General convergence result for continuous-discrete feedback particle filter

In this paper, we shall discuss the convergence of the continuous-discrete feedback particle filter (FPF) proposed in Yang et al. (2014). The FPF is an interacting system of N particles where the interaction is designed such that the empirical distribution of the particles approximates the posterior...

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Bibliographic Details
Published inInternational journal of control Vol. 95; no. 11; pp. 2972 - 2986
Main Authors Chen, Xiuqiong, Luo, Xue, Shi, Ji, Yau, Stephen S.-T.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.11.2022
Taylor & Francis Ltd
Subjects
continuous-discrete system
Convergence
Empirical analysis
Error analysis
Feedback control
feedback particle filter
Mathematical analysis
Optimal filtering
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Summary:In this paper, we shall discuss the convergence of the continuous-discrete feedback particle filter (FPF) proposed in Yang et al. (2014). The FPF is an interacting system of N particles where the interaction is designed such that the empirical distribution of the particles approximates the posterior distribution by an innovation error-based feedback control structure. Under some assumptions, it is proved that, for a class of functions ϕ and , the estimate of by FPF converges to its optimal estimate in sense, as the number of particles goes to infinity and the numerical approximation error of computing the control input U goes to zero. Furthermore, the bound of the estimation error is also delicately analyzed.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2021.1948105