TDOA Matrices: Algebraic Properties and Their Application to Robust Denoising With Missing Data

Measuring the time delay of arrival (TDOA) between a set of sensors is the basic setup for many applications, such as localization or signal beamforming. This paper presents the set of TDOA matrices, which are built from noise-free TDOA measurements, not requiring knowledge of the sensor array geome...

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Detalles Bibliográficos
Autores: Velasco Cerpa, José Francisco, Pizarro Pérez, Daniel|||0000-0003-0622-4884, Macías Guarasa, Javier|||0000-0002-3303-3963, Asaei, Afsaneh
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/64566
Acceso en línea:http://hdl.handle.net/10017/64566
https://dx.doi.org/10.1109/TSP.2016.2593690
Access Level:acceso abierto
Palabra clave:TDOA estimation
TDOA denoising
Skewsymmetric matrices
Matrix completion
Missing data
Electrónica
Electronics
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spelling TDOA Matrices: Algebraic Properties and Their Application to Robust Denoising With Missing DataVelasco Cerpa, José FranciscoPizarro Pérez, Daniel|||0000-0003-0622-4884Macías Guarasa, Javier|||0000-0002-3303-3963Asaei, AfsanehTDOA estimationTDOA denoisingSkewsymmetric matricesMatrix completionMissing dataElectrónicaElectronicsMeasuring the time delay of arrival (TDOA) between a set of sensors is the basic setup for many applications, such as localization or signal beamforming. This paper presents the set of TDOA matrices, which are built from noise-free TDOA measurements, not requiring knowledge of the sensor array geometry. We prove that TDOA matrices are rank-two and have a special singular value decomposition decomposition that leads to a compact linear parametric representation. Properties of TDOA matrices are applied in this paper to perform denoising, by finding the TDOA matrix closest to the matrix composed with noisy measurements. This paper shows that this problem admits a closed-form solution for TDOA measurements contaminated with Gaussian noise that extends to the case of having missing data. This paper also proposes a novel robust denoising method resistant to outliers, missing data and inspired in recent advances in robust low-rank estimation. Experiments in synthetic and real datasets show significant improvements of the proposed denoising algorithms in TDOA-based localization, both in terms of TDOA accuracy estimation and localization error.Ministerio de Economía, Comercio y EmpresaUniversidad de Alcalá20162016-07-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10017/64566https://dx.doi.org/10.1109/TSP.2016.2593690reponame:e_Buah Biblioteca Digital Universidad de Alcaláinstname:Universidad de Alcalá (UAH)InglésengMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 Not available TIN2013-47630-C2-1-Ropen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ebuah.uah.es:10017/645662026-06-18T11:13:07Z
dc.title.none.fl_str_mv TDOA Matrices: Algebraic Properties and Their Application to Robust Denoising With Missing Data
title TDOA Matrices: Algebraic Properties and Their Application to Robust Denoising With Missing Data
spellingShingle TDOA Matrices: Algebraic Properties and Their Application to Robust Denoising With Missing Data
Velasco Cerpa, José Francisco
TDOA estimation
TDOA denoising
Skewsymmetric matrices
Matrix completion
Missing data
Electrónica
Electronics
title_short TDOA Matrices: Algebraic Properties and Their Application to Robust Denoising With Missing Data
title_full TDOA Matrices: Algebraic Properties and Their Application to Robust Denoising With Missing Data
title_fullStr TDOA Matrices: Algebraic Properties and Their Application to Robust Denoising With Missing Data
title_full_unstemmed TDOA Matrices: Algebraic Properties and Their Application to Robust Denoising With Missing Data
title_sort TDOA Matrices: Algebraic Properties and Their Application to Robust Denoising With Missing Data
dc.creator.none.fl_str_mv Velasco Cerpa, José Francisco
Pizarro Pérez, Daniel|||0000-0003-0622-4884
Macías Guarasa, Javier|||0000-0002-3303-3963
Asaei, Afsaneh
author Velasco Cerpa, José Francisco
author_facet Velasco Cerpa, José Francisco
Pizarro Pérez, Daniel|||0000-0003-0622-4884
Macías Guarasa, Javier|||0000-0002-3303-3963
Asaei, Afsaneh
author_role author
author2 Pizarro Pérez, Daniel|||0000-0003-0622-4884
Macías Guarasa, Javier|||0000-0002-3303-3963
Asaei, Afsaneh
author2_role author
author
author
dc.subject.none.fl_str_mv TDOA estimation
TDOA denoising
Skewsymmetric matrices
Matrix completion
Missing data
Electrónica
Electronics
topic TDOA estimation
TDOA denoising
Skewsymmetric matrices
Matrix completion
Missing data
Electrónica
Electronics
description Measuring the time delay of arrival (TDOA) between a set of sensors is the basic setup for many applications, such as localization or signal beamforming. This paper presents the set of TDOA matrices, which are built from noise-free TDOA measurements, not requiring knowledge of the sensor array geometry. We prove that TDOA matrices are rank-two and have a special singular value decomposition decomposition that leads to a compact linear parametric representation. Properties of TDOA matrices are applied in this paper to perform denoising, by finding the TDOA matrix closest to the matrix composed with noisy measurements. This paper shows that this problem admits a closed-form solution for TDOA measurements contaminated with Gaussian noise that extends to the case of having missing data. This paper also proposes a novel robust denoising method resistant to outliers, missing data and inspired in recent advances in robust low-rank estimation. Experiments in synthetic and real datasets show significant improvements of the proposed denoising algorithms in TDOA-based localization, both in terms of TDOA accuracy estimation and localization error.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-07-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10017/64566
https://dx.doi.org/10.1109/TSP.2016.2593690
url http://hdl.handle.net/10017/64566
https://dx.doi.org/10.1109/TSP.2016.2593690
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 Not available TIN2013-47630-C2-1-R
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:e_Buah Biblioteca Digital Universidad de Alcalá
instname:Universidad de Alcalá (UAH)
instname_str Universidad de Alcalá (UAH)
reponame_str e_Buah Biblioteca Digital Universidad de Alcalá
collection e_Buah Biblioteca Digital Universidad de Alcalá
repository.name.fl_str_mv
repository.mail.fl_str_mv
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