On the stability and the exponential concentration of Extended Kalman-Bucy filters
DEL MORAL, Pierre
Quality control and dynamic reliability [CQFD]
School of Mathematics and Statistics [Sydney] [UNSW]
Quality control and dynamic reliability [CQFD]
School of Mathematics and Statistics [Sydney] [UNSW]
DEL MORAL, Pierre
Quality control and dynamic reliability [CQFD]
School of Mathematics and Statistics [Sydney] [UNSW]
< Reduce
Quality control and dynamic reliability [CQFD]
School of Mathematics and Statistics [Sydney] [UNSW]
Language
en
Document de travail - Pré-publication
English 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 ...Read more >
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.Read less <
English Keywords
Lyapunov exponents
non asymptotic exponential stability
extended Kalman-Bucy filter
Riccati equation
Concentration inequalities
Origin
Hal imported