Semidefinite Programming for NLOS Error Mitigation in TDOA Localization

Non-line-of-sight (NLOS) error mitigation for the time-of-arrival (TOA) localization has been extensively studied, but these methods cannot be directly applied for the time-difference-of-arrival (TDOA) systems. Recent work has applied convex optimization for NLOS error mitigation in TDOA systems. Issues remain unsolved with this technique include the convex hull problem, reference-anchor selection problem, and difficulties dealing with a wide range of NLOS-caused ranging errors. This letter proposes a new technique to transform a TDOA model into a TOA model and develops a semidefinite programming method with new constraints for effective NLOS error mitigation in TDOA systems. Major advantages of this method include: 1) it resolves the issues such as convex hull and reference-anchor selection issues that existing schemes are facing; 2) it does not require any a priori information about NLOS links or NLOS error statistics; and 3) it achieves a better performance than existing convex optimization schemes, which is verified in both simulation and real experiments.