On the stability and the exponential concentration of Extended Kalman-Bucy filters - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2016

On the stability and the exponential concentration of Extended Kalman-Bucy filters

Résumé

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.
Fichier principal
Vignette du fichier
Extended-Kalman-Bucy-2016-06-27.pdf (288.61 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01337709 , version 1 (27-06-2016)

Identifiants

  • HAL Id : hal-01337709 , version 1

Citer

Pierre del Moral, Aline Kurtzmann, Julian Tugaut. On the stability and the exponential concentration of Extended Kalman-Bucy filters. 2016. ⟨hal-01337709⟩
198 Consultations
173 Téléchargements

Partager

Gmail Facebook X LinkedIn More