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Recently, energy-based localization using acoustic energy measurements has received much attention in wireless sensor networks. Since the objective function of the energy-based maximum likelihood (ML) localization is non-convex, the global solutions are hardly obtained without good initial estimates. In this paper, we relax this non-convex problem as a convex semidefinite programming (SDP), based on which a good estimate can be obtained and be improved by a procedure called randomization. Simulation results show that the proposed method is effective and outperforms the existing methods.