Exploring the Design Space of Lunar GNSS in Frozen Orbit Conditions

Abstract: The past decade has witnessed a growing interest in lunar exploration missions. The autonomy of lunar surface and in-orbit missions is, however, dependent on accurate and instantaneous navigation services. These services can not be provided by current Global Navigation Satellite Systems (GNSS) whose signals suffer from poor geometry and coverage in the vicinity of the Moon. Preliminary results of a systems architecture study on a new satellite navigation system orbiting the moon are presented. Lunar frozen orbit conditions under J2, C22 and third-body perturbations are assumed. The 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) framework is used to optimize the satellite constellation design problem, with a fitness function that takes into account performance, cost, availability and station-keeping deltaV. The performance metric is based on the Geometric Dilution of Precision (GDOP), which is computed over a grid of 500 equidistant points on the lunar surface. Additionally, the input satellite orbits used in the GDOP computation are obtained from high-fidelity orbit propagation using NASA General Mission Analysis Toolbox. Finally, satellite costs are based on satellite dry mass estimates derived from the power budget analysis assuming a satellite lifetime of 10 years. Results show that Lunar GNSS constellation with 20 satellites at frozen orbits can achieve satisfactory performance at mid-latitudes but not at the poles.