Wavelet Transformation For Nonparametric Estimation Of HMM's

As a statistics model, Hidden Markov Model (HMM) have been widely used in pattern recognition and stochastic signal processing. Wavelet theory is a new signal analyzing theory and has been used in many signal processing field in recent years. In HMM, a important problem is the probability density function of observing process. For many practiced instances, the type of the probability density function is unknown. So density estimation is nonparametric estimation. We can apply many good qualities of wavelet orthogonal series to estimate the condition probability density function of HMM's.In this thesis, we first introduce give the definition of hidden Markov models. Then the methods to solve the three basic problems in the application of hidden Markov models are introduced, namely three basic arithmetic: forward-backward algorithm, Viterbi algorithm, Baum-Welch algorithm. Also we present commonly model of Hidden Markov Processes dynamic system.Second, we discuss the important theory in wavelet transformation multi-resolution analysis theory, and the corresponding algorithm-Mallat algorithm.At last, combining the related knowledge of Wavelet theory and hidden Markov models, we introduce wavelet transformation for nonparametric estimation of HMM's and discuss how to choose resolving scale of Haar-wavelet orthogonal series' estimation.