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Analysis of state space system identification methods based on instrumental variables and subspace fitting
KTH, Superseded Departments, Signals, Sensors and Systems.ORCID iD: 0000-0002-1927-1690
KTH, Superseded Departments, Signals, Sensors and Systems. (Signalbehandling)ORCID iD: 0000-0003-2298-6774
1997 (English)In: Automatica, ISSN 0005-1098, Vol. 33, no 9, 1603-1616 p.Article in journal (Refereed) Published
Abstract [en]

Subspace-based state-space system identification (4SID) methods have recently been proposed as an alternative to more traditional techniques for multivariable system identification. The advantages are that the user has simple and few design variables, and that the methods have robust numerical properties and relatively low computational complexities. Though subspace techniques have been demonstrated to perform well in a number of cases, the performance of these methods is neither fully understood nor analyzed. Our principal objective is to undertake a statistical investigation of subspace-based system identification techniques. The studied methods consist of two steps. The subspace spanned by the extended observability matrix is first estimated. The asymptotic properties of this subspace estimate are derived herein. In the second step, the structure of the extended observability matrix is used to find a system model estimate. Two possible methods are considered. The simplest one only uses a certain shift-invariance property, while in the other method a parametric representation of the null-space of the observability matrix is exploited. Explicit expressions for the asymptotic estimation error variances of the corresponding pole estimates are given.

Place, publisher, year, edition, pages
1997. Vol. 33, no 9, 1603-1616 p.
Keyword [en]
Instrumental variable methods, Multivariable systems, Parameter estimation, Statistical analysis, Subspace methods, System identification, Asymptotic stability, Matrix algebra, Multivariable control systems, Observability, State space methods, Statistical methods, Subspace based state space identification methods
National Category
Control Engineering
URN: urn:nbn:se:kth:diva-55416DOI: 10.1016/S0005-1098(97)00097-6ISI: A1997YG10800001OAI: diva2:471614
QC 20120104 NR 20140805Available from: 2012-01-02 Created: 2012-01-02 Last updated: 2013-09-05Bibliographically approved

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Wahlberg, BoOttersten, Björn
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