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Estimation, Control, and the Discrete Kalman Filter

  • Book
  • © 1989

Overview

Authors:
  1. Donald E. Catlin

    1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, USA

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Part of the book series: Applied Mathematical Sciences (AMS, volume 71)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Basic Probability

    • Donald E. Catlin
    Pages 1-60

  3. Minimum Variance Estimation—How the Theory Fits

    • Donald E. Catlin
    Pages 61-69

  4. The Maximum Entropy Principle

    • Donald E. Catlin
    Pages 70-91

  5. Adjoints, Projections, Pseudoinverses

    • Donald E. Catlin
    Pages 92-113

  6. Linear Minimum Variance Estimation

    • Donald E. Catlin
    Pages 114-124

  7. Recursive Linear Estimation (Bayesian Estimation)

    • Donald E. Catlin
    Pages 125-132

  8. The Discrete Kalman Filter

    • Donald E. Catlin
    Pages 133-163

  9. The Linear Quadratic Tracking Problem

    • Donald E. Catlin
    Pages 164-187

  10. Fixed Interval Smoothing

    • Donald E. Catlin
    Pages 188-199

  11. Back Matter

    Pages 200-275
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Keywords

About this book

In 1960, R. E. Kalman published his celebrated paper on recursive min­ imum variance estimation in dynamical systems [14]. This paper, which introduced an algorithm that has since been known as the discrete Kalman filter, produced a virtual revolution in the field of systems engineering. Today, Kalman filters are used in such diverse areas as navigation, guid­ ance, oil drilling, water and air quality, and geodetic surveys. In addition, Kalman's work led to a multitude of books and papers on minimum vari­ ance estimation in dynamical systems, including one by Kalman and Bucy on continuous time systems [15]. Most of this work was done outside of the mathematics and statistics communities and, in the spirit of true academic parochialism, was, with a few notable exceptions, ignored by them. This text is my effort toward closing that chasm. For mathematics students, the Kalman filtering theorem is a beautiful illustration of functional analysis in action; Hilbert spaces being used to solve an extremely important problem in applied mathematics. For statistics students, the Kalman filter is a vivid example of Bayesian statistics in action. The present text grew out of a series of graduate courses given by me in the past decade. Most of these courses were given at the University of Mas­ sachusetts at Amherst.

Authors and Affiliations

  • Department of Mathematics and Statistics, University of Massachusetts, Amherst, USA

    Donald E. Catlin

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