Parametric Estimation Of Nth-order Hidden Markov Model

This paper describes the structure of nth-order hidden markov model on condition that observation noise is not independent of the markov chain, and then researches the forward-backward algorithm and the Baum-Welch algorithm of the model, and derives the parametric estimation equations for the model assuming one observable sequence only. Furthermore, nth-order hidden Markov model is trained with multiple observable sequences and several new formulae solving model training problem are derived. Finally, the paper researches the Baum-Welch algorithm of nth-order hidden markov model relation with the observations ( HMM_n×n) and mixture of nth-order hidden markov model( MHMM_n).This paper is divided into five parts as follows:The first part describes the development of hidden markov model theory and related research at home and abroad, then introduces the study background of this dissertation. In the end, a kind of constrained optimization method is presented.The second part focuses on the forward-backward algorithm of nth-order hidden markov model.Firstly the third part introduces the Baum-Welch algorithm of nth-order hidden markov model, followed the model parameter estimation equations. Finally it's the introduction of the physical meaning of the model.The fourth part derives the parametric estimation equations for nth-order hidden markov model assuming multiple observable sequences.In the fifth part, the paper describes the structures of HMM_n×n and MHMM_n, and derives the update parametric estimation equations for these two models according to Baum-Welch algorithm.