DEL MORAL, Pierre; KURTZMANN, Aline; TUGAUT, Julian

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DEL MORAL, Pierre
Quality control and dynamic reliability [CQFD]
School of Mathematics and Statistics [Sydney] [UNSW]

KURTZMANN, Aline
Institut Élie Cartan de Lorraine [IECL]

TUGAUT, Julian
Probabilités, statistique, physique mathématique [PSPM]

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Résumé en anglais

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.< Réduire

Mots clés en anglais

Lyapunov exponents

non asymptotic exponential stability

extended Kalman-Bucy filter

Riccati equation

Concentration inequalities

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

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Résumé en anglais

Mots clés en anglais

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