Entropy based adaptive particle filter

We propose a particle filter for the estimation of a partially observed Markov chain that has a non dynamic component. Such systems arise when we include unknown parameters or when we decompose non ergodic systems to their ergodic classes. Our main assumption is that the value of the non dynamic component determines the limiting distribution of the observation process. In such cases, we do not want to resample the particles that correspond to the non dynamic component of the Markov chain. Instead, we take a weighted average of particle filters corresponding to different values of the non dynamic component. The computation of the weights is based on entropy and the number of particles corresponding to each particle filter is proportional to the weights.