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USING OPTIMAL MASS TRANSPORT FOR TRACKING AND INTERPOLATION OF TOEPLITZ COVARIANCE MATRICES
Lund Univ, Div Math Stat, Lund, Sweden..
Lund Univ, Div Math Stat, Lund, Sweden..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0001-5158-9255
2018 (English)In: 2018 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), IEEE , 2018, p. 4469-4473Conference paper, Published paper (Refereed)
Abstract [en]

In this work, we propose a novel method for interpolation and extrapolation of Toeplitz structured covariance matrices. By considering a spectral representation of Toeplitz matrices, we use an optimal mass transport problem in the spectral domain in order to define a notion of distance between such matrices. The obtained optimal transport plan naturally induces a way of interpolating, as well as extrapolating, Toeplitz matrices. The constructed covariance matrix interpolants and extrapolants preserve the Toeplitz structure, as well as the positive semi-definiteness and the zeroth covariance of the original matrices. We demonstrate the proposed method's ability to model locally linear shifts of spectral power for slowly varying stochastic processes, illustrating the achievable performance using a simple tracking problem.

Place, publisher, year, edition, pages
IEEE , 2018. p. 4469-4473
Keywords [en]
Covariance interpolation, Optimal mass transport, Toeplitz matrices, Spectral estimation
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-237153DOI: 10.1109/ICASSP.2018.8462284ISI: 000446384604127Scopus ID: 2-s2.0-85054273067OAI: oai:DiVA.org:kth-237153DiVA, id: diva2:1258545
Conference
2018 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP)
Funder
Swedish Research Council
Note

QC 20181025

Available from: 2018-10-25 Created: 2018-10-25 Last updated: 2019-08-20Bibliographically approved

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Karlsson, Johan

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CiteExportLink to record
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Citation style
  • apa
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