部分状态可见的隐马尔可夫模型的Viterbi算法  

Viterbi Algorithms for Hidden Markov Models with Partially Visible States

作　　者：宋延红[1] 王志成 Yan Hong SONG;Zhi Cheng WANG(School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,P.R.China)

机构地区：[1]中南财经政法大学统计与数学学院,武汉430073

出　　处：《数学学报（中文版）》2024年第3期500-510,共11页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11501576);教育部人文社会科学研究基金资助项目(23YJCZH189);中南财经政法大学中央高校基本科研业务费专项资金资助项目(2722023BY019)。

摘　　要：本文研究了隐马尔可夫模型的Viterbi算法,在已知隐马尔可夫模型的部分状态、初始概率分布、状态转移概率矩阵和观测概率矩阵的条件下,由此Viterbi算法给出最优状态序列的估计.相对于已有的算法,本文的算法考虑了部分可见状态对初始条件和递推公式的影响,并且本文的算法能保证预测的状态序列是整体最优的.最后,我们将本文的算法应用于故障识别,从而验证所设计算法的可行性.In the paper,Viterbi algorithms for hidden Markov models are studied.When partial states,initial probability distributions,transition probability matrices and observation probability matrices are given,the optimal state sequences are esti-mated by the Viterbi algorithms.Compared with existing algorithms,the algorithms presented in the paper have not only considered the influence of partially visible states on the initial conditions and recursion formulas,but also ensured that the predicted state sequences are overall optimal.Finally,fault recognition is investigated to verify the feasibility of the algorithms.

关 键 词：部分状态可见 隐马尔可夫模型 VITERBI算法 

分 类 号：O211.62[理学—概率论与数理统计]