In order to improve the positioning precision of satellites and minimize their positioning error

the optimal geometric configuration of the constellation and 4 satellites positioning problem which has relatively better geometric position and lesser number of satellites are studied on the basis of analysis on the positioning error of satellites. The relationship of the optimal geometric distribution of the constellation and the positioning error is given. Simulation results indicate that in the satellite constellation

the geometrical dilution of precision(GDOP)of the constellation is determined by the height and uniformity of the distribution of the satellites. The difference between the elevation and azimuth angle of topmost and lower satellites also are influence factors of GDOP. By the calculation and experiments

it is shown that in course of GPS systems positioning

there exists a set of optimal geometric configuration constellation consisted of four satellites

and the corresponding GDOP is minimum

i.e.1.5812.