Finite-Sample System Identification: An Overview and a New Correlation Method
Finite-Sample System Identification: An Overview and a New Correlation Method
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有限样本系统辨识：概述和新的相关方法
DOI：
10.1109/lcsys.2017.2720969
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发表时间：
2018
影响因子：
3
通讯作者：
E. Weyer
中科院分区：
文献类型：
--
作者：
A. Carè;B. Csáji;M. Campi;E. Weyer
有限样本系统辨识算法可用于在温和的统计假设下为未知模型参数建立有保证的置信域。已经证明，在许多情况下，这些严格建造的区域在大小和形状上与那些可以求助于渐近理论的区域相当。然而，后一种集合不能保证用于有限样本，有时可能会导致误导结果。有限样本方法背后的一般原理使它们实际上适用于许多甚至是非线性系统。虽然这些原则足够简单，但对随之而来的技术问题的严格处理使相应的理论变得复杂，不容易理解。这被认为是这些方法尚未被识别界广泛接受的原因之一，这封信旨在通过以简化的方式介绍这些方法的基本思想，为有限样本系统识别提供一个容易的接入点。然后我们回顾了到目前为止已提出的三类方法--1)省略符号显性相关区域(LSCR)；2)符号扰动和(SPS)；3)扰动数据集方法(PDMS)。通过找出这些方法固有的一些困难，我们还在这封信中提出了一种新的基于相关的符号摄动法，它克服了其中的一些困难。
Finite-sample system identification algorithms can be used to build guaranteed confidence regions for unknown model parameters under mild statistical assumptions. It has been shown that in many circumstances these rigorously built regions are comparable in size and shape to those that could be built by resorting to the asymptotic theory. The latter sets are, however, not guaranteed for finite samples and can sometimes lead to misleading results. The general principles behind finite-sample methods make them virtually applicable to a large variety of even nonlinear systems. While these principles are simple enough, a rigorous treatment of the attendant technical issues makes the corresponding theory complex and not easy to access. This is believed to be one of the reasons why these methods have not yet received widespread acceptance by the identification community and this letter is meant to provide an easy access point to finite-sample system identification by presenting the fundamental ideas underlying these methods in a simplified manner. We then review three (classes of) methods that have been proposed so far—1) Leave-out Sign-dominant Correlation Regions (LSCR); 2) Sign-Perturbed Sums (SPS); 3) Perturbed Dataset Methods (PDMs). By identifying some difficulties inherent in these methods, we also propose in this letter a new sign-perturbation method based on correlation which overcome some of these difficulties.