The GPS is used to determine the orbit of Geosynchronous Autonomous Transfer Vehicle (GATV). The visibility of the GPS satellites relative to the vehicle is analyzed in this paper. Moreover, inertial error, pseudorange and delta pesudorange models are established in the earth centered inertial coordinate system. The adaptive kalman filter with a fading factor is applied for the vehicle orbit determination. Simulation results show that even slope-lobe signal is used, GPS satellite visibility becomes lower as the vehicle flies higher. Usually, the visibility can not be improved effectively by increasing the receiver antenna gain and direct orbit determination is infeasible with only one epoch GPS observation. It is indicated that by using kalman filter, in the conditions of 1 km initial position deviation, 1 m/s initial velocity deviation, 10 m pseudorange mean square error and 0.05 m/s delta pseudorange mean square error, the final position deviation is smaller than 50 m while the velocity deviation is smaller than 0.02 m/s.