Abstract: The cost of satellite-based quantum positioning systems is expensive, and it is difficult to realize a standard quantum positioning system with six satellites or even reduced to three satellites. In order to further reduce the required number of satellites and the hardware cost of quantum positioning systems, this paper proposes a single satellite-based quantum positioning system and its enhancement system to further reduce ranging errors and improve positioning accuracy. The single-satellite-based quantum positioning system first aims to capture and track the ground target through the satellite, obtains the arrival time difference between the satellite and the ground target, the azimuth and pitch angle of the ground target with respect to the satellite, solves the position coordinates of the ground target in the pitch coordinate system of the satellite, and then converts the coordinates from the pitch coordinate system of the satellite to the geocentric inertial system to obtain the ground target position coordinates. On this basis, the satellite related data error, ranging link delay distance error and ground receiver measurement time deviation of the single-satellite positioning system are analyzed. The enhancement system is to plus a ground station in the single-satellite-based quantum positioning system, which can establish separate links with the ground station and the ground target, measure the arrival time difference between the two links, reduce the impact of the ranging link error, and finally make the error of the positioning system caused by environmental and other factors reach the centimeter level.