Methodology for optimizing a Constellation of a Lunar Global Navigation System with a multi-objective optimization algorithm

Global Navigation Satellite Systems (GNSS) are not only used in terrestrial applications, but also in Low-Earth orbit satellites and in higher altitude missions. NASA’s Magnetospheric Multiscale (MMS) mission has demonstrated the capabilities of existing GNSS systems to provide positioning, navigation, and timing (PNT) services in the Cis-lunar space.The resurgence in plans by national space agencies for Lunar exploration presents a need for accurate, precise, and reliable navigation systems to ensure the safety and success of future missions.Moreover, the increased amount of Moon missions over recent years, shows the requirement of navigation capabilities for Low Lunar orbiters, Moon landers, Moon rovers, and manned missions.The success of Global Navigation Satellite Systems (GNSS) on Earth, presents an opportunity for the study of a potential design requirements and expected performance of a Lunar GNSS constellation.We have approached this problem through the methodology of multi-objective optimization; numerically simulating the orbits, and using the Position Delution of Precision (PDoP) as the figure of merit to optimise a set of 200 constellation designs and improving them gradually over 1864 generations. Over 12,000 unique constellation designs were generated with the best 10 constellations presented in this paper for consideration and further study. Compared to the literature, these 10 constellations achieved a 44% improvement in PDoP (2.73) using the same number of satellites in each constellation, and meeting the performance requirements of planned Lunar missions