Abstract

The review of algorithms of estimation of stochastic processes with random structure and Markov switch obtained on a basis of mathematic tool of mixed Markov processes in discrete time is represented. It is shown that Markov property including continuous valued process with random structure in discrete time and Markov chain controlling its structure modification. There are considered recurrent optimal and quasi-optimal filtering algorithms describing the evolution of a posteriori probability density of the mixed process. Adaptive filters belong to devices class with feedbacks between channels. There is represented Bayesian decision rule for definition of the estimations of discrete and continuous components which are mutually coupled. There are considered recurrent optimal interpolation algorithms: at the fixed point, in the fixed interval and with constant delay and their analysis is carried out. There are represented examples of application of considered estimation algorithms for solution of applicable problems. There are considered two-step algorithms of mutual filtering and segmentation of textural images allowing to preserve computational advantages of single-dimension algorithms of estimation of the processes with random structure and adequate to digital devices with parallel architecture.

中文翻译：

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离散时间下随机结构和马尔可夫切换的随机过程的估计（综述）

摘要

提出了一种基于随机时间混合马尔可夫过程的数学工具获得的随机结构随机过程估计算法和马尔可夫开关的算法综述。结果表明，马尔可夫性质包括具有离散时间的随机结构的连续值过程和由马尔可夫链控制的结构修改。考虑了描述混合过程后验概率密度演化的递归最优和准最优滤波算法。自适应滤波器属于具有通道之间反馈的设备类。有贝叶斯决策规则，用于定义相互耦合的离散和连续分量的估计。考虑了循环最优插值算法：在固定点，在固定间隔和恒定延迟下进行分析。给出了考虑的估计算法用于解决适用问题的应用示例。已经考虑了纹理图像的相互过滤和分割的两步算法，从而保留了估计具有随机结构的过程的单维算法的计算优势，并且适合于具有并行结构的数字设备。