A Bias-Reduced Nonlinear WLS Method for TDOA/FDOA-Based Source Localization

Gang Wang, Shu Cai, Youming Li, Nirwan Ansari

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


We address the source localization problem by using both time-difference-of-arrival (TDOA) and frequency-difference-of-arrival (FDOA) measurements. We solve this problem in two steps, and in each step, we formulate a nonlinear weighted least squares (WLS) problem followed by a bias reduction scheme. In the first step, we formulate a nonlinear WLS problem using TDOA measurements only and derive the bias of the WLS solution, which is then used to develop an unbiased WLS solution by subtracting the bias from the WLS solution. In the second step, we formulate another nonlinear WLS problem by combining the results in the first step and the FDOA measurements. To avoid the potential risk of local convergence, this WLS problem is reduced to an approximate WLS problem, for which the globally optimal solution can be obtained. The bias of the WLS solution is also derived and then subtracted from the WLS solution to reduce the bias. Simulation results show that the bias of the proposed method is reduced and that the Cramer-Rao lower bound accuracy is also achieved.

Original languageEnglish (US)
Pages (from-to)8603-8615
Number of pages13
JournalIEEE Transactions on Vehicular Technology
Issue number10
StatePublished - Oct 2016

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Electrical and Electronic Engineering
  • Computer Networks and Communications
  • Automotive Engineering


  • Bias analysis
  • frequency difference of arrival (FDOA)
  • localization
  • nonlinear weighted least squares (WLS)
  • time difference of arrival (TDOA)


Dive into the research topics of 'A Bias-Reduced Nonlinear WLS Method for TDOA/FDOA-Based Source Localization'. Together they form a unique fingerprint.

Cite this