Sequential Monte Carlo smoothing with estimation in non-linear state space models

Jimmy Olsson, Olivier Cappé, Randal Douc and Eric Moulines

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
This paper concerns the use of Sequential Monte Carlo methods (SMC) for smoothing in general state space models. A well known problem when applying the standard SMC technique in the smoothing mode is that the resampling mechanism introduces degeneracy of the approximation in the path-space. However, when performing maximum likelihood estimation via the EM algorithm, all involved functionals will be of additive form for a large subclass of models. To cope with the problem in this case, a modification, relying on forgetting properties of the filtering dynamics, of the standard method is proposed. In this setting, the quality of the produced estimates is investigated both theoretically and through simulations.