On the convergence of the phase gradient autofocus algorithm for synthetic aperture radar imaging

Synthetic Aperture Radar (SAR) imaging is a class of coherent range and Doppler signal processing techniques applied to remote sensing. The aperture is synthesized by recording and processing coherent signals at known positions along the flight path. Demands for greater image resolution put an extreme burden on requirements for inertial measurement units that are used to maintain accurate pulse-to-pulse position information. The recently developed Phase Gradient Autofocus algorithm relieves this burden by taking a data-driven digital signal processing approach to estimating the range-invariant phase aberrations due to either uncompensated motions of the SAR platform or to atmospheric turbulence. Although the performance of this four-step algorithm has been demonstrated, its convergence has not been modeled mathematically. A new sensitivity study of algorithm performance is a necessary step towards this model. Insights that are significant to the application of this algorithm to both SAR and to other coherent imaging applications are developed. New details on algorithm implementation identify an easily avoided biased phase estimate. A new algorithm for defining support of the point spread function is proposed, which promises to reduce the number of iterations required even for rural scenes with low signal-to-clutter ratios