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To address the low location accuracy and poor robustness of existing methods, error correction to improve the Stage 2 of the original Two-Stage Weighted Least Squares (TSWLS)-based methods is proposed, which involves a robust moving source localization method with high accuracy based on Time Difference Of Arrival (TDOA) and Frequency Difference Of Arrival (FDOA) in the presence of receiver location errors. This newly proposed Stage 2 performs Taylor expansion on the nuisance variables introduced in Stage 1 to construct the error correction equation, thereby avoiding the rank deficiency problem and nonlinear mathematical operations in the original TSWLS-based methods; and improving the robustness and location accuracy of the method. Theoretical analysis indicates that the proposed method can attain the Cramer-Rao Lower Bound (CRLB) under small noise condition. Simulation results show the proposed method has stronger localization robustness and better anti-noise performance over the existing methods under the common level of receiver location and measurement error.