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Open-loop asymptotically efficient model reduction with the Steiglitz–McBride method
KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
2018 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 89, 221-234 p.Article in journal (Refereed) Published
Abstract [en]

In system identification, it is often difficult to use a physical intuition when choosing a noise model structure. The importance of this choice is that, for the prediction error method (PEM) to provide asymptotically efficient estimates, the model orders must be chosen according to the true system. However, if only the plant estimates are of interest and the experiment is performed in open loop, the noise model can be over-parameterized without affecting the asymptotic properties of the plant. The limitation is that, as PEM suffers in general from non-convexity, estimating an unnecessarily large number of parameters will increase the risk of getting trapped in local minima. Here, we consider the following alternative approach. First, estimate a high-order ARX model with least squares, providing non-parametric estimates of the plant and noise model. Second, reduce the high-order model to obtain a parametric model of the plant only. We review existing methods to do this, pointing out limitations and connections between them. Then, we propose a method that connects favorable properties from the previously reviewed approaches. We show that the proposed method provides asymptotically efficient estimates of the plant with open-loop data. Finally, we perform a simulation study suggesting that the proposed method is competitive with state-of-the-art methods.

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 89, 221-234 p.
Keyword [en]
High order arx-modeling, Maximum likelihood, Steiglitz–McBride, System identification
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-220956DOI: 10.1016/j.automatica.2017.12.016Scopus ID: 2-s2.0-85039723128OAI: oai:DiVA.org:kth-220956DiVA: diva2:1172660
Funder
Swedish Research Council, 015-05285; 2016-06079
Note

QC 20180110

Available from: 2018-01-10 Created: 2018-01-10 Last updated: 2018-01-10Bibliographically approved

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Galrinho, Miguel

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