RSS-Based Localization in WSNs Using Gaussian Mixture Model via Semidefinite Relaxation

Energy-based source localization methods are normally developed according to the channel path-loss models in which the noise is generally assumed to follow Gaussian distributions. In this letter, we represent the practical additive noise by the Gaussian mixture model, and develop a localization algorithm based on the received signal strength to achieve a maximum likelihood location estimator. By using Jensen's inequality and semidefinite relaxation, the initially proposed nonlinear and nonconvex estimator is relaxed into a convex optimization problem, which can be efficiently solved to obtain the globally optimal solution. Besides, the corresponding Cramer-Rao lower bound is derived for performance comparison. Simulation and experimental results show a substantial performance gain achieved by our proposed localization algorithm in wireless sensor networks.