论文标题:小波变换在隐马尔科夫模型非参数估计中的应用
Wavelet Transformation for Nonparametric Estimation of HMM"s
论文作者 敬晓龙
论文导师 马洪,论文学位 硕士,论文专业 概率论与数理统计
论文单位 四川大学,点击次数 79,论文页数 26页File Size710k
2003-03-01论文网 http://www.lw23.com/lunwen_43477052/ 隐马尔科夫模型;随机信号处理;非参数密度估计;小波正交级数;分解尺度
Hidden Markov Model,stochastic signal processing,nonparametric estimation,wavelet orthogonal series,resolving scale
隐马尔科夫模型(Hidden Markov Model，简记为HMM)作为一种统计模型，在模式识别与随机信号处理中有着广泛的应用。小波理论是近年来兴起的一种崭新的信号分析理论，在许多信号处理领域得到了成功的应用。本文研究小波变换在隐马尔科夫模型观测过程的概率密度估计中的应用。对于很多实际情况，HMM密度函数所属类型并不知道，此时的密度估计就是典型的非参数估计问题。我们利用小波正交级数的很多良好性质来估计隐马尔科夫模型中的条件概率密度函数。 在这篇论文中，首先给出了隐马尔科夫模型的定义，接着介绍了隐马尔科夫模型实际应用中所面临的三大基本问题的解决方案，即隐马尔科夫模型三大基本算法：前向一后向算法、Viterbi算法、Baum—Welch算法。然后给出了隐马尔科夫过程动态系统的一般模型。其次，介绍了小波变换中的重要理论—多分辨率分析理论，及其相应的分解和重构算法—Mallat算法。 最后，结合小波理论和隐马尔科夫模型的相关知识，将小波变换应用到隐马尔科夫模型非参数估计问题中来，并探讨了其中Haar小波正交级数估计量分解尺度的选取。
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.
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