Covariance analysis in SISO linear systems identification
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- 作者：Jonas Må ; rtensson <sup>jonas.martensson@ee.kth.sesup>Author Vitae ; Niklas Everitt <sup>neveritt@kth.sesup>Author Vitae ; Hå ; kan Hjalmarsson <sup>hakan.hjalmarsson@ee.kth.sesup>Author Vitae
- 关键词：System identification ; Asymptotic variance ; Linear SISO models
- 刊名：Automatica
- 出版年：2017
- 出版时间：March 2017
- 年：2017
- 卷：77
- 期：Complete
- 页码：82-92
- 全文大小：754 K
- 卷排序：77
文摘
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.