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Least-squares estimation of a class of frequency functions: A finite sample variance expression
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0002-9368-3079
University of Newcastle.
2006 (English)In: Automatica, ISSN 0005-1098, Vol. 42, no 4, 589-600 p.Article in journal (Refereed) Published
Abstract [en]

A new expression for the variance of scalar frequency functions estimated using the least-squares method is presented. The expression is valid for finite sample size and for a class of model structures, which includes finite impulse response, Laguerre and Kautz models, when the number of estimated parameters coincides with the number of excitation frequencies of the input. The expression gives direct insight into how excitation frequencies and amplitudes affect the accuracy of frequency function estimates. With the help of this expression, a severe sensitivity of the accuracy with respect to the excitation frequencies is exposed. The relevance of the expression when more excitation frequencies are used is also discussed.

Place, publisher, year, edition, pages
2006. Vol. 42, no 4, 589-600 p.
Keyword [en]
frequency function, model variance, FIR models, Laguerre models, Kautz models, periodic signals, system-identification, confidence-regions, orthonormal bases, experiment design, input-design, models, error
National Category
Control Engineering
Research subject
URN: urn:nbn:se:kth:diva-15554DOI: 10.1016/j.automatica.2005.12.021ISI: 000236340300007ScopusID: 2-s2.0-33144467611OAI: diva2:333595
Swedish Research Council, 621-2001-2147
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2012-01-19Bibliographically approved

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Hjalmarsson, Håkan
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