Network localization with noisy distances by non-convex optimization

A distance based network localization determines the positions of the nodes in the network subject to some distance constraints. The network localization problem may be modeled as a non-convex nonlinear optimization problem with distance constraints which are either convex or non-convex. Existing network localization algorithms either eliminate the non-convex distance constraints or relax them into convex constraints to employ the traditional convex optimization methods, e.g., SDP, for estimating positions of nodes with noisy distances. In practice, the estimated solution of such a converted problem gives errors due to the modification of constraints. In this paper, we employ the nonlinear Lagrangian method for non-convex optimization which efficiently estimates node positions solving the original network localization problem without any modification. The proposed method involves numerical computations. By increasing the number of iterations (not very high, usually less than hundred) in computations, a desired level of accuracy may be achieved.