Selection of GPS satellites for the optimum geometry

In GPS applications, the position and clock error of the station can be obtained from observations of four visible satellites. The selection of the four satellites, or their geometrical configuration with respect to the station, affects directly the positioning accuracy. The best accuracy is realized when the volume of the tetrahedron formed by the four satellites is maximised. In this paper, based on the work of Kihara et al., we have discussed in depth the property of the tetrahedron and derived formulae for computing its volume. A practical example demonstrates that our formulae are more reasonable and accurate.