This paper presents the Static Computational Optical Undersampled Tracker (SCOUT), an architecture for compressive motion tracking systems. The architecture uses compressive sensing techniques to track moving targets at significantly higher resolution than the detector array, allowing for low cost, low weight design and a significant reduction in data storage and bandwidth requirements. Using two amplitude masks and a standard focal plane array, the system captures many projections simultaneously, avoiding the need for time-sequential measurements of a single scene. Scenes with few moving targets on static backgrounds have frame differences that can be reconstructed using sparse signal reconstruction techniques in order to track moving targets. Simulations demonstrate theoretical performance and help to inform the choice of design parameters. We use the coherence parameter of the system matrix as an efficient predictor of reconstruction error to avoid performing computationally intensive reconstructions over the entire design space. An experimental SCOUT system demonstrates excellent reconstruction performance with 16X compression tracking movers on scenes with zero and nonzero backgrounds.