Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

A Lagrangian dual approach to the single-sourse localization problem

Language

English

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.

Keywords

Euclidean distance matrix, Lagrangian duality, low-rank approximation, orthogonal projection

Publication Date

2013

Source Publication Title

IEEE Transactions on Signal Processing

Volume

61

Issue

15

Start Page

3815

End Page

3826

Publisher

Institute of Electrical and Electronics Engineers

DOI

10.1109/TSP.2013.2264814

Link to Publisher's Edition

http://dx.doi.org/10.1109/TSP.2013.2264814

ISSN (print)

1053587X

This document is currently not available here.

Share

COinS