Hidden Markov chain identification

An identification scheme is developed for hidden Markov models (HMM). Unlike the realization problem, where one starts from exact probabilities, the identification problem makes a statistical inference from the pathwise output sequences. The basic principle in the identification of Markovian finite state systems from nonnumeric inputs and outputs is its lifting to a numerical representation via the vector valued indicator function. This allows the subsequent use of subspace methods which generate the relevant statistics for identification.