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Moment-based dirac mixture approximation of circular densities
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0002-2681-8383
2014 (English)In: IFAC Proceedings Volumes (IFAC-PapersOnline), 2014, 5040-5048 p.Conference paper (Refereed)
Abstract [en]

Given a circular probability density function, called the true probability density function, the goal is to find a Dirac mixture approximation based on some circular moments of the true density. When keeping the locations of the Dirac points fixed, but almost arbitrarily located, we are applying recent results on the circulant rational covariance extension problem to the problem of calculating the weights. For the case of simultaneously calculating optimal locations, additional constraints have to be deduced from the given density. For that purpose, a distance measure for the deviation of the Dirac mixture approximation from the true density is derived, which then is minimized while considering the moment conditions as constraints. The method is based on progressive numerical minimization, converges quickly and gives well-distributed Dirac mixtures that fulfill the constraints, i.e., have the desired circular moments.

Place, publisher, year, edition, pages
2014. 5040-5048 p.
Keyword [en]
Circular densities, Dirac mixture approximation, Moment problem
National Category
Control Engineering
URN: urn:nbn:se:kth:diva-175343ScopusID: 2-s2.0-84929773553ISBN: 9783902823625OAI: diva2:860356
19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014, 24 August 2014 through 29 August 2014

QC 20151012

Available from: 2015-10-12 Created: 2015-10-12 Last updated: 2015-10-12Bibliographically approved

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