Autonomous Constellation Fault Monitoring with Inter-satellite Links: A Rigidity-Based Approach

To address the need for robust positioning, navigation, and timing services in lunar environments, this paper proposes a novel fault detection framework for satellite constellations using inter-satellite ranging (ISR). Traditionally, navigation satellites can depend on a robust network of ground-based stations for fault monitoring. However, due to cost constraints, a comprehensive ground segment on the lunar surface is impractical for lunar constellations. Our approach leverages vertex redundantly rigid graphs to detect faults without relying on precise ephemeris. We model satellite constellations as graphs where satellites are vertices and inter-satellite links are edges. We identify faults through the singular values of the geometric-centered Euclidean distance matrix (GCEDM) of 2-vertex redundantly rigid sub-graphs. The proposed method is validated through simulations of constellations around the Moon, demonstrating its effectiveness in various configurations. This research contributes to the reliable operation of satellite constellations for future lunar exploration missions.