  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.
