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On the accuracy in errors-in-variables identification compared to prediction-error identification
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. (System Identification Group)ORCID iD: 0000-0002-9368-3079
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. (System Identification Group)ORCID iD: 0000-0002-3672-5316
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. (System Identification Group)ORCID iD: 0000-0003-0355-2663
Uppsala University.
2011 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, ISSN 0005-1098, Vol. 47, no 12, 2704-2712 p.Article in journal (Refereed) Published
Abstract [en]

Errors-in-variables estimation problems for single-inputsingle-output systems with Gaussian signals are considered in this contribution. It is shown that the Fisher information matrix is monotonically increasing as a function of the input noise variance when the noise spectrum at the input is known and the corresponding noise variance is estimated. Furthermore, it is shown that Whittle's formula for the Fisher information matrix can be represented as a Gramian and this is used to provide a geometric representation of the asymptotic covariance matrix for asymptotically efficient estimators. Finally, the asymptotic covariance of the parameter estimates for the system dynamics is compared for the two cases: (i) when the model includes white measurement noise on the input and the variance of the noise is estimated, and (ii) when the model includes only measurement noise on the output. In both cases, asymptotically efficient estimators are assumed. An explicit expression for the difference is derived when the underlying system is subject only to measurement noise on the output.

Place, publisher, year, edition, pages
2011. Vol. 47, no 12, 2704-2712 p.
Keyword [en]
Accuracy of identification, Asymptotic variance expressions, Error-in-variables identification, System identification, Asymptotic covariance matrix, Asymptotic variance, Asymptotically efficient, Errors in variables, Estimation problem, Explicit expressions, Gaussian signals, Geometric representation, Gramians, Input noise, Measurement Noise, Noise spectra, Noise variance, Parameter estimate, System Dynamics, Underlying systems, Asymptotic analysis, Covariance matrix, Errors, Estimation, Identification (control systems), Parameter estimation, Spurious signal noise, Fisher information matrix
National Category
Control Engineering
Research subject
SRA - ICT
Identifiers
URN: urn:nbn:se:kth:diva-60497DOI: 10.1016/j.automatica.2011.09.002ISI: 000298071000019Scopus ID: 2-s2.0-81155139625OAI: oai:DiVA.org:kth-60497DiVA: diva2:478569
Funder
Swedish Research Council, 621-2007-6364Swedish Research Council, 621-2007-6271Swedish Research Council, 621-2009-4017
Note

QC 20121019

Available from: 2012-01-16 Created: 2012-01-13 Last updated: 2017-12-08Bibliographically approved

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Hjalmarsson, HåkanMårtensson, JonasRojas, Cristian R.

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