Abstract
The purpose of this paper is to study fixed-point smoothing problems from the viewpoint of the information theory. For a linear stochastic system it is proved that the necessary and sufficient condition for maximizing the mutual information between a state and the smoothed estimate is to minimize the entropy of the smoothed estimation error. Based on this relation between the mutual information and the error entropy, the optimal fixed-point smoothing estimator for a discrete-time linear system is derived. Furthermore, a similar estimator for a continuous-time linear system is also considered by an analogous approach.
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