U. A. Khan, S. Kar and J. M. F. Moura, "A linear iterative algorithm
for distributed sensor localization," in 42nd IEEE
Asilomar Conference on Signals, Systems, and Computers,
Pacific Grove, CA, Oct. 2008, pp. 1160-1164 , invited
This paper presents a distributed sensor localization algorithm with inter-sensor distance information in~$m-$dimensional Euclidean space using only~$m+1$ anchors (sensors that know their exact locations). Under the assumption that the~$M$ sensors (with unknown locations) lie in the convex hull of the~$m+1$ anchors and the underlying network is connected, we derive a linear algorithm that employs barycentric coordinates and Cayley-Menger determinants. The algorithm is iterative and the iterations on each of the~$m$ coordinates (that describe the location of a sensor) are decoupled. The convergence of the algorithm is proved using the results from the theory of absorbing Markov processes. As the algorithm converges, the solution almost surely resides in the subspace spanned by the eigenvectors corresponding to the~$m+1$ anchors. With the locations of these~$m+1$ anchors known, we achieve a unique solution in that subspace with respect to the locations of the anchors.