U. A. Khan, S. Kar, B. Sinopoli and J. M. F. Moura, "Distributed sensor localization
in Euclidean spaces: Dynamic environments," in *46th
Annual Allerton Conference on Communication, Control and
Computing*, Monticello, IL, Sep. 2008, pp. 361-366,
*invited paper*.

## Abstract

In [1], we presented an algorithm to localize sensors in $m$-dimensional Euclidean space~$\mathbb{R}^n$ with unknown locations assuming the following:
(i) there are~$(m+1)$ sensors that know their absolute coordinates--the anchors; (ii) each sensor communicates with~$m+1$ of its neighbors; and (iii) the sensors lie in the convex hull of the anchors. The localization algorithm is a generalization of consensus--it is a weighted linear, iterative, and distributed algorithm. The weights are the barycentric coordinates of a sensor with respect to its neighbors, which are computed by the generalized volumes obtained from the intersensor distances in the Cayley-Menger determinants. This paper expands on this work to take advantage of when the number of anchors available possibly exceeds~$m+1$, a sensor can communicate with all sensors within its radius of communication, and when the network communication topology may be dynamic as, for example, when the network neighborhood structure changes over time. The paper shows that the algorithm converges to the exact sensor locations in the absence of noise.