Parameter Estimation Algorithms On Some HMMS

The Hidden Markov Models which consist of a hidden Markov process and an observation process are statistical models, and the short form is HMM. They were brought forward by Baum and his colleagues in the late sixties and early seventies. In 1970s, they were applied into speech recognition by Jenik and some other people. They have been developed to be one of the most efficient techniques. Now, they have been widely used in biostatistics, gene recognition, character recognition and image processing etc. There are three problems needed to be solved by using hidden Markov model, which are training, decoding and recognizing. The answers of these three problems consist of the theory of hidden Markov models. Parameter estimation is the core problem of the training process.These questions are discussed in the article:1. Forward algorithms is deduced and presented independently. On the foundation of it we presented a training method of CHMM parameters based on maximum mutual information.2. We discussed the convergence of MAP path, i.e. in the condition of global optimization, we researched into the convergence of hidden state sequence when observational state sequence is infinite.3. We introduced the theory of fuzzy sets into hidden Markov models, and put forward a new model which has a fuzzy layer. Then deduced forward and backward algorithms and Viterbi algorithm of the new model.4. We introduced the theory of type-2 fuzzy sets into the training of discrete HMM parameters based on fuzzy clustering. And then put forward an improved algorithm which is named T2FCM-FE-HMMS.The conference of MAP path in general instance will be researched, in addition, some algorithms haven to be improved on by experiment in the future.