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A Kinematic Differential Global Positioning System (KDGPS) algorithm is developed. A number of mobile receivers is considered, one of which will be designated the 'reference station' which will have known position and velocity information at the beginning of the time interval examined. Satellite clock biases are used to model Selective Availability. The measurement situation on hand is properly modeled and a centralized estimation algorithm processing several epochs of data. The effect of uncertainty in the reference receiver's position and the level of receiver noise is examined. Monte Carlo simulations are performed to examine the ability of the algorithm to correctly estimate the non-reference mobile users' position and velocity despite substantial satellite clock errors and receiver measurement noise.