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This paper proposes a low computational cost method for the near-field narrowband source localization problem, which does not require multidimensional search or high-order statistics. The proposed method is based on the second-order statistics (SOS) of the outputs of a uniform linear array (ULA). More precisely, the range and angle parameters are estimated through a weighted linear prediction (LP) algorithm applied to a properly chosen array output correlation sequence. Detailed performance analysis and derivation of the optimal weightings are provided. Simulation results are finally presented to validate the theoretical analysis results and to assess the performance of the proposed method.