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This study investigates practical processing methods aiming at detecting ground moving targets and estimating their motion parameters for an experimental three-channel airborne synthetic aperture radar-ground moving target indication (SAR-GMTI) system. It focuses on two key points of GMTI processing: adaptive clutter suppression and resolving of velocity ambiguities. Different from the conventional clutter suppression based on SAR images or in range-Doppler domain of the entire-aperture pulses, the clutter cancellation is proposed to be performed in the Doppler domain of short-aperture pulses to avoid the superposition of clutter echoes from different ground patches in azimuth; meanwhile, the ground moving target signals are focused with the full aperture to maximise the signal-to-noise ratio. To resolve the velocity ambiguity, a joint strategy is proposed that combines the estimates of the along-track interferometric phases and the Doppler spectrum information of a ground moving target according to the Chinese remainder theorem. The implementations of the processing operations are verified with real data from the experimental three-channel airborne SAR-GMTI system.