  We propose an efficient solution to peer-to-peer localization in a wireless
sensor network which works in two stages. At the first stage the optimization
problem is relaxed into a convex problem, given in the form recently proposed
by Soares, Xavier, and Gomes. The convex problem is efficiently solved in a
distributed way by an ADMM approach, which provides a significant improvement
in speed with respect to the original solution. In the second stage, a soft
transition to the original, non-convex, non relaxed formulation is applied in
such a way to force the solution towards a local minimum. The algorithm is
built in such a way to be fully distributed, and it is tested in meaningful
situations, showing its effectiveness in localization accuracy and speed of
convergence, as well as its inner robustness.
