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The Fundamental Role of General Orthonormal Bases in System Identification
University of Newcastle, Australia.
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.
1999 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, 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]
Fourier series, Toeplitz matrices, Identification, Poles and zeros
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-95670DOI: 10.1109/9.774110OAI: oai:DiVA.org:liu-95670DiVA: diva2:637189
Available from: 2013-07-16 Created: 2013-07-16 Last updated: 2017-12-06

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Gustafsson, Fredrik

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