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This paper presents a novel algorithm, the particle-based, rapid incrementalsmoother (PaRIS), for efficient online approximation of smoothed expectationsof additive state functionals in general hidden Markov models. The algorithm,which has a linear computational complexity under weak assumptions and verylimited memory requirements, is furnished with a number of convergence results,including a central limit theorem. An interesting feature of PaRIS, whichsamples on-the-fly from the retrospective dynamics induced by the particlefilter, is that it requires two or more backward draws per particle in order tocope with degeneracy of the sampled trajectories and to stay numerically stablein the long run with an asymptotic variance that grows only linearly with time.

Efficient particle-based online smoothing in general hidden Markov models: the PaRIS algorithm