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A fast solver for the circulant rational covariance extension problem
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0002-9778-1426
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0001-5158-9255
2015 (English)In: 2015 European Control Conference, ECC 2015, Institute of Electrical and Electronics Engineers (IEEE), 2015, 727-733 p.Conference paper, Published paper (Refereed)
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Text
Abstract [en]

The rational covariance extension problem is to parametrize the family of rational spectra of bounded degree that matches a given set of covariances. This article treats a circulant version of this problem, where the underlying process is periodic and we seek a spectrum that also matches a set of given cepstral coefficients. The interest in the circulant problem stems partly from the fact that this problem is a natural approximation of the non-periodic problem, but is also a tool in itself for analysing periodic processes. We develop a fast Newton algorithm for computing the solution utilizing the structure of the Hessian. This is done by extending a current algorithm for Toeplitz-plus-Hankel systems to the block-Toeplitz-plus-block-Hankel case. We use this algorithm to reduce the computational complexity of the Newton search from O(n3) to O(n2), where n corresponds to the number of covariances and cepstral coefficients.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2015. 727-733 p.
Keyword [en]
Bounded degree, Cepstral coefficients, Fast solvers, Hankel systems, Newton algorithm, Periodic problems, Periodic process, Rational covariance extension problem, Control
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-186818DOI: 10.1109/ECC.2015.7330629Scopus ID: 2-s2.0-84963853505ISBN: 9783952426937 (print)OAI: oai:DiVA.org:kth-186818DiVA: diva2:938601
Conference
European Control Conference, ECC 2015, 15 July 2015 through 17 July 2015
Note

QC 20160617

Available from: 2016-06-17 Created: 2016-05-13 Last updated: 2016-06-17Bibliographically approved

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf