Recursive algorithms for the Bayes solution of the fixed-point and fixed-lag smoothing problems

Recursive algorithms for the Bayes solutions of the fixed-point and fixed-lag smoothing problems are obtained. Recursive algorithms for the respective smoothed a posteriori densities are derived under assumptions that the signal to be estimated is a Markov process and the observation is a signal embedded in independent noise (not necessarily additive) which is also independent of the signal. The recursive algorithm for the fixed-point smoothing is applied to a binary Markov signal corrupted by an independent noise in a nonlinear manner.