On the stability and the 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 and fully observable 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
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