Estimation, Control, and the Discrete Kalman Filter

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

    PDF

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.

• Bias
• Computer-Aided Design (CAD)
• Estimator
• Normal
• Operator
• Paro
• Tracking
• bayesian statistics
• best fit
• calculus
• construction
• dynamische Systeme
• filtering
• statistics

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

  Donald E. Catlin

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