Skip to main content
SpringerLink
Log in
Book cover

Applied Stochastic Analysis pp 30–37Cite as

Some results on the filtering Riccati equation with random parameters

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 177))

Abstract

We consider the Kalman filter in a random stationary environment. The associated Riccati equation has random parameters. We first describe some recent results we have obtained on the asymptotic behavior of this equation under a.s. stabilizability and detectability assumptions. They depend on contraction properties of Hamiltonian matrices. Then we give a simple self-contained proof under a stronger detectability condition.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  • Anderson B.D.O. and Moore J.B. (1979), “Optimal filtering”, Prentice Hall, New Jersey.

    Google Scholar 

  • Anderson B.D.O. and Moore J.B. (1981), “Detectability and stabilizability of time-varying discrete time linear systems”, Siam J. Control and Optimization, 19, 20–32.

    Article  Google Scholar 

  • Bougerol Ph. (1990), “Filtre de Kalman Bucy et exposants de Lyapounov”. To appear in the Proceedings of the Oberwolfach Conference on Lyapunov Exponents, Springer Lecture Notes.

    Google Scholar 

  • Bougerol Ph. (1991a), “Kalman filtering with random coefficients and contractions”, Preprint.

    Google Scholar 

  • Bougerol Ph. (1991b), “Almost sure stabilizability and Riccati's equation for linear systems with random parameters”, Preprint.

    Google Scholar 

  • Furstenberg H. and Kifer Y. (1983), “Random matrix products and measures on projective spaces”. Israel J. Math., 46, 12–32.

    Google Scholar 

  • Kingman J.F.C. (1973), “Subadditive ergodic theory”, Ann. of Probab., 1, p 883–909.

    Google Scholar 

  • Whittle P. (1982), “Optimization over time”, Vol. 1, Wiley.

    Google Scholar 

  • Wojtkowski M. (1985), “Invariant families of cones and Lyapunov exponents”, Ergodic Th. Dyn. Systems, 5, 145–161.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Probabilités, Université Pierre et Marie Curie, 4, Place Jussieu, 75252, Paris Cedex 05, France

    Philippe Bougerol

Authors
  1. Philippe Bougerol
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Ioannis Karatzas Daniel Ocone

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag

About this paper

Cite this paper

Bougerol, P. (1992). Some results on the filtering Riccati equation with random parameters. In: Karatzas, I., Ocone, D. (eds) Applied Stochastic Analysis. Lecture Notes in Control and Information Sciences, vol 177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007046

Download citation

  • DOI: https://doi.org/10.1007/BFb0007046

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55296-3

  • Online ISBN: 978-3-540-47017-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation