A modified hidden Markov model

This paper considers two discrete time, finite state processes XX and YY. In the usual hidden Markov model XX modulates the values of YY. However, the values of YY are then i.i.d. given XX. In this paper a new model is considered where the Markov chain XX modulates the transition probabilities of the second, observed chain YY. This more realistically can represent problems arising in DNA sequencing. Algorithms for all related filters, smoothers and parameter estimations are derived. Versions of the Viterbi algorithms are obtained.