In this paper, a 2-stage robust distributed algorithm is proposed for
cooperative sensor network localization using time of arrival (TOA) data
without identification of non-line of sight (NLOS) links. In the first stage,
to overcome the effect of outliers, a convex relaxation of the Huber loss
function is applied so that by using iterative optimization techniques, good
estimates of the true sensor locations can be obtained. In the second stage,
the original (non-relaxed) Huber cost function is further optimized to obtain
refined location estimates based on those obtained in the first stage. In both
stages, a simple gradient descent technique is used to carry out the
optimization. Through simulations and real data analysis, it is shown that the
proposed convex relaxation generally achieves a lower root mean squared error
(RMSE) compared to other convex relaxation techniques in the literature. Also
by doing the second stage, the position estimates are improved and we can
achieve an RMSE close to that of the other distributed algorithms which know
\textit{a priori} which links are in NLOS.Comment: Accepted in WPNC 201