Global optimization of GPS type satellite constellations

The paper studies satellite constellations for GPS-type navigation. As the number of satellites considered here is small (between 4 and 9), optimization of the parameters of the constellation is required in order to obtain a maximal coverage area. Due to the necessary meshing of the earth, the optimality criterion, which characterizes this coverage, is a discontinuous function of the parameters, so that classical local-optimization algorithms, based on differentiability, are not appropriate. A global optimization method is used that proceeds by adaptive random search within an apriori domain for the parameters. The method has proved highly flexible regarding the definition of the criterion and seems a promising tool for the complex optimization problem. Its application to the determination of optimal GPS-type constellations is presented. After preliminary tuning, the coverage areas obtained with this approach were much larger than those derived by symmetry considerations.