Phase Gradient Autofocus Algorithm (PGA) - MATLAB Implementation and Motion Compensation

The Phase Gradient Autofocus Algorithm (PGA) stands as one of the most classical and frequently utilized autofocus and motion error compensation techniques in Synthetic Aperture Radar systems. This algorithm processes phase information from radar echo signals to achieve high-resolution target imaging. In MATLAB implementation, PGA typically involves key computational stages including phase error estimation through gradient calculation, phase correction using iterative refinement, and image quality enhancement via aperture-dependent compensation. The algorithm employs Fourier transform operations for signal processing and incorporates windowing techniques to isolate dominant scatterers for accurate phase error extraction. Through PGA implementation, developers can effectively compensate for motion-induced blurring and distortion, significantly improving both imaging quality and system performance of SAR platforms. The MATLAB code structure generally includes functions for phase gradient computation, circular shifting operations for phase alignment, and iterative loops for convergence optimization.