Non-parametric frequency function estimation using transient impulse response modelling
2012 (English)In: 16th IFAC Symposium on System Identification, IFAC , 2012, 43-48 p.Conference paper (Refereed)
Recently, Hägg, Hjalmarsson and Wahlberg proposed a novel non-parametric method that directly estimates the frequency response at N equidistant frequencies when N measurements are available. The specific feature of the method is that together with these estimates, the transient, or, equivalently, the leakage, is explicitly estimated. The estimates are obtained by solving a least-squares problem. The method involves three design variables, the number of estimated transient terms, a number of auxiliary impulse response coefficients (that also are estimated), and the size of a frequency window. At present there is no analysis of how these design variables affect the properties of the method, which we will call TRIMM (TRansient Impulse response Modeling Method). In this contribution we provide bias and variance analysis for two extreme cases of the window size. We show that at one extreme value, the method coincides with the Empirical Transfer Function Estimate, and at the other extreme it is close to directly estimating a FIR model. This indicates that TRIMM provides an intermediate between non-parametric and parametric estimation. The results allows us to quantify bias and variance errors at the two extreme cases under study, and gives insight into how to choose the design variables in a systematic way.
Place, publisher, year, edition, pages
IFAC , 2012. 43-48 p.
, IFAC Proceedings Volumes (IFAC-PapersOnline), ISSN 1474-6670 ; 16
Analysis of variance, Frequency response methods, Parameter identification, System identification
Research subject SRA - ICT
IdentifiersURN: urn:nbn:se:kth:diva-74321DOI: 10.3182/20120711-3-BE-2027.00327ScopusID: 2-s2.0-84867073321ISBN: 978-390282306-9OAI: oai:DiVA.org:kth-74321DiVA: diva2:489372
Universite Libre de Bruxelles;Bruxelles; 11 July 2012 through 13 July 2012
FunderICT - The Next Generation
QC 201211222012-02-022012-02-022013-04-15Bibliographically approved