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A lagrangian dual approach to the single source localization problem

A lagrangian dual approach to the single source localization problem
A lagrangian dual approach to the single source localization problem
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 et al. [“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.
euclidean distance matrix, lagrangian duality, orthogonal projection, low-rank approximation
1053-587X
3815-3826
Qi, Hou-Duo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Xiu, Naihua
8e84e128-101b-4b57-aa47-e6002470ae9d
Yuan, Xiaoming
978cd495-5842-4d95-a1f9-93e19d8c54db
Qi, Hou-Duo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Xiu, Naihua
8e84e128-101b-4b57-aa47-e6002470ae9d
Yuan, Xiaoming
978cd495-5842-4d95-a1f9-93e19d8c54db

Qi, Hou-Duo, Xiu, Naihua and Yuan, Xiaoming (2013) A lagrangian dual approach to the single source localization problem. IEEE Transactions on Signal Processing, 61 (5), 3815-3826. (doi:10.1109/TSP.2013.2264814).

Record type: Article

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 et al. [“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.

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e-pub ahead of print date: 23 May 2013
Published date: 1 August 2013
Keywords: euclidean distance matrix, lagrangian duality, orthogonal projection, low-rank approximation
Organisations: Operational Research

Identifiers

Local EPrints ID: 358009
URI: http://eprints.soton.ac.uk/id/eprint/358009
ISSN: 1053-587X
PURE UUID: 1bcc7389-57f8-4d4f-95a9-29a94eaf26a1
ORCID for Hou-Duo Qi: ORCID iD orcid.org/0000-0003-3481-4814

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Date deposited: 08 Oct 2013 12:39
Last modified: 09 Jan 2022 03:17

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Contributors

Author: Hou-Duo Qi ORCID iD
Author: Naihua Xiu
Author: Xiaoming Yuan

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