On the Stability and the Exponential Concentration of Extended Kalman-Bucy filters

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 inequaliti...

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Published in:arXiv.org 2016-10
Main Authors: Pierre Del Moral, Kurtzmann, Aline, Tugaut, Julian
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Language:English
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Asymptotic properties
Confidence intervals
Estimates
Inequalities
Initial conditions
Nonlinear filters
Norms
Stability
Stochastic processes
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Kurtzmann, Aline
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description 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.
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subjects Asymptotic properties
Confidence intervals
Estimates
Inequalities
Initial conditions
Nonlinear filters
Norms
Stability
Stochastic processes
title On the Stability and the Exponential Concentration of Extended Kalman-Bucy filters
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