Optimal sequential estimation of discrete processes with Markov interrupted observations

This short paper considers the problem of sequential estimation of discrete-time processes corrupted by additive noise when there is time-varying uncertainty regarding the presence of the process at each stage of the observation sequence. A recursive Bayes' optimal solution is derived that does not require a growing amount of memory and computation for its implementation but that, however, requires recursion on continuous functions to be performed. Digital computer implementation of the proposed algorithms is discussed and some simulation results are presented.