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Variance Properties of a Two-Step ARX Estimation Procedure
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2001 (English)Report (Other academic)
Abstract [en]

In this contribution we discuss some variance properties of a two-step ARX estimation scheme. An expression for the covariance of the final low order model is calculated and it is discussed how one should minimize this covariance. The implication of the results isthat identification of the dynamics of a system could very easily be performed with standard linear least squares (two times), even if the measurement noise is heavily colored. We also show a numerical example, where this two-step estimation scheme gives a variance which is close (but not equal) to the the Cramér-Rao lower bound. Moreover, we show that the point estimate of the covariance is close to the one obtained through Monte Carlo simulations.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2001. , 8 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2393
Keyword [en]
Identification methods, Estimation
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-55804ISRN: Variance Properties of a Two-Step ARX Estimation ProcedureOAI: oai:DiVA.org:liu-55804DiVA: diva2:316527
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-09-08Bibliographically approved
In thesis
1. Variance Expressions and Model Reduction in System Identification
Open this publication in new window or tab >>Variance Expressions and Model Reduction in System Identification
2002 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Although system identification is now a mature research field, some problems remain unsolved. Examples of unsolved or partly unsolved problems are; accuracy of subspace identification algorithms, identification via model reduction, identification for control, and identification of non-linear systems. Some problems that fall into these categories are studied in this thesis.

This thesis discusses variance expressions in system identification. In particular, variance expressions for reduced models are analyzed.

The topic of model reduction via system identification has received little attention during the years. To understand how the variance of a high order model affects the reduced model, a general expression for the variance of the low order model as a function of the reduction method used is derived. This allows the analysis of all model reduction methods that can be written as a minimization criterion, where the function to be minimized is twice continuously differentiable. Many methods can be studied using this approach. However, the popular method of model reduction by balanced truncation of states does not immediately fit into this framework.

Many unsolved problems in system identification may be studied with the use of bootstrap methods. This statistical tool, used to assess accuracy in estimation problems, may be adopted to a series of problems in system identification and signal processing. The thesis presents how bootstrap can be adopted in the prediction error framework. In addition, we demonstrate how bootstrap can be applied to problems of constructing condence regions with a simultaneous confidence degree and calculating the variance of undermodeled models.

The thesis briefly discusses how set membership identification and prediction error identification can be combined into a more robust estimate. Finally, insights into how model validation can be performed in a more user informative way are also given.

Place, publisher, year, edition, pages
Linköping: Linköping University, 2002. 192 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 730
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-98162 (URN)91-7373-253-2 (ISBN)
Public defence
2002-02-22, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Supervisors
Available from: 2013-10-09 Created: 2013-09-30 Last updated: 2013-10-09Bibliographically approved

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Ljung, lennart

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