Abstract: Compressed sensing has been widely used in the field of synthetic aperture radar imaging because of its simplicity and high efficiency. Synthetic aperture radar imaging based on compressed sensing needs to establish an observation model, and the error of the observation model will reduce the reconstruction performance of the original scene. Most of the early models assumed that the mathematical model of the observation process was accurate and reconstructed the original scene on this basis. However, in practice, the observation position usually has errors, so it is necessary to take into account the influence of radar observation position errors. Different from existing imaging methods that consider position error, the proposed method first focuses on the influence of observed position error on radar imaging, and then takes the observed position error as a part of the imaging process, directly estimates and compensates the error, and uses the idea of alternate optimization to alternately reconstruct the target and estimate and compensate the observed position error. The simulation results show that this method can effectively improve the image quality.