Traditional ground moving target indicator (GMTI) processing attempts to separate moving objects in the scene from stationary clutter. Techniques such as space-time adaptive processing (STAP) require the use of an unknown covariance matrix of the interference (clutter, jamming, and thermal noise) that must be estimated from the remaining data not currently under test. Many problems exist with estimating the interference covariance including: heterogeneous, contaminated, and/or limited training data. There are many existing techniques for obtaining an interference covariance matrix estimate, most of which incorporate some kind of prior knowledge to improve the estimate. We propose a Bayesian framework that estimates both clutter and movers on a range-by- range basis without the explicit estimation of an interference covariance matrix. The approach incorporates the knowledge of an approximate digital elevation map (DEM), platform kinematics (platform velocity, crab angle, and antenna spacings), and the belief that movers are sparse in the scene. Computation using this Bayesian model is enabled by recent algorithm developments for fast inference on linear mixing models. The signal model and required processing steps are detailed. We test our approach using the KASSPER I dataset and compare the results to other current approaches.