连续时间马尔可夫跳变线性系统运行模式的平稳线性均方滤波器

Q4 Mathematics

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2020-01-01 DOI:10.56082/annalsarscimath.2020.1-2.501

Fortià V. Vergés, M. Fragoso

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引用次数: 0

摘要

本文进一步研究了一类马尔可夫跳变线性系统(MJLSs)的部分观测马尔可夫参数(运行模式)的滤波问题。我们对作者在最近的一篇论文中设计的最佳线性均方滤波器(BLMSF)导出了一个平稳滤波器。在包含马尔可夫链遍历性的适当假设下，得到了最佳线性均方滤波器的误差协方差矩阵收敛于平稳值。这种方案的优点是它更容易实现，因为滤波器增益计算可以离线执行，从而导致线性时不变滤波器。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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STATIONARY LINEAR MEAN SQUARE FILTER FOR THE OPERATION MODE OF CONTINUOUS-TIME MARKOVIAN JUMP LINEAR SYSTEMS

This paper makes a further foray on the study of the filtering problem for the class of Markov jump linear systems (MJLSs) with partial observations of the Markov parameter (the operation mode). We derive a stationary filter for the best linear mean square filter (BLMSF) devised in a recent paper by the authors. It amounts here to obtain the convergence of the error covariance matrix of the best linear mean square filter to a stationary value under some suitable assumptions which includes ergodicity of the Markov chain. The advantage of this scheme is that it is easier to implement since the filter gain computation can be performed offline, leading to a linear time-invariant filter.

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来源期刊

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Mathematics-Mathematics (all)

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

25 weeks

期刊介绍： The journal Mathematics and Its Applications is part of the Annals of the Academy of Romanian Scientists (ARS), in which several series are published. Although the Academy is almost one century old, due to the historical conditions after WW2 in Eastern Europe, it is just starting with 2006 that the Annals are published. The Editor-in-Chief of the Annals is the President of ARS, Prof. Dr. V. Candea and Academician A.E. Sandulescu (†) is his deputy for this domain. Mathematics and Its Applications invites publication of contributed papers, short notes, survey articles and reviews, with a novel and correct content, in any area of mathematics and its applications. Short notes are published with priority on the recommendation of one of the members of the Editorial Board and should be 3-6 pages long. They may not include proofs, but supplementary materials supporting all the statements are required and will be archivated. The authors are encouraged to publish the extended version of the short note, elsewhere. All received articles will be submitted to a blind peer review process. Mathematics and Its Applications has an Open Access policy: all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. No submission or processing fees are required. Targeted topics include : Ordinary and partial differential equations Optimization, optimal control and design Numerical Analysis and scientific computing Algebraic, topological and differential structures Probability and statistics Algebraic and differential geometry Mathematical modelling in mechanics and engineering sciences Mathematical economy and game theory Mathematical physics and applications.