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Finite model order accuracy in Hammerstein model estimation
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.ORCID iD: 0000-0002-3672-5316
2012 (English)In: Automatica, ISSN 0005-1098, Vol. 48, no 10, 2640-2646 p.Article in journal (Refereed) Published
Abstract [en]

Hammerstein models is one of the most commonly used model classes used for identifying nonlinear systems. A static input nonlinearity followed by a linear dynamical part is an adequate way to model many real-life systems. This paper investigates the asymptotic (in terms of sample size) variance of Hammerstein model estimates. The work extends earlier results by Ninness and Gibson (2002) in the following ways. Not only frequency function estimation but estimation of general quantities is considered. The expressions are not restricted to be valid asymptotically in the model order. In addition, the results cover model structures having noise models and allow for data generated under feedback. The increase in variance due to the estimation of the input nonlinearity is characterized. In particular, under open loop operation, white additive noise and the assumption of a separable process, it is shown that the variance increase is exactly a term that was observed in Ninness and Gibson (2002) to result in good agreement with simulations. This term vanishes in the formal asymptotic in model order analysis in Ninness and Gibson (2002).

Place, publisher, year, edition, pages
Elsevier, 2012. Vol. 48, no 10, 2640-2646 p.
Keyword [en]
System identification, Prediction error identification, Hammerstein models, Asymptotic covariance
National Category
Control Engineering
URN: urn:nbn:se:kth:diva-102847DOI: 10.1016/j.automatica.2012.06.067ISI: 000309251000029ScopusID: 2-s2.0-84865460903OAI: diva2:557061
Swedish Research Council, 621-2007-6271 621-2009-4017ICT - The Next Generation

QC 20120927

Available from: 2012-09-27 Created: 2012-09-26 Last updated: 2013-04-11Bibliographically approved

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Hjalmarsson, HåkanMårtensson, Jonas
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