An Efficient Constrained Weighted Least Squares Method With Bias Reduction for TDOA-Based Localization

Kun-Der Lin, Bor-Shing Lin, Geng-An Lin, Bor-Shyh Lin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


This paper addresses the source location problem by using time-difference-of-arrival (TDOA) measurements. The two-stage weighted least squares (TWLS) algorithm has been widely used in the TDOA location. However, the estimation accuracy of the source location is poor and the bias is significant when the measurement noise is large. Owing to the nonlinear nature of the system model, we reformulate the localization problem as a constrained weighted least squares problem and derive the theoretical bias of the source location estimate from the maximum-likelihood (ML) estimation. To reduce the location bias and improve location accuracy, a novel bias-reduced method is developed based on an iterative constrained weighted least squares algorithm. The new method imposes a set of linear equality constraints instead of the quadratic constraints to suppress the bias. Numerical simulations demonstrate the significant performance improvement of the proposed method over the traditional methods. The bias is reduced significantly and the Cramer-Rao lower bound accuracy can also be achieved.

Original languageEnglish
Pages (from-to)10167-10173
Number of pages7
JournalIEEE Sensors Journal
Issue number8
StatePublished - 15 Apr 2021


  • Sensors
  • Noise measurement
  • Position measurement
  • Location awareness
  • Maximum likelihood estimation
  • Covariance matrices
  • Closed-form solutions
  • TDOA
  • Bias reduction
  • weighted least squares
  • maximum-likelihood estimation


Dive into the research topics of 'An Efficient Constrained Weighted Least Squares Method With Bias Reduction for TDOA-Based Localization'. Together they form a unique fingerprint.

Cite this