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We describe a hybrid-state filtering algorithm that enables tracking of moving and stationary vehicles, on the basis of moving-target-indicator (MTI) measurements and SAR-based imagery detections. We use a hybrid-state model for vehicle dynamics with discrete states move and stop, and the discrete state influences the continuous-state dynamics through the process noise. We present a near-optimal recursive filter that is a hybrid-state extension to the well-known extended Kalman filter (EKF). We study the performance of the filter with a number of target trajectories. All of the data that we use is simulated. Our framework can be easily extended to include other sensor types, including EO-based imagery detections and signal intelligence measurements. Also, the filtering algorithm can be used as part of a multi-sensor multi-target tracking algorithm.