Edge-based semidefinite programming relaxation of sensor network localization with lower bound constraints.

In this paper, we strengthen the edge-based semidefinite programming relaxation (ESDP) recently proposed by Wang, Zheng, Boyd, and Ye (SIAM J. Optim. 19:655-673, ) by adding lower bound constraints. We show that, when distances are exact, zero individual trace is necessary and sufficient for a sensor to be correctly positioned by an interior solution. To extend this characterization of accurately positioned sensors to the noisy case, we propose a noise-aware version of ESDP ( ρ-ESDP) and show that, for small noise, a small individual trace is equivalent to the sensor being accurately positioned by a certain analytic center solution. We then propose a postprocessing heuristic based on ρ-ESDP and a distributed algorithm to solve it. Our computational results show that, when applied to a solution obtained by solving ρ-ESDP proposed of Pong and Tseng (Math. Program. doi:), this heuristics usually improves the RMSD by at least 10%. Furthermore, it provides a certificate for identifying accurately positioned sensors in the refined solution, which is not common for existing refinement heuristics. [ABSTRACT FROM AUTHOR]