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:
https://lup.lub.lu.se/record/41584623-5a04-4290-a7b6-383a027e498d
- author
- Elvander, Filip
LU
; Jakobsson, Andreas
LU
and Karlsson, Johan
- organization
- publishing date
- 2018
- 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
- IEEE - 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
- 2022-04-25 17:11:15
@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}},
keywords = {{Covariance interpolation; Optimal mass transport; Toeplitz matrices; Spectral estimation}},
language = {{eng}},
pages = {{4469--4473}},
publisher = {{IEEE - 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}},
}