Resume
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
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Références
Balakrishnan, A.V. (1984): Kalman Filtering Theory. Optimization Software, New York.
Bougerol, P. (1990): Kalman filtering with random coefficients and contractions (Preprint).
Loomis, L.H. et Sternberg, S.: Advanced Calculus. Addison Wesley, Reading, Ma.
Osseledets, V.I. (1968): The multiplicative ergodic theorem. The Lyapunov characteristic numbers of a dynamical system. Trans. Mosc. Math. Soc., 19, 197–231.
Whittle, P. (1982): Optimization over time. Vol. 1. Wiley, Chichester, New-York.
Wojtkowski, M. (1985): Invariant families of cones and Lyapunov exponents. Ergod. Th. & Dynam. Sys., 5, 145–161.
Wojtkowski, M. (1988): Measure theoretic entropy of the system of hard spheres. Ergod. Th. & Dynam. Sys., 8, 133–153.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0086662
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54662-7
Online ISBN: 978-3-540-46431-0
eBook Packages: Springer Book Archive
