A stochastic realization approach to the smoothing problem

The purpose of this paper is to develop a theory of smoothing for finiite dimensional linear stochastic systems in the context of stochastic realization theory. The basic Idea is to embed the given stochastic system in a class of similar systems all having the same output process and the same Kalman-Bucy filter. This class has a lattice structure with a smallest and a largest element; these two elements completely determine the smoothing estimates. This approach enables us to obtain stochastic interpretations of many important smoothing formulas and to explain the relationship between them. Copyright © 1979 by The Institute of Electricala and Electronics Engineers Inc.