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On Stability of a Class of Filters for Nonlinear Stochastic Systems

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date

2020

Department

Department of Electrical Engineering and Automation

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Language

en

Pages

27

Series

SIAM Journal on Control and Optimization, Volume 58, issue 4, pp. 2023-2049

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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Keywords

Nonlinear systems, Kalman filtering, Nonlinear stability analysis, Extended Kalman Filter, Performance evaluation, Exponential stability, Uniform propagation, Discrete, Convergence, Observer, Accuracy, Equation, Chaos

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DOI

10.1137/19M1285974

Citation

Karvonen, T, Bonnabel, S, Moulines, E & Särkkä, S 2020, 'On Stability of a Class of Filters for Nonlinear Stochastic Systems', SIAM Journal on Control and Optimization, vol. 58, no. 4, pp. 2023-2049. https://doi.org/10.1137/19M1285974

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https://urn.fi/URN:NBN:fi:aalto-202010235934

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[article-cris] Sähkötekniikan korkeakoulu / ELEC

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