Finite dimensional hybrid smoothers

Three finite dimensional hybrid smoothers that achieve maximum a posteriori (MAP) state sequence estimates are presented. The hybrid smoothers exactly cross-couple one or both of two optimal smoothers, the hidden Markov model smoother and the Kalman smoother, according to the signal model requirements. We consider two broad classes of signal models for which these hybrid smoothers are applicable, those of jump Markov linear systems, and bilinear systems, both of which are used to model a wide range of physical processes in all areas of science, engineering and economics. Unlike other state estimation algorithms, our hybrid smoothers do not attempt to approximate the infinite dimensional conditional mean estimator. Rather they obtain MAP state sequence estimates, via the expectation-maximization (EM) algorithm. The two cross-coupled optimal smoothers achieve the E and M steps of the algorithm, resulting in structurally simple hybrid smoothers