Modeling And Applications Of Hidden Markov Models

The hidden Markov model (HMM) is a sort of statistical signal model. The basal theory of this model was brought forward in 1960s by L. E. Baum, then it has been gradually applied to many fields such as speech recognition, gene relative analysis and gene recognition, character recognition, image processing, target tracking and signal processing etc. There are three problems needed to be solved by HMM , which are training, recognizing and decoding. The answers for those three problems consist of the theory of HMM. Parameter estimation is the core problem of the training process.Three questions are discussed in the article.1.The betterment of traditional HMM-BHMM. With new BHMM, new forward-backward variables are defined and also recursive formulas are given about forward-backward variables. In addition, with Kullback-Leibler information measure, the reestimation formulas of the parameters about BHMM are brought forward using new forward-backward variables.2. Application of HMM in speech signal processing. In previous literature, time correlation is never considered. In the article, a new modeling method is put forward by which time correlation is considered, and the model is abbreviated to CHMM. Finally, in this paper the reestimation formulas of the parameters about CHMM are given.3. HMM with duration and its tracking for target. In literature'281 ,the definition of HMM with duration is based on that observation chain is consecutive random process, while the definition of HMM with duration is based on that observation chain is disperse random process in the thesis. And when observation chain is disperse random process, the parameter about HMM is quite different from that in literature'28'. Besides the reestimation formulas of the parameters about HMM with duration is given. In literature[24,25,26,27],the tracking for frequency was discussed using traditional HMM, but in practice ,the frequency may persist in sticking around some domain, so tracking for frequency using HMM with duration is put forward in the thesis.