Conventional hidden Markov models provide a discrete distribution over a finite number of states. In some modeling scenarios, particularly those representing data from a physical systems, such discrete states are, at best, an idealization, since the physical system may exhibit a continuous transition between states. In this paper, a hidden Markov model is presented that generalizes this by introduction of a state that may take any value in a simplex. The Dirichlet distribution is used to provide a representation of the probability distribution of the states. The transition probability density is assumed to be Dirichlet, and the output distribution is assumed to be a state-dependent mixture. An estimation of the state distribution using propagation and update steps is developed. Approximations of the state estimates remain in the set of Dirichlet distributions, so computationally efficient state propagation is possible. A forward/backward (smoothing) algorithm is also developed.
Continuum-State Hidden Markov Models with Dirichlet State Distributions
Journal of Aerospace Information Systems ; 12 , 12 ; 800-824
2015-01-08
25 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
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