Exact and approximate solutions of source localization problems

Amir Beck, Petre Stoica, Jian Li

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)1770-1778
Number of pages9
JournalIEEE Transactions on Signal Processing
Issue number5
StatePublished - 2008
Externally publishedYes


  • 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


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