Near-field target positioning and far-field localization are traditionally regarded as two distinct challenges. As the modified polar representation (MPR) model was proposed, the localization method based on this model has been widely studied. Several closed-form positioning solutions considering measurement noise and sensor position errors were proposed in MPR. However, the sensor position error is usually modeled as Gaussian white noise for static sensors, which is not available to motion sensors such as the unmanned aerial vehicles (UAVs). With the existence of inertial navigation errors and body vibration errors of drones, a novel position error model is built for motion sensors in this paper. In order to obtain an optimal target estimation, a two-step overlapped sub-aperture (OSA) localization method is developed to refine the final estimate by correlation of these sub-apertures. This approach can minimize the deviation of estimate caused by measurement errors and sensor position errors and optimize the target estimates. Simulation results demonstrate that the proposed method achieves higher localization accuracy compared to earlier methods when the motion error of the sensor position is considered.