Covariance analysis in SISO linear systems identification. (March 2017)

• Record Type: Journal Article
• Authors: Mårtensson, Jonas; Everitt, Niklas; Hjalmarsson, Håkan
• Is Part Of: Automatica. Volume 77(2017)
• Page Start: 82
• Page End: 92
• Publication Date: 2017-03
• Subjects: System identification -- Asymptotic variance -- Linear SISO models; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2016.11.025
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: In this paper, we analyze the asymptotic covariance of models of causal single-input single-output linear time invariant systems. Expressions for the asymptotic (co)variance of system properties estimated using the prediction error method are derived. These expressions delineate the impacts of model structure, model order, true system dynamics, and experimental conditions. A connection to results on frequency function estimation is established. Also, simple model structure independent upper bounds are derived. Explicit variance expressions and bounds are provided for common system properties such as impulse response coefficients and non-minimum phase zeros. As an illustration of the insights the expressions provide, they are used to derive conditions on the input spectrum which make the asymptotic variance of non-minimum phase zero estimates independent of the model order and model structure.