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The Stochastic Dynamic System

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Mathematics of Kalman-Bucy Filtering

Part of the book series: Springer Series in Information Sciences ((SSINF,volume 14))

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Abstract

In the design and analysis of a physical dynamic system, filtering refers to the estimation of the system state on the basis of system measurements contaminated by random noise. The Kalman-Bucy filter, being an algorithm for computing estimates of the state vector, deals with a stochastic dynamic system driven by forces whose random components are modeled by Brownian motion. In this chapter we are concerned with this system. Since only a sample of the stochastic processes is realized at the end of each physical experiment modeled by the dynamic system, the use of sample calculus is appropriate in the mathematical model.

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References

  1. E. Hille, R. S. Phillips: Functional Analysis and Semigroups (American Mathematical Society, Providence, RI 1957)

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  2. E. Hille: Lectures on Ordinary Differential Equations (Addison-Wesley, Reading, MA 1969)

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  4. P. A. Ruymgaart, T. T. Soong: A Sample Treatment of Langevin-Type Stochastic Differential Equations, J. Math. Analysis Appl. 34, 325–338 (1971)

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  5. A. H. Zemanian: Distribution Theory and Transform Analysis (McGraw-Hill, New York 1965)

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Authors and Affiliations

  1. Department of Mathematics, University of Technology, Delft, Delft, The Netherlands

    Dr. Peter A. Ruymgaart

  2. Faculty of Engineering and Applied Sciences, State University of New York at Buffalo, Buffalo, NY, 14260, USA

    Professor Tsu T. Soong

Authors
  1. Dr. Peter A. Ruymgaart
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  2. Professor Tsu T. Soong
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© 1985 Springer-Verlag Berlin Heidelberg

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Ruymgaart, P.A., Soong, T.T. (1985). The Stochastic Dynamic System. In: Mathematics of Kalman-Bucy Filtering. Springer Series in Information Sciences, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-96842-6_3

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  • DOI: https://doi.org/10.1007/978-3-642-96842-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-96844-0

  • Online ISBN: 978-3-642-96842-6

  • eBook Packages: Springer Book Archive

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