Minimum Number of Satellites for Three-Dimensional Continuous Worldwide Coverage

Global positioning by means of satellites requires simultaneous observation by at least four satellites. The problem is to determine the minimum number of satellites and the corresponding orbital geometry necessary to satisfy this requirement on a continuous basis. To model the problem, a fixed number of users are assumed uniformly distributed in a known manner over the surface of the earth, and the satellites are restricted to exist in either three or four orbital planes. However, the orbit radius and inclination angle are left as variables. Under these assumptions, and starting with a small number of satellites which will be increased afterwards, an algorithm is developed to determine the visibility of satellites at each surface location. In this way it is possible to specify the minimum number of satellites needed by any desired orbital geometry. It is found that the number of satellites required for three-dimensional continuous worldwide coverage decreases as the orbit radius is increased. There appears to be no general trend regarding the effect of the inclination angle on the minimum number of satellites.