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The acoustic energy-based source localization problem is addressed. Based on the noisy acoustic energy measurements, we obtain a nonlinear and non-convex weighted least squares (WLS) formulation for this problem, whose globally optimal solution is hardly obtained without a good initial estimate. To overcome this difficulty, we first transform the original measurement model to obtain an approximate WLS formulation, and then employ the semidefinite relaxation (SDR) technique to obtain a semidefinite programming (SDP), which can be solved very efficiently. The SDP solution is further refined using the conventional Gaussian randomization procedure. Moreover, we propose an alternating estimation procedure to handle the localization problem when the decay factor is unknown. Simulation results show that the proposed SDR method significantly outperforms the existing methods.