Generalized fixed-interval smoothers for discrete-time systems

The generalized fixed-interval smoothing problem involves predictive information concerning the final state in addition to a priori information concerning the initial state. Forwards and backwards Markovian models which incorporate the predictive and a priori information, respectively, are constructed by simply using the standard smoothing formulae. The generalized backward- or forward-pass fixed-interval smoothing algorithm and two-filter smoothing algorithm are described in a unified manner. It is then shown that the generalized smoothers include as special cases almost all existing smoothers, e.g., Rauch–Tung–Striebel smoother, Mayne–Fraser two-filter smoother, Wall–Willsky–Sandell two-filter smoother and Desai–Weinert–Yusypchuk smoother. Simulation examples are included to illustrate the characteristics of the present fixed-interval smoothers.