# Estimation, Control, and the Discrete Kalman Filter

• Donald E. Catlin
Book

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

1. Front Matter
Pages i-xiii
2. Donald E. Catlin
Pages 1-60
3. Donald E. Catlin
Pages 61-69
4. Donald E. Catlin
Pages 70-91
5. Donald E. Catlin
Pages 92-113
6. Donald E. Catlin
Pages 114-124
7. Donald E. Catlin
Pages 125-132
8. Donald E. Catlin
Pages 133-163
9. Donald E. Catlin
Pages 164-187
10. Donald E. Catlin
Pages 188-199
11. Back Matter
Pages 200-275

### 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
• Print ISBN 978-1-4612-8864-0
• Online ISBN 978-1-4612-4528-5
• Series Print ISSN 0066-5452
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