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Energy based source localization methods have received great interest due to their low cost and simple implementation. The problem of source localization based on received signal strength difference (RSSD) measurements with unknown transmit power is considered in this letter. An efficient two stage estimator is presented. First, a minimax optimization problem is developed to minimize the mean square error of the proposed RSSD based model. Then, semidefinite relaxation is employed to transform this nonconvex and nonlinear problem into a convex optimization problem. This can be efficiently solved to obtain the optimal solution of the corresponding semidefinite programming problem. Performance results are presented, which confirm the efficiency of the proposed method that achieves the Cramér-Rao lower bound for sufficiently large signal to noise ratios.Index Terms-Source localization, minimax optimization, received signal strength difference (RSSD), semidefinite programming (SDP).

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