A fast solver for the circulant rational covariance extension problem
2015 (English)In: 2015 European Control Conference, ECC 2015, Institute of Electrical and Electronics Engineers (IEEE), 2015, 727-733 p.Conference paper (Refereed)Text
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.
Bounded degree, Cepstral coefficients, Fast solvers, Hankel systems, Newton algorithm, Periodic problems, Periodic process, Rational covariance extension problem, Control
IdentifiersURN: urn:nbn:se:kth:diva-186818DOI: 10.1109/ECC.2015.7330629ScopusID: 2-s2.0-84963853505ISBN: 9783952426937OAI: oai:DiVA.org:kth-186818DiVA: diva2:938601
European Control Conference, ECC 2015, 15 July 2015 through 17 July 2015
QC 201606172016-06-172016-05-132016-06-17Bibliographically approved