Efficient Motion Compensation of a Moving Object on SAR Imagery Based on Velocity Correlation Function

Current motion compensation algorithms for a moving object on synthetic aperture radar (SAR) imagery by refocusing are accurate, but they suffer from a severe computational efficiency problem. If the step size of an assumed target velocity is too large, one could miss the true target velocity, whereas too small a step size would lead to a considerable computation load. To address this issue, the way motion error affects a compressed signal should be understood. In this paper, we introduce the concept of velocity correlation function (VCF) to describe the sensitivity of an SAR compressed signal to motion error. We propose its analytical model by straightforwardly tackling conventional matched filtering, and then we thoroughly compare the model with the experimentally obtained VCF for each static and moving object on real L-band airborne/spaceborne SAR imagery. The analytically derived VCF is well validated, as it shows excellent agreement with those experiments. Finally, the VCF is generalized to a velocity correlation map to visualize a sensitivity of SAR system parameters to target motion in both the range and the azimuth directions simultaneously.