Localization of networks using various ranging bias models

Joseph Shmuel Picard, Anthony Joseph Weiss

Research output: Contribution to journalArticlepeer-review


Given a network of stations with incomplete and possibly imprecise inter-station range measurements, it is required to find the relative positions of the stations. Several models for the bias in the range estimates are discussed. We present a set of iterative algorithms that cope successfully with the various bias models and provide Maximum Likelihood position estimates. Proof of convergence is provided. A procedure, albeit designed for precise measurements, is also proposed for the initialization of the iterative algorithms. We also present compact, matrix form expression for the Cramér-Rao Bound (CRB). Numerical examples are provided to corroborate the results.

Original languageEnglish
Pages (from-to)553-562
Number of pages10
JournalWireless Communications and Mobile Computing
Issue number5
StatePublished - Jun 2008


  • Ad-hoc networks
  • Alternating projections
  • Cramér-Rao bound
  • Location estimation
  • Maximum likelihood estimation
  • Phase retrieval
  • Wireless sensor network


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