Owing to the platform instability and precision limitations of motion sensors, motion errors negatively affect the quality of synthetic aperture radar (SAR) images. The autofocus Back Projection (BP) algorithm based on the optimization of image sharpness compensates for motion errors through phase error estimation. This method can attain relatively good performance, while assuming the same phase error for all pixels, i.e., it ignores the spatial variance of motion errors. To overcome this drawback, a high-precision motion error compensation method is presented in this study. In the proposed method, the Antenna Phase Centers (APC) are estimated via optimization using the criterion of maximum image intensity. Then, the estimated APCs are applied for BP imaging. Because the APC estimation equals the range history estimation for each pixel, high-precision phase compensation for every pixel can be achieved. Point-target simulations and processing of experimental data validate the effectiveness of the proposed method.