Compressive System Identification in the Linear Time-Invariant framework

Roland Toth, Borhan M. Sanandaji, Kameshwar Poolla, Tyrone L. Vincent

Research output: Chapter in Book/Report/Conference proceedingConference contribution

32 Scopus citations

Abstract

Selection of an efficient model parametrization (model order, delay, etc.) has crucial importance in parametric system identification. It navigates a trade-off between representation capabilities of the model (structural bias) and effects of over-parametrization (variance increase of the estimates). There exists many approaches to this widely studied problem in terms of statistical regularization methods and information criteria. In this paper, an alternative ℓ 1 regularization scheme is proposed for estimation of sparse linear-regression models based on recent results in compressive sensing. It is shown that the proposed scheme provides consistent estimation of sparse models in terms of the so-called oracle property, it is computationally attractive for large-scale over-parameterized models and it is applicable in case of small data sets, i.e., underdetermined estimation problems. The performance of the approach w.r.t. other regularization schemes is demonstrated in an extensive Monte Carlo study. © 2011 IEEE.
Original languageEnglish (US)
Title of host publicationIEEE Conference on Decision and Control and European Control Conference
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages783-790
Number of pages8
ISBN (Print)9781612848013
DOIs
StatePublished - Dec 2011
Externally publishedYes

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