On the Stability of Kalman--Bucy Diffusion Processes

Abstract : The Kalman--Bucy filter is the optimal state estimator for an Ornstein--Uhlenbeck diffusion given that the system is partially observed via a linear diffusion-type (noisy) sensor. Under Gaussian assumptions, it provides a finite-dimensional exact implementation of the optimal Bayes filter. It is generally the only such finite-dimensional exact instance of the Bayes filter for continuous state-space models. Consequently, this filter has been studied extensively in the literature since the seminal 1961 paper of Kalman and Bucy. The purpose of this work is to review, re-prove and refine existing results concerning the dynamical properties of the Kalman--Bucy filter so far as they pertain to filter stability and convergence. The associated differential matrix Riccati equation is a focal point of this study with a number of bounds, convergence, and eigenvalue inequalities rigorously proven. New results are also given in the form of exponential and comparison inequalities for both the filter and the Riccati flow.
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SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2017, 55 (6), pp.4015 - 4047. 〈10.1137/16M1102707〉
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https://hal.inria.fr/hal-01669244
Contributeur : Pierre Del Moral <>
Soumis le : mercredi 20 décembre 2017 - 16:32:52
Dernière modification le : jeudi 11 janvier 2018 - 17:22:02

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Adrian Bishop, Pierre Del Moral. On the Stability of Kalman--Bucy Diffusion Processes. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2017, 55 (6), pp.4015 - 4047. 〈10.1137/16M1102707〉. 〈hal-01669244〉

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