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On Stability of a Class of Filters for Nonlinear Stochastic Systems

Abstract : This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous-and discrete-time filters for stochastic dynamic systems with nonlinear state dynamics and linear measurements under certain strong assumptions. The class of filters encompasses the extended and unscented Kalman filters and most other Gaussian assumed density filters and their numerical integration approximations. The stability results are in the form of time-uniform mean square bounds and exponential concentration inequalities for the filtering error. In contrast to existing results, it is not always necessary for the model to be exponentially stable or fully observed. We review three classes of models that can be rigorously shown to satisfy the stringent assumptions of the stability theorems. Numerical experiments using synthetic data validate the derived error bounds.
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https://hal.inria.fr/hal-03033016
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Submitted on : Tuesday, December 1, 2020 - 10:39:16 AM
Last modification on : Wednesday, November 17, 2021 - 12:31:09 PM
Long-term archiving on: : Tuesday, March 2, 2021 - 6:41:01 PM

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Toni Karvonen, Silvère Bonnabel, Eric Moulines, Simo Särkkä. On Stability of a Class of Filters for Nonlinear Stochastic Systems. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2020, 58, pp.2023 - 2049. ⟨10.1137/19m1285974⟩. ⟨hal-03033016⟩

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