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hal.structure.identifierQuality control and dynamic reliability [CQFD]
hal.structure.identifierSchool of Mathematics and Statistics [Sydney] [UNSW]
dc.contributor.authorDEL MORAL, Pierre
hal.structure.identifierInstitut Élie Cartan de Lorraine [IECL]
dc.contributor.authorKURTZMANN, Aline
hal.structure.identifierProbabilités, statistique, physique mathématique [PSPM]
dc.contributor.authorTUGAUT, Julian
dc.date.accessioned2024-04-04T03:14:32Z
dc.date.available2024-04-04T03:14:32Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194065
dc.description.abstractEnThe 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.
dc.language.isoen
dc.subject.enLyapunov exponents
dc.subject.ennon asymptotic exponential stability
dc.subject.enextended Kalman-Bucy filter
dc.subject.enRiccati equation
dc.subject.enConcentration inequalities
dc.title.enOn the stability and the exponential concentration of Extended Kalman-Bucy filters
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Probabilités [math.PR]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-01337709
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01337709v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=DEL%20MORAL,%20Pierre&KURTZMANN,%20Aline&TUGAUT,%20Julian&rft.genre=preprint


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