Lecture Notes in Control and Information Sciences vol:341 pages:367-374
In this paper we consider a finite state Markov chain with two outputs, an observed output and a to-be-estimated output, and derive a recursive estimator for the to-be-estimated output from an observed output string. The main point of this article is to illustrate that for this kind of filtering problem, it is not needed to have a positive hidden Markov realization of the joint process, but it suffices to have a quasi-realization. We also present an approximate quasi-realization algorithm. We perform a simulation comparing the behavior of the exact, experimental and approximate quasi-realizations and checking the performance of the estimator.