To address the need for robust positioning, navigation, and timing services in lunar environments, this paper proposes a novel onboard clock phase jump detection framework for satellite constellations using range measurements obtained from dual one-way inter-satellite links. Our approach leverages vertex redundantly rigid graphs to detect faults without relying on prior knowledge of satellite positions or clock biases, providing flexibility for lunar satellite networks with diverse satellite types and operators. We model satellite constellations as graphs, where satellites are vertices and inter-satellite links are edges. The proposed algorithm detects and identifies satellites with clock jumps by monitoring the singular values of the geometric-centered Euclidean distance matrix (GCEDM) of 5-clique sub-graphs. The proposed method is validated through simulations of a GPS constellation and a notional constellation around the Moon, demonstrating its effectiveness in various configurations.

To address the need for robust positioning, navigation, and timing services in lunar and Martian environments, this paper proposes a novel fault detection framework for satellite constellations using inter-satellite ranging (ISR). Traditional fault monitoring methods rely on intense monitoring from ground-based stations, which are impractical for lunar and Martian missions due to cost constraints. Our approach leverages graph-rigidity theory to detect faults without relying on precise ephemeris. We model satellite constellations as graphs where satellites are vertices and inter-satellite links are edges. By analyzing the Euclidean Distance Matrix (EDM) derived from ISR measurements, we identify faults through the singular values of the geometric-centered EDM (GCEDM). A neural network predictor is employed to handle the diverse geometry of the graph, enhancing fault detection robustness. The proposed method is validated through simulations of constellations around Mars and the Moon, demonstrating its effectiveness in various configurations. This research contributes to the reliable operation of satellite constellations for future lunar and Martian exploration missions.