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$${{\mathcal{L}}}_{1}$$ -Optimal Filtering of Markov Jump Processes. II. Numerical Analysis of Particular Realizations Schemes
Automation and Remote Control ( IF 0.7 ) Pub Date : 2021-02-10 , DOI: 10.1134/s0005117920120024
A. V. Borisov

Part II of the paper deals with particular numerical schemes used to realize the filtering algorithm for Markov jump processes by indirect observations corrupted by Wiener noises. The orders of accuracy of these numerical schemes are determined. The cases of additive and multiplicative noises in observations are investigated separately: as shown below, the same schemes in these cases have different accuracy. For observations with additive noises, schemes of orders \(\frac{1}{2}\), 1 and 2 are proposed; for observations with multiplicative noises, schemes of orders 1 and 2. The theoretical results are illustrated with numerical examples.



中文翻译:

$$ {{\ mathcal {L}}} _ {1} $$-马尔可夫跳转过程的最佳过滤。二。特殊实现方案的数值分析

本文的第二部分介绍了一些特殊的数值方案,这些数值方案用于通过Wiener噪声破坏的间接观测来实现Markov跳跃过程的滤波算法。确定这些数值方案的精度等级。分别研究观测值中加性和乘性噪声的情况:如下所示,在这些情况下,相同的方案具有不同的精度。对于具有加性噪声的观测,提出了阶数\(\ frac {1} {2} \)的方案,建议采用1和2的方案。对于具有乘性噪声的观测,采用1级和2级方案。通过数值示例说明理论结果。

更新日期:2021-02-10
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