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Covariance interpolation and geometry of power spectral densities
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2015 (English)In: 2009 European Control Conference, ECC 2009, 2015, 4505-4510 p.Conference paper (Refereed)
Abstract [en]

When methods of moments are used for identification of power spectral densities, a model is matched to estimated second order statistics such as, e.g., covariance estimates. There is an infinite family of power spectra consistent with such an estimate and in applications, such as identification, we want to single out the most representative spectrum. Here, we choose a prior spectral density to represent a priori information, and the spectrum closest to it in a given quasi-distance is determined. Depending on the selected quasi-distance, the geometry of the space of power spectral densities varies, and the structure of the minimizing spectral density changes with it. Recently, the Kullback-Leibler divergence, the Itakura-Saito divergence and Hellinger distances has been shown to determine power spectral densities of rational form and with tractable properties. Here, starting instead with the structure of the power spectral density, different (quasi-)distances and geometries for power spectral densities are derived.

Place, publisher, year, edition, pages
2015. 4505-4510 p.
Keyword [en]
Geometry, Method of moments, Power spectral density, Hellinger distance, Itakura-Saito divergences, Kullback Leibler divergence, Methods of moments, Power-spectra, Priori information, Second order statistics, Spectral density
National Category
URN: urn:nbn:se:kth:diva-167391ScopusID: 2-s2.0-84955201844ISBN: 9783952417393OAI: diva2:814487
2009 10th European Control Conference, ECC 2009, 23 August 2009 through 26 August 2009

QC 20150527

Available from: 2015-05-27 Created: 2015-05-22 Last updated: 2016-06-14Bibliographically approved

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Enqvist, Per
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