A convex relaxation for approximate maximum-likelihood 2D source localization from range measurements

This paper addresses the problem of locating a single source from noisy range measurements in wireless sensor networks. An approximate solution to the maximum likelihood location estimation problem is proposed, by redefining the problem in the complex plane and relaxing the minimization problem into semidefinite programming form. Existing methods solve the source localization problem either by minimizing the maximum likelihood function iteratively or exploiting other semidefinite programming relaxations. In addition, using squared range measurements, exact and approximate least squares solutions can be calculated. Our relaxation for source localization in the complex plane (SLCP) is motivated by the near-convexity of the objective function and constraints in the complex formulation of the original (non-relaxed) problem. Simulation results indicate that the SLCP algorithm outperforms existing methods in terms of accuracy, particularly in the presence of outliers and when the number of anchors is larger than three.