Design Strategy for Cislunar Space Navigation Constellations Based on Navigation and Autonomous Navigation Performance

This paper proposes a bi-objective design strategy for cislunar navigation constellations, simultaneously optimizing navigation performance for target users and the autonomous navigation performance of constellation itself. The design variables include orbital characteristic parameters and inter-satellite phases, while the objectives are defined as the worst-case Geometric/Position Dilution of Precision (GDOP/PDOP) for users and the constellation's aggregated Dynamic and Geometric Dilution of Precision (DAGDOP). To address phase jump issues, the optimization is formulated on a product manifold and solved using the Riemannian steepest descent algorithm via the Pymanopt toolbox. Three constellations are designed by this strategy, which are six-satellite constellation for the Lunar South Pole station, a twenty-satellite constellation for lunar surface and lunar orbit users, and an eight-satellite constellation for a LEO-to-DRO transfer trajectory. Simulation results demonstrate that the optimized designs achieve the required geometric visibility, maintain GDOP/PDOP below specified usable thresholds (e.g., max PDOP of 5.96 for the South Pole, max GDOP of 2.28 for the transfer), and exhibit stable autonomous navigation performance. The study confirms the feasibility of the proposed strategy for designing practical, high-performance navigation constellation deployments across diverse cislunar mission scenarios.