Exploring the Design Space of Lunar GNSS in Frozen Orbit Conditions

We have witnessed a growing interest in lunar exploration missions in the last few years, with the announcement of NASA's Deep Space Gateway, the launch of several uncrewed missions and the involvement of private companies. However, there is currently no reliable means of accurate and instantaneous navigation in the vicinity of the Moon. This poses operational limitations on the autonomy of lunar robotic and small satellite missions. We present the preliminary results of a systems architecture study conducted on a new satellite navigation system orbiting the Moon that would effectively extend the Global Navigation Satellite Systems (GNSS) space service volume to cislunar space. We constrain the analysis to lunar frozen orbits under J2, C22 and third-body perturbations, to achieve stable lunar orbits. The problem formulation includes the following design decisions: (1) Orbit semi-major axis, (2) Number of satellites, (3) Number of orbital planes, (4) Satellite phasing in adjacent planes, (5) Orbit eccentricity and (6) Argument of periapsis. The Borg Multi-Objective Evolutionary Algorithm (MOEA) is used to optimize the satellite constellation design using multiple crossover and mutation operators that can adaptively be selected at runtime. The fitness function takes into account performance, cost, availability and station-keeping delta-V. Specifically, the performance metric assessment is based on the Geometric Dilution of Precision (GDOP), which is computed over a grid of 500 equidistant points on the lunar surface. The input satellite orbits used in the GDOP computation are obtained from high-fidelity orbit propagation using NASA's General Mission Analysis Toolbox (GMAT). The space segment cost model considers satellite constellation development and production costs. Single satellite costs are based on satellite dry mass estimates derived from the power budget analysis assuming a satellite lifetime of 10 years. The results of the study show that high-performing Lunar GNSS constellations relying on frozen orbits alone can be achieved with 20 satellites but they may be suboptimal for high-latitude regions.