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Synthetic aperture radar (SAR) systems onboard small aircrafts suffer from trajectory deviations and instabilities of antenna orientation. These kinds of motion errors lead to significant geometric distortions in SAR images. In order to correct the distortions, we propose a time-domain multi-look stripmap SAR processing algorithm with built-in geometric correction. In the algorithm, the azimuth reference functions and range migration curves are designed to produce SAR images directly on a correct rectangular grid on the ground plane. The proposed technique has been successfully tested by using a Ku-band airborne SAR system installed onboard light-weight aircraft.