An Improved Time-Domain Autofocus Method Based on 3-D Motion Errors Estimation

Spatial-variant phase errors (PEs) are important factors which defocus the synthetic aperture radar (SAR) image. In time-domain SAR imaging, the exact calculation of instantaneous range is carried out to realize imaging. Accurate trajectory is the key to compensate spatial-variant PEs and ensure image focus. Thus, an improved time-domain autofocus method based on three-dimensional motion errors (3-D MEs) estimation is proposed in this article. First, an improved maximizing-maximum-pixel-value method is used to estimate nonspatial-variant PEs. Meanwhile, a theoretical explanation combined with
$N$
-dimensional Euclidean space is described. Then, residual PEs and wrapped PEs are discussed successively. A part-overlapped partitioning scheme for sub-block images (SBIs) and a wrapped-PE model are proposed for 3-D MEs estimation. Then, the estimation problem is turned into a mixed integer programming problem, which can be solved by the combination of genetic algorithm (GA) and Tikhonov regularization. Finally, the well-focused image is obtained through updated trajectory. The effectiveness of the proposed method is proven by results of simulation and real SAR data processing.