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Filtre de Kalman Bucy et exposants de Lyapounov

Chapter 1: Linear Random Dynamical Systems

Part of the Lecture Notes in Mathematics book series (LNM,volume 1486)

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On considère la situation du filtrage linéaire à coefficients aléatoires stationnaires. On montre que les généralisations des résultats de Kalman sur le comportement asymptotique du filtre, que nous avions obtenues à partir de propriétés de contraction, peuvent aussi être montrées en utilisant le théorème d'Osseledets et un résultat de M. Wojtkowski. Le filtre est exponentiellement stable avec un taux déterminé par le plus petit exposant de Lyapounov positif d'un produit de matrices symplectiques.

Keywords

  • Matrice Symplectiques
  • Multiplicative Ergodic Theorem
  • Measure Theoretic Entropy
  • Lyapunov Characteristic Number
  • Nous Montrons

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Références

  1. Balakrishnan, A.V. (1984): Kalman Filtering Theory. Optimization Software, New York.

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  2. Bougerol, P. (1990): Kalman filtering with random coefficients and contractions (Preprint).

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  3. Loomis, L.H. et Sternberg, S.: Advanced Calculus. Addison Wesley, Reading, Ma.

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  4. Osseledets, V.I. (1968): The multiplicative ergodic theorem. The Lyapunov characteristic numbers of a dynamical system. Trans. Mosc. Math. Soc., 19, 197–231.

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  5. Whittle, P. (1982): Optimization over time. Vol. 1. Wiley, Chichester, New-York.

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  6. Wojtkowski, M. (1985): Invariant families of cones and Lyapunov exponents. Ergod. Th. & Dynam. Sys., 5, 145–161.

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  7. Wojtkowski, M. (1988): Measure theoretic entropy of the system of hard spheres. Ergod. Th. & Dynam. Sys., 8, 133–153.

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© 1991 Springer-Verlag

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Bougerol, P. (1991). Filtre de Kalman Bucy et exposants de Lyapounov. In: Arnold, L., Crauel, H., Eckmann, JP. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086662

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  • DOI: https://doi.org/10.1007/BFb0086662

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54662-7

  • Online ISBN: 978-3-540-46431-0

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