On the stability and the concentration of extended Kalman-Bucy filters

DOI10.1214/18-EJP188zbMATH Open1401.93199arXiv1606.08251MaRDI QIDQ1990224

Author name not available (Why is that?)

Publication date: 25 October 2018

Published in: (Search for Journal in Brave)

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 $chi$-square concentration inequalities and Laplace estimates with spectral and random matrices theory, and the non asymptotic stability theory of quadratic type stochastic processes.

Full work available at URL: https://arxiv.org/abs/1606.08251

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: On the stability and the concentration of extended Kalman-Bucy filters

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q1990224)