Bayesian estimation of forgetting factor in adaptive filtering and change detection

An adaptive filter is derived in a Bayesian framework from the assumption that the difference in the parameter distribution from one time to another is bounded in terms of the Kullback-Leibler divergence. We show an explicit link to the general concepts of exponential forgetting, and outline the details for a linear Gaussian model with unknown parameter and covariance. We extend the problem to an unknown forgetting factor, where we provide a particular prior that allows for abrupt changes in forgetting, which is useful in change detection problems. The Rao-Blackwellized particle filter is used for the implementation, and its performance is assessed in a simulation of system with abrupt changes of parameters.