Trade-off Analysis for Lunar Augmented Navigation Service (LANS) Constellation Design

The establishment of a sustainable human presence on the Moon demands robust positioning, navigation, and timing (PNT) services capable of supporting both surface and orbital operations. This paper presents a comprehensive trade-off analysis of lunar frozen-orbit constellations for the Lunar Augmented Navigation Service (LANS), focusing on how the number of satellites and orbital parameters influence coverage, position dilution of precision (PDOP), orbit determination accuracy, receiver noise, and orbit insertion cost. Three Walker-constellation families based on frozen elliptical and circular orbits are examined to characterize their relative advantages across different semi-major axes and inclinations. Results show that larger semi-major axes enhance both polar and global coverage, though the optimal inclination depends on the constellation type and target service region. The south elliptical lunar frozen orbit (ELFO) Walker constellation provides superior performance for polar coverage and PDOP, whereas the circular lunar frozen orbit (CLFO) Walker configuration achieves the best global uniformity. Orbit determination errors and receiver noise both increase with larger semi-major axes and higher inclinations, reflecting weaker geometric observability and reduced received signal power at apolune for eccentric orbits. Orbit insertion analysis reveals clear trade-offs among transfer duration, characteristic energy ($C_3$) at trans-lunar injection, and insertion $\Delta V$: shorter transfers require higher insertion $\Delta V$, while low-energy transfers achieve smaller $\Delta V$ at the cost of months-long durations and higher $C_3$. These findings provide a systematic framework for designing LANS constellations for both regional and global coverage.