Recursive equation for conditional-mean particle smoother in nonlinear Bayesian smoothing

This paper develops a novel approach for recursive state estimation in nonlinear Bayesian smoothing. The new approach is based on simple distributional identities concerning the smoothing density. For forward filtering, they simplify derivation of particle filter (Gordon et al., 1993; Kitagawa, 1993). Most importantly, for backward smoothing they derive a new form of the smoothing density which gives a recursive equation for the conditional-mean particle smoother. It represents a nonlinear counterpart of the Rauch-Tung-Striebel (Rauch et al., 1965) equation for the smoother of general state-space models. Numerical study shows that the proposed conditional-mean particle smoother improves particle filtering estimates of state as confirmed by Binomial test on the estimation errors.