A recursive algorithm for the Bayes solution of the smoothing problem

The optimum fixed interval smoothing problem is solved using a Bayesian approach, assuming that the signal is Markov and is corrupted by independent noise (not necessarily additive). A recursive algorithm to compute the a posteriori smoothed density is obtained. Using this recursive algorithm, the smoothed estimate of a binary Markov signal corrupted by an independent noise in a nonlinear manner is determined demonstrating that the Bayesian approach presented in this paper is not restricted to the Gauss-Markov problem.