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This paper presents a novel technique to estimate the initial coordinates and velocity vector of moving targets, including those with velocities above the Nyquist limit, using a single synthetic aperture radar (SAR) sensor without increasing the pulse repetition frequency (PRF). The basic reasoning is that, although the returned echoes may be undersampled in the azimuth direction, their phase and amplitude are informative with respect to the moving target trajectory parameters. Therefore, the so-called blind angle ambiguity, inherent to systems using a single SAR sensor, is overcome. The proposed method samples the data in the spatial domain, along the signature curve which depends on the moving target trajectory parameters. The resulting algorithm is a highly efficient (from the computational point of view) ID matched filter. The effectiveness of the proposed scheme is illustrated using simulated SAR data and real data from the MSTAR public release data set, corresponding to a static SAR scene and a static BTR-60 with simulated motion.