A geometrical perspective on localization

ABSTRACT

A large number of localization algorithms for wireless sensor networks (WSNs) are evaluated against the Cramer-Rao Bound (CRB) as an indicator of how good the algorithm performs. The CRB defines the lower bound on the precision of an unbiased localization estimator. The CRB concept, borrowed from GPS localization, however, does not translate well to WSNs. In this paper, we show in which cases the CRB fails to capture troublesome anchor configurations leading to erroneous lower bounds. We continue with a study on the geometrical configurations of anchors favorable to localization algorithms. We conclude by proposing a metric to characterize the stability of the geometry of a certain anchor topology. Future work will address the combination of geometry and statistical metrics with the goal of obtaining a clear image on localization algorithms boundaries.

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INDEX TERMS

Primary Classification:
  C. Computer Systems Organization
  C.2 COMPUTER-COMMUNICATION NETWORKS
      C.2.4 Distributed Systems
          Subjects: Distributed applications

General Terms:
Algorithms, Design, Theory

Keywords:
cramer-rao bound, localization algorithm, localization boundaries