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Range cell migration (RCM) correction and azimuth spectrum being contained entirely in baseband are critical for ground moving-target imaging (GMTIm). Without the azimuth spectrum entirely contained within baseband and a proper RCM correction, the image will be defocused, or artifacts may appear in the image. An instantaneous-range-Doppler algorithm of GMTIm based on deramp-keystone processing is proposed. The main idea is to focus all the targets in the scene at an arbitrarily chosen azimuth time. With our proposed algorithm, RCMs of all targets in the scene are removed without a priori knowledge of their accurate motion parameters. The targets with azimuth spectrum not entirely in baseband, i.e., azimuth spectrum within an ambiguous pulse repeating frequency (PRF) band or spanning neighboring PRF bands, can also be effectively dealt with simultaneously. Theoretical analysis shows that no interpolation is needed. The simulated and real data are used to validate the effectiveness of this method.