Robust Distance Matrix Completion for Localization using Frank-Wolfe Iterations

Metin Vural, Chun Yuan, Nicola Kleppmann, Peter Jung

Abstract: In this study, a new semidefinite programming- based algorithm is introduced for the Euclidean distance matrix completion (EDMC) problem with noisy and incomplete distance measurements. A penalty metric that measures the data misfit is minimized over the spectrahedron with projection-free convex optimization. The optimality trade-off between the trace of a positive semidefinite matrix and a loss function is traced over a Pareto frontier using the Regula falsi method, which is simple, derivative-free, and cost-effective nonlinear equation root finding iteration. One field that the EDMC problem is often used in is wireless sensor networks (WSNs) localization. A test setup has been created by using real signal strength measurements for a 3D- localization problem in WSNs to inspect the performance of the introduced algorithm. It is shown that the proposed approach efficiently solves the optimization problem and the results are consistent with the generic semidefinite solver CVX.