A Representation Theorem for the Error of Recursive Estimators
A Representation Theorem for the Error of Recursive Estimators
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递归估计器误差的表示定理
DOI：
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发表时间：
1992
期刊：
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通讯作者：
L. Gerencsér
中科院分区：
文献类型：
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作者：
L. Gerencsér
本文的目的是提出一种先进的和鲜为人知的技术，以严格和简洁的方式分析由于统计不确定性引起的广泛的线性随机系统的性能退化。本文的主要技术进步是关于具有强制有界的DFL格式的一个强逼近定理，在该定理中，对于任意q值1，所谓的残差项的lq -范数以速率N-frac12-epsiv和某些epsiv >趋近于零。这是对文献[L]中给出的ARMA过程递归预测误差或RPE估计结果的重要推广。Gerencser，系统控制专栏。， 21(1993)，第347-351页。本文将提出两个有用的推论。在第一种方法中，估计误差过程的标准变换将显示为l -混合。第二部分给出了估计量的渐近协方差矩阵。本文将介绍在ARMAX系统中最小方差自整定调节器的应用
The objective of this paper is to present advanced and less known techniques for the analysis of performance degradation due to statistical uncertainty for a wide class of linear stochastic systems in a rigorous and concise manner. The main technical advance of the present paper is a strong approximation theorem for the Djereveckii-Fradkov-Ljung (DFL) scheme with enforced boundedness, in which, for any q ges 1, the Lq-norms of the so-called residual terms are shown to tend to zero with rate N-frac12-epsiv with some epsiv > 0. This is a significant extension of previous results for the recursive prediction error or RPE estimator of ARMA processes given in [L. Gerencser, Systems Control Lett., 21 (1993), pp. 347-351. Two useful corollaries will be presented. In the first a standard transform of the estimation-error process will be shown to be L-mixing. In the second the asymptotic covariance matrix of the estimator will be given. An application to the minimum-variance self-tuning regulator for ARMAX systems will be described