Abstract

The problem of logical recognition of the operating mode and dynamic estimation of the intra-mode state vector of a discrete-time stochastic Markov system with a random structure is considered. To develop an estimation algorithm implemented at the pace of system time on a computer of limited power, a method for designing a new finite-dimensional optimal structure filter is proposed. Its state vector consists of several latest estimates, and the current estimate is found in the form of an optimal-accuracy dependence on the last measurement and the vector of the previous filter state. The structural functions of the filter are designed in advance, which can be performed by the Monte Carlo method by obtaining their multivariate histograms. Due to the computational complexity of this procedure, algorithms are also proposed for constructing two numerical-analytical approximations of the filter, which take into account only the first two moments of random variables.

中文翻译：

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高阶最优递归逻辑动力滤波器及其协方差逼近

摘要

研究了具有随机结构的离散随机马尔可夫系统的工作模式逻辑识别和模式内状态矢量的动态估计问题。为了开发一种在有限功率的计算机上以系统时间的速度实现的估计算法，提出了一种设计新的有限维最优结构滤波器的方法。它的状态向量由几个最新估计值组成，并且当前估计值以对最后一次测量和先前滤波器状态的向量的最佳精度依赖性的形式找到。滤波器的结构功能是预先设计的，可以通过获取蒙特卡罗方法的多元直方图来执行。由于此过程的计算复杂性，