Abstract

In this paper, we consider the problem of the root-mean-square optimal estimation of the current state of a continuous stochastic object of observation exposed to continuous and pulsed random impacts based on the results of discrete measurements of its output at certain clock time points. To obtain real-time estimates using a low-performance computer, a new discrete finite-dimensional filter that provides estimates only at certain clock and possibly inter-cycle time points is proposed. The vector of its state is composed of the last few clock estimates, while the next estimate is sought in the form of its explicit dependence on the last measurement and the previous state of the filter. The number of previous clock estimates to be taken into account can be selected from the condition of a compromise between the required estimation accuracy and the available measurement processing speed. The prediction between measurements is based on the optimal clock and inter-cycle estimates heuristically. The filter synthesis algorithm and methods for constructing its covariance approximations are presented. An example is considered.

中文翻译：

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跳跃扩散马尔可夫信号的大阶最优递归非线性滤波器

摘要

在本文中，我们基于在某些时钟时间点对其输出进行离散测量的结果，考虑了受到连续和脉冲随机影响的连续随机观察对象的当前状态的均方根最优估计问题。为了使用低性能计算机获得实时估计，提出了一种新的离散有限维滤波器，该滤波器仅在某些时钟以及可能的周期间时间点提供估计。它的状态向量由最近的几个时钟估计组成，而下一个估计则以其显式依赖于滤波器的最后一次测量和先前状态的形式来寻找。可以从所需估计精度和可用测量处理速度之间折衷的条件中选择要考虑的先前时钟估计的数量。测量之间的预测是基于最佳时钟和启发式的周期间估计。提出了滤波器合成算法和构造其协方差近似的方法。考虑一个例子。