A Modified Iteration-Free SPGA Based on Removing the Linear Phase

In traditional Stripmap SAR imaging, the platform motion error will bring the phase error in the azimuthal direction to the image, which will have a series of effects on the imaging quality. The traditional autofocus algorithm-Stripmap Phase Gradient Algorithm (SPGA)-can estimate any order phase error above the second order in theory, but it is difficult to estimate the linear phase error, which leads to the discontinuity of the estimated phase error. It usually needs multiple iterations to focus an image, which is inefficient. Moreover, because the linear phase error cannot be estimated, the traditional SPGA cannot eliminate the target offset in the image, resulting in the distortion of the image in the azimuthal direction. According to the continuity of phase error, we propose a modified iteration-free SPGA based on removing the linear phase. Without iteration, the proposed autofocus algorithm can achieve comparable or even better results than traditional SPGA. In the simulation experiments, piecewise linear errors are added to the images of multiple targets. SPGA still fails to focus the image after six iterations. The average ILSR and ILSR are -7.11 dB and -3.99 dB, respectively, and the average number of point target drift is 8.42 pixels. The proposed algorithm optimizes the average ILSR and ILSR to -12.34 dB and -9.87 dB and reduces the average number of point target drift to 0.16 pixels. In the actual data processing, using image entropy as the evaluation criterion, the time consumption is only 19.25% of SPGA under the condition of achieving the same focusing quality.