Hidden AR process and adaptive Kalman filter

IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
Yury A. Kutoyants
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引用次数: 0

Abstract

This work discusses a model of a partially observed linear system that depends on some unknown parameters. An approximation of the unobserved component is proposed, which involves three steps. First, a method of moment estimator of unknown parameters is constructed, and second, this estimator is used to define the one-step MLE-process. Finally, the last estimator is substituted into the equations of the Kalman filter. The solution of obtained equations provides us with the desired approximation (adaptive Kalman filter). The asymptotic properties of all the mentioned estimators and both maximum likelihood and Bayesian estimators of the unknown parameters are detailed. The asymptotic efficiency of adaptive filtering is discussed.

隐藏的 AR 过程和自适应卡尔曼滤波器
这项工作讨论的是一个部分观测到的线性系统模型,它取决于一些未知参数。本文提出了对未观测部分的近似方法,包括三个步骤。首先,构建未知参数的矩估计方法;其次,使用该估计方法定义一步 MLE 过程。最后,将最后一个估计器代入卡尔曼滤波方程。方程的求解为我们提供了所需的近似值(自适应卡尔曼滤波器)。本文详细介绍了所有上述估计器的渐近特性,以及未知参数的最大似然估计器和贝叶斯估计器。讨论了自适应滤波的渐近效率。
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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来源期刊
CiteScore
2.00
自引率
0.00%
发文量
39
审稿时长
6-12 weeks
期刊介绍: Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.
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