Improved phase gradient autofocus algorithm based on segments of variable lengths and minimum-entropy phase correction

Unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) is an essential tool for modern remote sensing applications. Owing to its size and weight constraints, UAV is very sensitive to atmospheric turbulence that causes serious trajectory deviations. In this study, an improved phase gradient autofocus (PGA) motion compensation approach is proposed for UAV-SAR imagery. The approach is implemented in two steps. The first step determines the length of each segment depending on number of good quality scatterers and motion errors obtained from navigation data. In the second step, a novel minimum-entropy phase correction based on the discrete cosine transform (DCT) coefficients is proposed. In this approach, transform phase error estimated by PGA to DCT-coefficients that represent the phase error in the frequency or time-frequency domain. The entropy of a focused image is utilised as the optimisation function of the DCT-coefficients to improve the final image quality. Finally, real-data experiments show that the proposed approach is appropriate for highly precise imaging of UAV-SAR equipped with only low-accuracy inertial navigation systems.