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The fundamental role of general orthonormal bases in system identification
University of Newcastle.
KTH, Superseded Departments, Signals, Sensors and Systems. (Reglerteknik, Automatic Control)ORCID iD: 0000-0002-9368-3079
Linköping University.
1999 (English)In: IEEE Transactions on Automatic Control, ISSN 00189286 (ISSN), Vol. 44, no 7, 1384-1406 p.Article in journal (Refereed) Published
Abstract [en]

The purpose of this paper is threefold. Firstly, it is to establish that contrary to what might be expected, the accuracy of well-known and frequently used asymptotic variance results can depend on choices of fixed poles or zeros in the model structure. Secondly, it is to derive new variance expressions that can provide greatly improved accuracy while also making explicit the influence of any fixed poles or zeros. This is achieved by employing certain new results on generalized Fourier series and the asymptotic properties of Toeplitz-like matrices in such a way that the new variance expressions presented here encompass pre-existing ones as special cases. Via this latter analysis a new perspective emerges on recent work pertaining to the use of orthonormal basis structures in system identification. Namely, that orthonormal bases are much more than an implementational option offering improved numerical properties. In fact, they are an intrinsic part of estimation since, as shown here, orthonormal bases quantify the asymptotic variability of the estimates whether or not they are actually employed in calculating them.

Place, publisher, year, edition, pages
1999. Vol. 44, no 7, 1384-1406 p.
Keyword [en]
Parameter estimation, System identification, Asymptotic stability, Mathematical models, Matrix algebra, Poles and zeros, General orthonormal bases
National Category
Control Engineering
Research subject
URN: urn:nbn:se:kth:diva-60576DOI: 10.1109/9.774110OAI: diva2:479495
NR 20140805Available from: 2012-01-17 Created: 2012-01-13 Last updated: 2012-01-17Bibliographically approved

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Hjalmarsson, Håkan
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