Sensitivity of two autofocus algorithms to spatially variant phase errors

In this paper we study the performance of two existing autofocus algorithms in a difficult SAR scenario. One algorithm is the well known phase gradient autofocus (PGA) algorithm and the other is the more recent AUTOCLEAN. The latter was introduced particularly with ISAR autofocus of a small target in mind and has been shown to outperform the PGA when range misalignment is present. This was expected as AUTOCLEAN, as opposed to PGA, has a built-in ability to compensate for range misalignment. In most available studies of the above autofocus algorithms spatially variant phase errors are absent or insignificant. The data used here is far-field SAR data collected over a large range of aspect angles. The target area is large, hence significant motion through resolution cells (MTRC) occurs due to target scene rotation. The polar format algorithm (PFA) is applied prior to autofocus to handle MTRC and compensate for off-track platform motion. However, the platform motion measurements used in PFA are not precise enough to compensate for the off-track motion and left after PFA are phase errors corrupting the data. These phase errors are spatially variant due to the large target scene and this violates the models for the autofocus algorithms above. This in contrast with the previously mentioned studies. We show that the performances of the autofocus algorithms considered are much deteriorated by the presence of spatially variant phase error but in different ways since the averaging of the phase error estimates is made differently in the two algorithms. Based on our numerical study of the two autofocus methods we try to rank them with respect to their sensitivity to spatially variant phase errors.