implementation envisaged involves digital computation.