Backward-pass multiple model adaptive filtering for a fixed-interval smoother

A method of backward-pass multiple model adaptive filtering is developed for a stochastic system, in which the a priori information concerning multiple possible initial states and the predictive information concerning a single final state are available. It is shown that a backwards markovian model which incorporates the a priori information can be directly constructed by using the recursion of a backward-pass fixed-interval smoother. The filter based on this new model reduces to a reverse-time realization of the well-known multiple model (or partitioned) adaptive filter. This filter can also be efficiently implemented by a two-filter form, which can process the observations with a single backward-pass Kalman (or information) filter. The problem description was motivated by the need to construct multiple model adaptive fixed-interval smoothers for stochastic systems with unknown parameters.