Exact and approximate solutions of source localization problems

Amir Beck; Petre Stoica; Jian Li

doi:10.1109/TSP.2007.909342

Exact and approximate solutions of source localization problems

Amir Beck, Petre Stoica, Jian Li

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1770-1778
Number of pages	9
Journal	IEEE Transactions on Signal Processing
Volume	56
Issue number	5
DOIs	https://doi.org/10.1109/TSP.2007.909342
State	Published - 2008
Externally published	Yes

Keywords

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

Access to Document

10.1109/TSP.2007.909342

Cite this

@article{8c10aff185134649872dd59ce1bc99cf,

title = "Exact and approximate solutions of source localization problems",

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 = "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",

author = "Amir Beck and Petre Stoica and Jian Li",

year = "2008",

doi = "10.1109/TSP.2007.909342",

language = "אנגלית",

volume = "56",

pages = "1770--1778",

journal = "IEEE Transactions on Signal Processing",

issn = "1053-587X",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "5",

}

TY - JOUR

T1 - Exact and approximate solutions of source localization problems

AU - Beck, Amir

AU - Stoica, Petre

AU - Li, Jian

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - Efficiently and globally optimal solution

KW - Generalized trust region subproblems (GTRS)

KW - Least squares

KW - Nonconvex

KW - Quadratic function minimization

KW - Range measurements

KW - Range-difference measurements

KW - Single quadratic constraint

KW - Source localization

KW - Squared range observations

UR - http://www.scopus.com/inward/record.url?scp=64349108140&partnerID=8YFLogxK

U2 - 10.1109/TSP.2007.909342

DO - 10.1109/TSP.2007.909342

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:64349108140

VL - 56

SP - 1770

EP - 1778

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 5

ER -

Exact and approximate solutions of source localization problems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this