  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.
