A new constrained weighted least squares algorithm for TDOA-based localization

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

  • Lanxin Lin
  • H. C. So
  • Frankie K.W. Chan
  • Y. T. Chan
  • K. C. Ho

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)2872-2878
Journal / PublicationSignal Processing
Volume93
Issue number11
Online published12 Apr 2013
Publication statusPublished - Nov 2013

Abstract

The linear least squares (LLS) technique is widely used in time-difference-of-arrival based positioning because of its computational efficiency. Two-step weighted least squares (2WLS) and constrained weighted least squares (CWLS) algorithms are two common LLS schemes where an additional variable is introduced to obtain linear equations. However, they both have the same measurement matrix that becomes ill-conditioned when the sensor geometry is a uniform circular array and the source is close to the array center. In this paper, a new CWLS estimator is proposed to circumvent this problem. The main strategy is to separate the source coordinates and the additional variable to different sides of the linear equations where the latter is first solved via a quadratic equation. In doing so, the matrix to be inverted has a smaller condition number than that of the conventional LLS approach. The performance of the proposed method is analyzed in the presence of zero-mean white Gaussian disturbances. Numerical examples are also included to evaluate its localization accuracy by comparing with the existing 2WLS and CWLS algorithms as well as the Cramér-Rao lower bound. © 2013 Elsevier B.V. All rights reserved.

Research Area(s)

  • Constrained optimization, Source localization, Time-difference-of-arrival, Weighted least squares

Citation Format(s)

A new constrained weighted least squares algorithm for TDOA-based localization. / Lin, Lanxin; So, H. C.; Chan, Frankie K.W.; Chan, Y. T.; Ho, K. C.

In: Signal Processing, Vol. 93, No. 11, 11.2013, p. 2872-2878.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review