In this work, a generalized phase gradient autofocus (GPGA) algorithm is developed which is applicable with both the polar format algorithm (PFA) and back projection algorithm (BPA). The GPGA algorithm preserves the four crucial signal processing steps comprising the PGA algorithm, while alleviating the constraint of using a single scatterer per range cut for phase error estimation which exists with the PGA algorithm. The GPGA algorithm, whether using the PFA or BPA, yields an approximate maximum marginal likelihood estimate (MMLE) of phase errors having marginalized over unknown complex-valued reflectivities of selected scatterers. Also, in this work a new approximate MMLE, termed the max-semi definite relaxation (Max-SDR) phase estimator, is proposed for use with the GPGA algorithm. The Max-SDR phase estimator provides a phase error estimate with a worst-case approximation bound compared to the solution set of MMLEs. Additionally, in this work a specialized interior-point method (IPM)is presented for more efficiently performing Max-SDR phase estimation. Lastly, simulation and experimental results are presented.
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