Rank one phase error estimation for range-Doppler imaging

A range-Doppler image is corrupted when each pulse in the corresponding range-time array contains a single time-dependent phase error. A previously devised algorithm, the rank one phase estimation (ROPE) technique developed by F. Dyson, et al. (1992), estimates the phase errors, which are then removed so that range-Doppler imaging can proceed in the usual manner. The iterative algorithm works homogeneously across the two-dimensional range-time array (no bright scatterers are necessary for focusing). The estimation technique is model based, but image recovery is successful for many images that do not fit the model. Extensions of both theory and application of the previously devised algorithm are presented. Theoretical insights pertaining to convergence, initialization, optimality, and recovery for images that do not fit the model are presented. Several examples, drawn from simulations, postmission corrupted field data, and field data that are intrinsically corrupted, are also contained herein.