Auxiliary two-filter particle smoothing for one generalized hidden Markov model

平滑的 算法 颗粒过滤器 数学 二次方程 马尔可夫链 采样(信号处理) 滤波器(信号处理) 计算机科学 计算复杂性理论 数学优化 隐马尔可夫模型 应用数学 人工智能 统计 计算机视觉 几何学
作者
Yunqi Chen,Zhibin Yan,Xing Zhang
出处
期刊:Isa Transactions [Elsevier BV]
标识
DOI:10.1016/j.isatra.2024.04.009
摘要

This paper develops two-filter particle smoothing (TFPS) algorithms for the nonlinear fixed-interval smoothing problem of one generalized hidden Markov model (GHMM), where the current observation depends not only on the current state, but also on one-step previous state. Firstly, by Bayesian approach, the two-filter smoothing (TFS) formula for GHMM is established to calculate smoothing densities. In this TFS formula, the backward information prediction density is generally not a density of the state. This results in a difficulty that the normal sequential Monte Carlo (SMC) sampling technique cannot be directly applied to design corresponding TFPS algorithms based on the TFS formula. To solve this difficulty, a generalized TFS formula for GHMM is then proposed by introducing a sequence of artificial densities. By combining this generalized TFS formula, SMC, and the auxiliary variable sampling technique, a basic auxiliary TFPS (ATFPS) algorithm with quadratic computational complexity is proposed, and a simplified ATFPS algorithm with linear computational complexity is further developed. Finally, the effectiveness and superiority of the two proposed ATFPS algorithms for GHMM are verified via simulation examples and real experimental data.
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