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Estimation, Control, and the Discrete Kalman Filter

  • Donald E. Catlin

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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Donald E. Catlin
    Pages 1-60
  3. Donald E. Catlin
    Pages 70-91
  4. Donald E. Catlin
    Pages 92-113
  5. Donald E. Catlin
    Pages 114-124
  6. Donald E. Catlin
    Pages 125-132
  7. Donald E. Catlin
    Pages 133-163
  8. Donald E. Catlin
    Pages 164-187
  9. Donald E. Catlin
    Pages 188-199
  10. Back Matter
    Pages 200-275

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Donald E. Catlin
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of MassachusettsAmherstUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4528-5
  • Copyright Information Springer-Verlag New York 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8864-0
  • Online ISBN 978-1-4612-4528-5
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site
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