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Article: A Lagrangian dual approach to the single-source localization problem
Title | A Lagrangian dual approach to the single-source localization problem |
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Authors | |
Keywords | low-rank approximation orthogonal projection Euclidean distance matrix Lagrangian duality |
Issue Date | 2013 |
Citation | IEEE Transactions on Signal Processing, 2013, v. 61, n. 15, p. 3815-3826 How to Cite? |
Abstract | The single-source localization problem (SSLP), which is nonconvex by its nature, appears in several important multidisciplinary fields such as signal processing and the global positioning system. In this paper, we cast SSLP as a Euclidean distance embedding problem and study a Lagrangian dual approach. It is proved that the Lagrangian dual problem must have an optimal solution under the generalized Slater condition. We provide a sufficient condition for the zero-duality gap and establish the equivalence between the Lagrangian dual approach and the existing Generalized Trust-Region Subproblem (GTRS) approach studied by Beck ['Exact and Approximate Solutions of Source Localization Problems,' IEEE Trans. Signal Process., vol. 56, pp. 1770-1778, 2008]. We also reveal new implications of the assumptions made by the GTRS approach. Moreover, the Lagrangian dual approach has a straightforward extension to the multiple-source localization problem. Numerical simulations demonstrate that the Lagrangian dual approach can produce localization of similar quality as the GTRS and can significantly outperform the well-known semidefinite programming solver SNLSDP for the multiple source localization problem on the tested cases. © 1991-2012 IEEE. |
Persistent Identifier | http://hdl.handle.net/10722/250869 |
ISSN | 2023 Impact Factor: 4.6 2023 SCImago Journal Rankings: 2.520 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Qi, Hou Duo | - |
dc.contributor.author | Xiu, Naihua | - |
dc.contributor.author | Yuan, Xiaoming | - |
dc.date.accessioned | 2018-02-01T01:53:56Z | - |
dc.date.available | 2018-02-01T01:53:56Z | - |
dc.date.issued | 2013 | - |
dc.identifier.citation | IEEE Transactions on Signal Processing, 2013, v. 61, n. 15, p. 3815-3826 | - |
dc.identifier.issn | 1053-587X | - |
dc.identifier.uri | http://hdl.handle.net/10722/250869 | - |
dc.description.abstract | The single-source localization problem (SSLP), which is nonconvex by its nature, appears in several important multidisciplinary fields such as signal processing and the global positioning system. In this paper, we cast SSLP as a Euclidean distance embedding problem and study a Lagrangian dual approach. It is proved that the Lagrangian dual problem must have an optimal solution under the generalized Slater condition. We provide a sufficient condition for the zero-duality gap and establish the equivalence between the Lagrangian dual approach and the existing Generalized Trust-Region Subproblem (GTRS) approach studied by Beck ['Exact and Approximate Solutions of Source Localization Problems,' IEEE Trans. Signal Process., vol. 56, pp. 1770-1778, 2008]. We also reveal new implications of the assumptions made by the GTRS approach. Moreover, the Lagrangian dual approach has a straightforward extension to the multiple-source localization problem. Numerical simulations demonstrate that the Lagrangian dual approach can produce localization of similar quality as the GTRS and can significantly outperform the well-known semidefinite programming solver SNLSDP for the multiple source localization problem on the tested cases. © 1991-2012 IEEE. | - |
dc.language | eng | - |
dc.relation.ispartof | IEEE Transactions on Signal Processing | - |
dc.subject | low-rank approximation | - |
dc.subject | orthogonal projection | - |
dc.subject | Euclidean distance matrix | - |
dc.subject | Lagrangian duality | - |
dc.title | A Lagrangian dual approach to the single-source localization problem | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1109/TSP.2013.2264814 | - |
dc.identifier.scopus | eid_2-s2.0-84880528983 | - |
dc.identifier.volume | 61 | - |
dc.identifier.issue | 15 | - |
dc.identifier.spage | 3815 | - |
dc.identifier.epage | 3826 | - |
dc.identifier.isi | WOS:000321669200009 | - |
dc.identifier.issnl | 1053-587X | - |