2nd International ICST Conference on Broadband Networks

Research Article

An analysis of the maximum likelihood estimator for localization problems

  • @INPROCEEDINGS{10.1109/ICBN.2005.1589711,
        author={Mingbo Zhao and Sergio D.  Servetto},
        title={An analysis of the maximum likelihood estimator for localization problems},
        proceedings={2nd International ICST Conference on Broadband Networks},
        publisher={IEEE},
        proceedings_a={BROADNETS},
        year={2006},
        month={2},
        keywords={},
        doi={10.1109/ICBN.2005.1589711}
    }
    
  • Mingbo Zhao
    Sergio D. Servetto
    Year: 2006
    An analysis of the maximum likelihood estimator for localization problems
    BROADNETS
    IEEE
    DOI: 10.1109/ICBN.2005.1589711
Mingbo Zhao1, Sergio D. Servetto1
  • 1: School of Electrical and Computer Engineering – Cornell University, http://cn.ece.cornell.edu/

Abstract

We study the behavior of the maximum likelihood (ML) estimator for localization via triangulation, under Gaussian noise. Likelihood maximization is a non-convex problem, with possibly multiple solutions. In this paper we present an algorithm for solving this non-convex problem, which under some reasonable assumptions, is guaranteed to produce the exact ML estimate. A nice feature of our algorithm is that it is readily amenable to analysis: we give (a) a characterization of a domain in which, if the algorithm is started with an initial estimate within that domain, a standard steepest descent method is guaranteed to converge to a global minimum; (b) the distribution of the estimate; and (c) a measure of sensitivity to noise of the estimate. Many numerical examples and plots are included to illustrate these concepts