Springer Series in Information Sciences

Mathematics of Kalman-Bucy Filtering

Authors: Ruymgaart, P.A., Soong, Tsu T.

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  • ISBN 978-3-642-96842-6
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About this Textbook

Since their introduction in the mid 1950s, the filtering techniques developed by Kalman, and by Kalman and Bucy have been widely known and widely used in all areas of applied sciences. Starting with applications in aerospace engineering, their impact has been felt not only in all areas of engineering but also in the social sciences, biological sciences, medical sciences, as well as all other physical sciences. Despite all the good that has come out of this develĀ­ opment, however, there have been misuses because the theory has been used mainly as a tool or a procedure by many applied workers without them fully understanding its underlying mathematical workings. This book addresses a mathematical approach to Kalman-Bucy filtering and is an outgrowth of lectures given at our institutions since 1971 in a sequence of courses devoted to Kalman-Bucy filters. The material is meant to be a theoretical complement to courses dealing with applications and is designed for students who are well versed in the techniques of Kalman-Bucy filtering but who are also interested in the mathematics on which these may be based. The main topic addressed in this book is continuous-time Kalman-Bucy filtering. Although the discrete-time Kalman filter results were obtained first, the continuous-time results are important when dealing with systems developing in time continuously, which are hence more appropriately modĀ­ eled by differential equations than by difference equations. On the other hand, observations from the former can be obtained in a discrete fashion.

Table of contents (5 chapters)

  • Elements of Probability Theory

    Ruymgaart, Peter A. (et al.)

    Pages 1-29

  • Calculus in Mean Square

    Ruymgaart, Peter A. (et al.)

    Pages 30-79

  • The Stochastic Dynamic System

    Ruymgaart, Peter A. (et al.)

    Pages 80-99

  • The Kalman-Bucy Filter

    Ruymgaart, Peter A. (et al.)

    Pages 100-153

  • A Theorem by Liptser and Shiryayev

    Ruymgaart, Peter A. (et al.)

    Pages 154-157

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-642-96842-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Mathematics of Kalman-Bucy Filtering
Authors
Series Title
Springer Series in Information Sciences
Series Volume
14
Copyright
1985
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer Verlag Berlin Heidelberg
eBook ISBN
978-3-642-96842-6
DOI
10.1007/978-3-642-96842-6
Series ISSN
0720-678X
Edition Number
1
Topics