Sensor network localization by eigenvector synchronization over the euclidean group

Mihai Cucuringu, Yaron Lipman, Amit Singer

Research output: Contribution to journalArticlepeer-review

83 Scopus citations


We present a new approach to localization of sensors from noisy measurements of a subset of their Euclidean distances. Our algorithm starts by finding, embedding, and aligning uniquely realizable subsets of neighboring sensors called patches. In the noise-free case, each patch agrees with its global positioning up to an unknown rigid motion of translation, rotation, and possibly reflection. The reflections and rotations are estimated using the recently developed eigenvector synchronization algorithm, while the translations are estimated by solving an overdetermined linear system. The algorithm is scalable as the number of nodes increases and can be implemented in a distributed fashion. Extensive numerical experiments show that it compares favorably to other existing algorithms in terms of robustness to noise, sparse connectivity, and running time. While our approach is applicable to higher dimensions, in the current article, we focus on the two-dimensional case.

Original languageEnglish (US)
Article number19
JournalACM Transactions on Sensor Networks
Issue number3
StatePublished - Jul 2012

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications


  • Distance geometry
  • Eigenvectors
  • Rigidity theory
  • Sensor networks
  • Spectral graph theory
  • Synchronization


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