On the stability and the exponential concentration of Extended Kalman-Bucy filtersReportar como inadecuado

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1 CQFD - Quality control and dynamic reliability IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest 2 School of Mathematics and Statistics 3 Probabilités et statistiques IECL - Institut Élie Cartan de Lorraine 4 ICJ - Institut Camille Jordan Villeurbanne

Abstract : The exponential stability and the concentration properties of a class of extended Kalman-Bucy filters are analyzed. New estimation concentration inequalities around partially observed signals are derived in terms of the stability properties of the filters. These non asymptotic exponential inequalities allow to design confidence interval type estimates in terms of the filter forgetting properties with respect to erroneous initial conditions. For uniformly stable signals, we also provide explicit non-asymptotic estimates for the exponential forgetting rate of the filters and the associated stochastic Riccati equations w.r.t. Frobenius norms. These non asymptotic exponential concentration and quantitative stability estimates seem to be the first results of this type for this class of nonlinear filters. Our techniques combine χ-square concentration inequalities and Laplace estimates with spectral and random matrices theory, and the non asymptotic stability theory of quadratic type stochastic processes.

Keywords : Concentration inequalities Riccati equation extended Kalman-Bucy filter non asymptotic exponential stability Lyapunov exponents

Autor: Pierre Del Moral - Aline Kurtzmann - Julian Tugaut -

Fuente: https://hal.archives-ouvertes.fr/


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