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Minimal Itakura-Saito distance and Covariance interpolation
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0001-5158-9255
2008 (English)In: 47TH IEEE CONFERENCE ON DECISION AND CONTROL, 2008 (CDC 2008), 2008, 137-142 p.Conference paper (Refereed)
Abstract [en]

Identification of power spectral densities rely on measured second order statistics such as, e.g. covariance estimates. In the family of power spectra consistent with such an estimate a representative spectra is singled out; examples of such choices are the Maximum entropy spectrum and the Correlogram. Here, we choose a prior spectral density to represent a priori information, and the spectrum closest to the prior in the Itakura-Saito distance is selected. It is known that this can be seen as the limit case when the cross-entropy principle is applied to a gaussian process. This work provides a quantitative measure of how close a finite covariance sequence is to a spectral density in the Itakura-Saito distance. It is given by a convex optimization problem and by considering its dual the structure of the optimal spectrum is obtained. Furthermore, it is shown that strong duality holds and that a covariance matching coercive spectral density always exists. The methods presented here provides tools for discrimination between power spectrum, identification of power spectrum, and for incorporating given data in this process.

Place, publisher, year, edition, pages
2008. 137-142 p.
, IEEE Conference on Decision and Control, ISSN 0191-2216
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-121716ISI: 000307311600023ScopusID: 2-s2.0-62949138645ISBN: 978-1-4244-3124-3OAI: diva2:619669
47th IEEE Conference on Decision and Control, DEC 09-11, 2008, Cancun, MEXICO

QC 20130506

Available from: 2013-05-06 Created: 2013-05-03 Last updated: 2013-05-06Bibliographically approved

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Enqvist, PerKarlsson, Johan
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