Analysis on the Azimuth Shift of a Moving Target in SAR Image

As we know, a moving target’s azimuth shift in synthetic aperture radar (SAR) image is proportional to the projected velocity of its across-track velocity in the slant-range plane. Therefore, we can relocate the moving target in SAR image after estimating its velocity. However, when the Doppler ambiguity occurs due to the limitation of the SAR system’s pulse repetition frequency (PRF), this relationship will not hold any more, in this case, we cannot relocate the moving target to the right position. The Doppler spectrum of a moving target with arbitrary velocity may entirely situate in a PRF band or span in two neighboring PRF bands. In this paper, we conduct a detailed theoretical analysis on the moving target’s azimuth shift for these two scenarios. According to the derived formulas, one can relocate a moving target with arbitrary velocity to the right position no matter the Doppler ambiguity occurs or not. Simulated data are processed to validate the analysis.