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In synthetic aperture radar (SAR), images are formed by focusing the response of stationary objects to a single spatial location. On the other hand, moving targets cause phase errors in the standard formation of SAR images that cause displacement and defocusing effects. SAR imagery also contains significant sources of non-stationary spatially-varying noises, including antenna gain discrepancies, angular scintillation (glints) and complex speckle. In order to account for this intricate phenomenology, this work combines the knowledge of the physical, kinematic, and statistical properties of SAR imaging into a single unified Bayesian structure that simultaneously (a) estimates the nuisance parameters such as clutter distributions and antenna miscalibrations and (b) estimates the target signature required for detection/inference of the target state. Moreover, we provide a Monte Carlo estimate of the posterior distribution for the target state and nuisance parameters that infers the parameters of the model directly from the data, largely eliminating tuning of algorithm parameters. We demonstrate that our algorithm competes at least as well on a synthetic dataset as state-of-the-art algorithms for estimating sparse signals. Finally, performance analysis on a measured dataset demonstrates that the proposed algorithm is robust at detecting/estimating targets over a wide area and performs at least as well as popular algorithms for SAR moving target detection.

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