In a synthetic aperture radar (SAR) targets on the ground that are moving become smeared as a result of velocity components parallel to the motion of the radar and are moved to radically different angular positions if they have velocity components perpendicular to the motion of the radar. Methods for restoring moving targets to their correct size and position are described. The samples collected for SAR processing are frequency-modulated RF pulses. Mathematically this leads to spectra that are described by Fresnel integrals. For stationary targets, the spectrum is symmetrical around the origin. If there is a moving target in a range cell, its Doppler spectrum will be displaced from the origin and may undergo other changes as a result of its nonzero velocity. Proper compensation to locate the target at the correct position requires that the spectrum be translated to a position dependent on the along-track velocity rather than to the origin. From the central frequency, the along-range velocity component can be estimated and the length of the translation can then be found. After translation, the spectrum is converted back to the time domain and the customary SAR processing is performed.
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