Subspace averaging and order determination for source enumeration

In this paper, we address the problem of subspace averaging, with special emphasis placed on the question of estimating the dimension of the average. The results suggest that the enumeration of sources in a multi-sensor array, which is a problem of estimating the dimension of the array manifold, and...

ver descrição completa

Detalhes bibliográficos
Autores: Garg, Vaibhav|||0000-0002-6639-3324, Santamaría Caballero, Luis Ignacio|||0000-0003-0040-7436, Ramírez García, David, Scharf, Louis L.
Tipo de documento: artigo
Data de publicação:2019
País:España
Recursos:Universidad de Cantabria (UC)
Repositório:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglês
OAI Identifier:oai:repositorio.unican.es:10902/17953
Acesso em linha:http://hdl.handle.net/10902/17953
Access Level:Acceso aberto
Palavra-chave:Array processing
Dimension
Grassmann manifold
Order estimation
Source enumeration
Subspace averaging
id ES_9564393df2b2e9a1d38da2eb41767ca6
oai_identifier_str oai:repositorio.unican.es:10902/17953
network_acronym_str ES
network_name_str España
repository_id_str
spelling Subspace averaging and order determination for source enumerationGarg, Vaibhav|||0000-0002-6639-3324Santamaría Caballero, Luis Ignacio|||0000-0003-0040-7436Ramírez García, DavidScharf, Louis L.Array processingDimensionGrassmann manifoldOrder estimationSource enumerationSubspace averagingIn this paper, we address the problem of subspace averaging, with special emphasis placed on the question of estimating the dimension of the average. The results suggest that the enumeration of sources in a multi-sensor array, which is a problem of estimating the dimension of the array manifold, and as a consequence the number of radiating sources, may be cast as a problem of averaging subspaces. This point of view stands in contrast to conventional approaches, which cast the problem as one of identifiying covariance models in a factor model. We present a robust formulation of the proposed order fitting rule based on majorization-minimization algorithms. A key element of the proposed method is to construct a bootstrap procedure, based on a newly proposed discrete distribution on the manifold of projection matrices, for stochastically generating subspaces from a function of experimentally determined eigenvalues. In this way, the proposed subspace averaging (SA) technique determines the order based on the eigenvalues of an average projection matrix, rather than on the likelihood of a covariance model, penalized by functions of the model order. By means of simulation examples, we show that the proposed SA criterion is especially effective in high-dimensional scenarios with low sample support.The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Yuejie Chi. The work of V. Garg and I. Santamaria was supported in part by the Ministerio de Economía y Competitividad (MINECO) of Spain, and in part by the AEI/FEDER funds of the E.U., under Grants TEC2016-75067-C4-4-R (CARMEN), TEC2015-69648-REDC, and BES-2017-080542. The work of D. Ramírez was supported in part by the Ministerio de Ciencia, Innovación y Universidades under Grant TEC2017-92552-EXP (aMBITION), in part by the Ministerio de Ciencia, Innovación y Universidades, jointly with the European Commission (ERDF), under Grants TEC2015-69868-C2-1-R (ADVENTURE) and TEC2017-86921-C2-2-R (CAIMAN), and in part by The Comunidad de Madrid under Grant Y2018/TCS-4705 (PRACTICOCM). The work of L. L. Scharf was supported in part by the U.S. NSF under Contract CISE-1712788.Institute of Electrical and Electronics Engineers Inc.Universidad de Cantabria20192019-06-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttp://hdl.handle.net/10902/17953IEEE Transactions on Signal Processing, 2019, 67(11), 3028-3041reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/179532026-06-02T12:39:31Z
dc.title.none.fl_str_mv Subspace averaging and order determination for source enumeration
title Subspace averaging and order determination for source enumeration
spellingShingle Subspace averaging and order determination for source enumeration
Garg, Vaibhav|||0000-0002-6639-3324
Array processing
Dimension
Grassmann manifold
Order estimation
Source enumeration
Subspace averaging
title_short Subspace averaging and order determination for source enumeration
title_full Subspace averaging and order determination for source enumeration
title_fullStr Subspace averaging and order determination for source enumeration
title_full_unstemmed Subspace averaging and order determination for source enumeration
title_sort Subspace averaging and order determination for source enumeration
dc.creator.none.fl_str_mv Garg, Vaibhav|||0000-0002-6639-3324
Santamaría Caballero, Luis Ignacio|||0000-0003-0040-7436
Ramírez García, David
Scharf, Louis L.
author Garg, Vaibhav|||0000-0002-6639-3324
author_facet Garg, Vaibhav|||0000-0002-6639-3324
Santamaría Caballero, Luis Ignacio|||0000-0003-0040-7436
Ramírez García, David
Scharf, Louis L.
author_role author
author2 Santamaría Caballero, Luis Ignacio|||0000-0003-0040-7436
Ramírez García, David
Scharf, Louis L.
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Array processing
Dimension
Grassmann manifold
Order estimation
Source enumeration
Subspace averaging
topic Array processing
Dimension
Grassmann manifold
Order estimation
Source enumeration
Subspace averaging
description In this paper, we address the problem of subspace averaging, with special emphasis placed on the question of estimating the dimension of the average. The results suggest that the enumeration of sources in a multi-sensor array, which is a problem of estimating the dimension of the array manifold, and as a consequence the number of radiating sources, may be cast as a problem of averaging subspaces. This point of view stands in contrast to conventional approaches, which cast the problem as one of identifiying covariance models in a factor model. We present a robust formulation of the proposed order fitting rule based on majorization-minimization algorithms. A key element of the proposed method is to construct a bootstrap procedure, based on a newly proposed discrete distribution on the manifold of projection matrices, for stochastically generating subspaces from a function of experimentally determined eigenvalues. In this way, the proposed subspace averaging (SA) technique determines the order based on the eigenvalues of an average projection matrix, rather than on the likelihood of a covariance model, penalized by functions of the model order. By means of simulation examples, we show that the proposed SA criterion is especially effective in high-dimensional scenarios with low sample support.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-06-01
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/10902/17953
url http://hdl.handle.net/10902/17953
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
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
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers Inc.
publisher.none.fl_str_mv Institute of Electrical and Electronics Engineers Inc.
dc.source.none.fl_str_mv IEEE Transactions on Signal Processing, 2019, 67(11), 3028-3041
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869413818376912896
score 15,300719

Registros relacionados