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语音识别中，动态时间规整（Ｄｙｎａｍｉｃ Ｔｉｍｅ Ｗａｒｐｉｎｇ，简称ＤＴＷ）和隐马尔可夫模型（Ｈｉｄｄｅｎ Ｍａｒｋｏｖ Ｍｏｄｅｌ，简称 ＨＭＭ）是最有效的两种识别算法，并且 ＤＴＷ和 ＨＭＭ在本质上是一致的~［１］。根据 ＤＴＷ和 ＨＭＭ的本质联系和各自所对应的声学模型，在前期工作中建立了一种广义声学模型 ~［２］［３］（Ｇｅｎｅｒａｌ Ｍｏｄｅｌ，简称 ＧＭ），并指出 ＤＴＷ和ＨＭＭ 只是 ＧＭ的特例，且 ＤＴＷ和 ＨＭＭ都可以转化为 ＧＭ。并在此基础上，首次将 Ｆｉｓｈｅｒ算法~［４］引进ＧＭ的学习算法，确保了ＧＭ状态分割的收敛性，并且这种分割在最小离差意义上是全局精确最优的。最后，从大数定理的角度出发，对 ＧＭ算法的收敛性进行了分析， 从理论上论证了该算法的依概率收敛性，并为实际应用中 ＧＭ算法的有效性提供了理论依据。
In speech recognition, Dynamic Time Warping (DTW) and Hidden Markov Model (HMM) are the most effective two recognition algorithms, and DTW and HMM are essentially the same [ 1]. According to the essential relationship between DTW and HMM and their corresponding acoustic models, a generalized acoustic model ~ [2] [3] (General Model) was established in the previous work and pointed out that DTW and HMM are only special cases of GM , And both DTW and HMM can be converted to GM. Based on this, for the first time Fisher algorithm ~ [4] is introduced into GM learning algorithm to ensure the convergence of GM state segmentation, and this segmentation is globally accurate and optimal in the sense of minimum dispersion. Finally, from the point of view of the theorem of large numbers, the convergence of the GM algorithm is analyzed, the probability convergence of the algorithm is demonstrated theoretically, and the theoretical basis of the validity of the GM algorithm is provided.