U. A. Khan, S. Kar, and J. M.F. Moura, "Distributed sensor localization
using barycentric coordinates," in 3rd International
Workshop on Computational Advances in Multi-
Sensor Adaptive Processing, Aruba, Dutch Antilles, Dec.
2009, pp. 65-68.
In this paper, we review our work on distributed sensor localization using barycentric coordinates. We present an algorithm for localization in $m$-dimensional Euclidean spaces. The algorithm is distributed and requires at least $m+1$ anchors. Anchors are the nodes that know their exact locations. We require that the non-anchor nodes (all the network nodes that do not know their locations) lie in the convex hull of at least $m+1$ anchors. Using barycentric coordinates, each non-anchor node updates its location estimate as a linear combination of its (carefully chosen) neighboring nodes. Under minimal network connectivity assumptions, we show that the distributed localization algorithm converges to the exact sensor locations. We further extend the localization algorithm to include imperfect barycentric computation, communication link failures, and communication noise. We show that, with the aid of stochastic approximation, the localization algorithm converges almost surely to the exact locations under the random phenomena described before.