Recurrent Estimation of Hidden Markov Model Transition Probabilities from Aggregate Data

Recurrent estimation of Hidden Markov Model transition probabilities using aggregate data is considered. The problem is reduced to equivalent identification problem for discrete stochastic dynamical system under constraints. Using a combination of the regularized method of penalty functions and Lagrange multipliers method, an estimate of transition matrix was obtained from the aggregate data as well as recurrent estimation algorithms which used a sequence of observations and providing real-time estimates. The efficiency of proposed method is illustrated by numerical examples.