Forgetting in Marginalized Particle Filtering and its Relation to Forward Smoothing

The problem of degeneracy in marginalized particle filtering is addressed. In particular, we note that the degeneracy is caused by loss of entropy of the posterior distribution and design maximum entropy estimates to prevent this. The main technique used in this report is known as forgetting. Itis shown that it can be used to suppress the problem with degeneracy, however, it is not a proper cure for the problem of stationary parameters. The problem of marginal-marginalized particle filter for sufficient statistics is also studied. The resulting algorithm is found to have remarkable similarities with the algorithm known as forward smoothing