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Unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) is very important for battlefield awareness. For SAR systems mounted on a UAV, the motion errors can be considerably high due to atmospheric turbulence and aircraft properties, such as its small size, which makes motion compensation (MOCO) in UAV SAR more urgent than other SAR systems. In this paper, based on 3-D motion error analysis, a novel 3-D MOCO method is proposed. The main idea is to extract necessary motion parameters, i.e., forward velocity and displacement in line-of-sight direction, from radar raw data, based on an instantaneous Doppler rate estimate. Experimental results show that the proposed method is suitable for low- or medium-altitude UAV SAR systems equipped with a low-accuracy inertial navigation system.