A Geometric Approach to Variance Analysis in System Identification: Theory and Nonlinear Systems
2007 (English)In: PROCEEDINGS OF THE 46TH IEEE CONFERENCE ON DECISION AND CONTRO, 2007, Vol. FrA17.2, 5092-5097 p.Conference paper (Refereed)
This paper addresses the problem of quantifying the model error ("variance-error") in estimates of dynamic systems. It is shown that, under very general conditions, the asymptotic (in data length) covariance of an estimated system property (represented by a smooth function of estimated system parameters) can be interpreted in terms of an orthogonal projection of a certain function gamma, associated with the property of interest, onto a subspace determined by the model structure and experimental conditions. An explicit method to construct a suitable gamma, in such a way that the individual impacts of model structure, model order and experimental conditions become visible, is presented. The technique is used to derive asymptotic variance expressions for a Hammerstein model and a nonlinear regression problem.
Place, publisher, year, edition, pages
2007. Vol. FrA17.2, 5092-5097 p.
, IEEE conference on decision and control - proceedings, ISSN 0191-2216
covariance analysis, covariance matrices, geometry, identification, nonlinear systems, regression analysis, Hammerstein model, asymptotic covariance matrix, dynamic system, geometric approach, nonlinear regression problem, nonlinear system, system identification, variance analysis, Accuracy of identification, Asymptotic variance expressions
Research subject SRA - ICT
IdentifiersURN: urn:nbn:se:kth:diva-7540DOI: 10.1109/CDC.2007.4434584ISI: 000255181701278ScopusID: 2-s2.0-39549096274ISBN: 978-1-4244-1497-0OAI: oai:DiVA.org:kth-7540DiVA: diva2:12596
46th IEEE Conference on Decision and Control New Orleans, LA, DEC 12-14, 2007
FunderSwedish Research Council, 621-2007-6271
QC 20100810.2007-10-152007-10-152012-01-19Bibliographically approved