  We describe a novel method for dynamic estimation of multi-dipole states from
Magneto/Electro-encephalography (M/EEG) time series. The new approach builds on
the recent development of particle filters for M/EEG; these algorithms
approximate, with samples and weights, the posterior distribution of the neural
sources at time t given the data up to time t. However, for off-line inference
purposes it is preferable to work with the smoothing distribution, i.e. the
distribution for the neural sources at time t conditioned on the whole time
series. In this study, we use a Monte Carlo algorithm to approximate the
smoothing distribution for a time-varying set of current dipoles. We show,
using numerical simulations, that the estimates provided by the smoothing
distribution are more accurate than those provided by the filtering
distribution, particularly at the appearance of the source. We validate the
proposed algorithm using an experimental dataset recorded from an epileptic
patient. Improved localization of the source onset can be particularly relevant
in source modeling of epileptic patients, where the source onset brings
information on the epileptogenic zone.
