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

Elvander, Filip LU ; Jakobsson, Andreas LU and Karlsson, Johan (2018) IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 p.4469-4473
Abstract
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 abil- ity to model locally linear shifts of spectral power for slowly varying stochastic... (More)
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 abil- ity to model locally linear shifts of spectral power for slowly varying stochastic processes, illustrating the achievable performance using a simple tracking problem. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Covariance interpolation, Optimal mass transport, Toeplitz matrices, Spectral estimation
host publication
Acoustics, Speech and Signal Processing (ICASSP), 2018 IEEE International Conference on
pages
5 pages
publisher
Institute of Electrical and Electronics Engineers Inc.
conference name
IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018
conference location
Calgary, Canada
conference dates
2018-04-15 - 2018-04-20
external identifiers
  • scopus:85054273067
ISBN
978-1-5386-4658-8
DOI
10.1109/ICASSP.2018.8462284
language
English
LU publication?
yes
id
41584623-5a04-4290-a7b6-383a027e498d
date added to LUP
2018-09-12 14:02:57
date last changed
2020-01-22 07:13:01
@inproceedings{41584623-5a04-4290-a7b6-383a027e498d,
  abstract     = {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 abil- ity to model locally linear shifts of spectral power for slowly varying stochastic processes, illustrating the achievable performance using a simple tracking problem.},
  author       = {Elvander, Filip and Jakobsson, Andreas and Karlsson, Johan},
  booktitle    = {Acoustics, Speech and Signal Processing (ICASSP), 2018 IEEE International Conference on},
  isbn         = {978-1-5386-4658-8},
  language     = {eng},
  pages        = {4469--4473},
  publisher    = {Institute of Electrical and Electronics Engineers Inc.},
  title        = {Using Optimal Mass Transport for Tracking and Interpolation of Toeplitz Covariance Matrices},
  url          = {http://dx.doi.org/10.1109/ICASSP.2018.8462284},
  doi          = {10.1109/ICASSP.2018.8462284},
  year         = {2018},
}