  In this paper, we explore the multiple source localisation problem in the
cerebral cortex using magnetoencephalography (MEG) data. We model neural
currents as point-wise dipolar sources which dynamically evolve over time, then
model dipole dynamics using a probabilistic state space model in which dipole
locations are strictly constrained to lie within the cortex. Based on the
proposed models, we develop a Bayesian particle filtering algorithm for
localisation of both known and unknown numbers of dipoles. The algorithm
consists of a region of interest (ROI) estimation step for initial dipole
number estimation, a Gibbs multiple particle filter (GMPF) step for individual
dipole state estimation, and a selection criterion step for selecting the final
estimates. The estimated results from the ROI estimation are used to adaptively
adjust particle filter's sample size to reduce the overall computational cost.
The proposed models and the algorithm are tested in numerical experiments.
Results are compared with existing particle filtering methods. The numerical
results show that the proposed methods can achieve improved performance metrics
in terms of dipole number estimation and dipole localisation.
