  This paper considers node localization in static sensor networks using
range-only measurements. Similar to state- of-the-art algorithms, such as ECHO
and DILOC, we rely on barycentric coordinates of the nodes to transform the
non-convex node localization problem into a linear system of equations. The
main contribution of this paper is a simple closed-form expression for
generalized barycentric coordinates, which extends existing algorithms from two
to n dimensions and allows arbitrary anchor-node configurations. The result
relies on a connection between the Cayley-Menger bi-determinants of subsets of
n+1 neighbor nodes and the signed volume of the simplices defined by these
neighbor nodes. Hence, for noise-free measurements, the proposed method
computes the optimal sensor network embedding as the solution of a linear
system with coefficients obtained from the generalized barycentric node
coordinates. Using simulations, we provide comparisons with DILOC and Matlab's
MDS implementation. We also show that it is possible to improve our algorithm
run time using fewer subsets of neighbor nodes.
