General convergence result for continuous-discrete feedback particle filter. Issue 11 (2nd November 2022)

• Record Type: Journal Article
• Authors: Chen, Xiuqiong; Luo, Xue; Shi, Ji; Yau, Stephen S.-T.
• Is Part Of: International journal of control. Volume 95:Issue 11(2022)
• Page Start: 2972
• Page End: 2986
• Publication Date: 2022-11-02
• Subjects: Optimal filtering -- feedback particle filter -- continuous-discrete system -- convergence; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2021.1948105
• Languages: English
• ISSNs: 0020-7179

Abstract

ABSTRACT: 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 ∀ p ≥ 2, the estimate of ϕ ( X t n ) by FPF converges to its optimal estimate E [ ϕ ( X t n ) | F t n ] in L p 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.