  We consider the problem of estimating neural activity from measurements of
the magnetic fields recorded by magnetoencephalography. We exploit the temporal
structure of the problem and model the neural current as a collection of
evolving current dipoles, which appear and disappear, but whose locations are
constant throughout their lifetime. This fully reflects the physiological
interpretation of the model. In order to conduct inference under this proposed
model, it was necessary to develop an algorithm based around state-of-the-art
sequential Monte Carlo methods employing carefully designed importance
distributions. Previous work employed a bootstrap filter and an artificial
dynamic structure where dipoles performed a random walk in space, yielding
nonphysical artefacts in the reconstructions; such artefacts are not observed
when using the proposed model. The algorithm is validated with simulated data,
in which it provided an average localisation error which is approximately half
that of the bootstrap filter. An application to complex real data derived from
a somatosensory experiment is presented. Assessment of model fit via marginal
likelihood showed a clear preference for the proposed model and the associated
reconstructions show better localisation.
