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 , 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.
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