Particle filtering applied to the EEG inverse problem with dependent noises

Abstract

The fact that the process noise and the measurement noise, are dependent in discrete time models that come from sampling continous time models, is often neglected in the Hidden Markov Models literature. Here we introduce a variant of the traditional Hidden Markov Model to apply to the EEG inverse problem. This variant takes into account that the presentmeasurement and the next state are conditionally dependent given the present state. The corresponding particle predictor is obtained. Different simulations were realized with a non linear example well known in the literature in order to compare the efficiency of the proposed method with the classical approach of filtering where the present measurement and the next state are conditionally independent given the present state. Both approaches, have the same Root Mean Square Error (RMSE) in this context of independency. However, when there is dependence, the estimates obtained by this method have lower RMSE than those obtained by the classical method.