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Space-Time Adaptive Processing (STAP) is an advanced signal processing methodology for the Ground Moving Target Indication (GMTI) mode of airborne and spaceborne surveillance radar systems. It is used to mitigate motion-induced spread-Doppler clutter that interferes with the echo from ground targets. This course will develop and clearly illustrate the GMTI problem from first principles, showing the need for STAP processing. Traditional STAP processing solutions will be derived from a detection probabilistic perspective - the most pertinent metric for radar.