Using Optimal Mass Transport for Tracking and Interpolation of Toeplitz Covariance Matrices

Filip Elvander, Andreas Jakobsson, Johan Karlsson

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussaConference article in proceedingsScientificvertaisarvioitu

Abstrakti

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 ex-trapolants 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.
AlkuperäiskieliEnglanti
Otsikko2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
KustantajaIEEE
Sivut4469-4473
Sivumäärä5
ISBN (elektroninen)978-1-5386-4658-8
ISBN (painettu)978-1-5386-4659-5
DOI - pysyväislinkit
TilaJulkaistu - 20 huhtik. 2018
OKM-julkaisutyyppiA4 Artikkeli konferenssijulkaisussa
TapahtumaIEEE International Conference on Acoustics, Speech, and Signal Processing - Calgary, Kanada
Kesto: 15 huhtik. 201820 huhtik. 2018
https://2018.ieeeicassp.org/

Julkaisusarja

NimiProceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing
ISSN (painettu)1520-6149
ISSN (elektroninen)2379-190X

Conference

ConferenceIEEE International Conference on Acoustics, Speech, and Signal Processing
LyhennettäICASSP
Maa/AlueKanada
KaupunkiCalgary
Ajanjakso15/04/201820/04/2018
www-osoite

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