Forward/backwardstate and modelparameter estimation for continuum-state hidden Markov models (CHMM) with Dirichlet state distributions

In this paper, the foundations of the theory of the continuum-state HMM (cHMM) are extended to include a forward/ backward algorithm producing probability densities analogous to those in conventional HMMs, and algorithms for estimating the parameters of the state transition density and the constituent output densities. The α and β densities are approximated as Dirichlet distributions, providing for nearly closed form, “closed” operations. The EM algorithm is extended to apply to the parameter estimation problem. Major results are presented, with details and proofs omitted due to space.