Exact and Approximate Solutions of Source Localization Problems

Author

Beck, Amir ; Stoica, Petre ; Li, Jian

Volume

56

Issue

5

fYear

2008

fDate

5/1/2008 12:00:00 AM

Firstpage

1770

Lastpage

1778

Abstract

We consider least squares (LS) approaches for locating a radiating source from range measurements (which we call R-LS) or from range-difference measurements (RD-LS) collected using an array of passive sensors. We also consider LS approaches based on squared range observations (SR-LS) and based on squared range-difference measurements (SRD-LS). Despite the fact that the resulting optimization problems are nonconvex, we provide exact solution procedures for efficiently computing the SR-LS and SRD-LS estimates. Numerical simulations suggest that the exact SR-LS and SRD-LS estimates outperform existing approximations of the SR-LS and SRD-LS solutions as well as approximations of the R-LS and RD-LS solutions which are based on a semidefinite relaxation.

Keywords

approximation theory; array signal processing; least squares approximations; optimisation; sensor arrays; approximate solution; least squares approach; nonconvex problem; optimization problem; passive sensor array; radiating source localization problem; semidefinite relaxation; squared range-difference measurement; Efficiently and globally optimal solution; generalized trust region subproblems (GTRS); least squares; nonconvex; quadratic function minimization; range measurements; range-difference measurements; single quadratic constraint; source localization; squared range observations;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2007.909342

Filename

4472183