Seeking GDOP-optimal Flower Constellations for global coverage problems through evolutionary algorithms

In this paper, given a certain number of satellites (NsatNsat), which is limited due to the sort of mission or economical reasons, the Flower Constellation with NsatNsat satellites which has the best geometrical configuration for a certain global coverage problem is sought by using evolutionary algorithms. In particular, genetic algorithm and particle swarm optimization algorithm are used. As a measure of optimality, the Geometric Dilution Of Precision (GDOP) value over 30000 points randomly and uniformly distributed over the Earth surface during the propagation time is used. The GDOP function, which depends on the geometry of the satellites with respect to the 30000 points over the Earth surface (as ground stations), corresponds to the fitness function of the evolutionary algorithms used throughout this work. Two different techniques are shown in this paper to reduce the computational cost of the search process: one that reduces the search space and the other that reduces the propagation time. The GDOP-optimal Flower Constellations are obtained when the number of satellites varies between 18 and 40. These configurations are analyzed and compared. Owing to the Flower Constellation theory we find explicit examples where eccentric orbits outperform circular ones for a global positioning system.