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In this paper, we propose a new algorithm for fast estimation of camera motion directly in MPEG compressed domain, which starts from an existing and commonly used camera motion model to characterize the relationship between corresponding points of the neighboring frames, and then exploits the MPEG motion estimation and compensation techniques to derive closed-form estimation of all the three camera motion parameters, including pan, tilt, and zoom. The proposed algorithm features in extremely low computing cost and high processing speed with 50% improvement over the representative existing algorithms. It is suitable for implementation on hardware, such as Pan-Tilt-Zoom (PTZ) video camera. Furthermore, the three separated processing units (pan, tilt, and zoom) can be integrated into one simplified Fast PTZ Processing Unit. Comparative experiments also reveal that the proposed algorithm achieves similar estimation precision for all the three camera motion parameters.