Symmetric Subset Selection and Rapid Reconfiguration for LEO-Enabled GNSS Monitoring Using a 2D Necklace Flower Constellation Framework

• 2D Necklace Flower Constellation selects symmetric LEO satellite subsets • Necklace Problem + linear congruences yield fast, systematic subset selection • 24-satellite subsets achieve 100% four-fold BDS-3 full-arc monitoring coverage • Equivalent-necklace reconfiguration recovers failures with zero orbital maneuvers • Boosts 5–6-fold coverage redundancy for resilient GNSS space-based monitoring The rapid expansion of large-scale Low Earth Orbit (LEO) satellite constellations offers new opportunities for space-based monitoring of Global Navigation Satellite Systems (GNSS). However, leveraging these constellations introduces challenges such as data redundancy and onboard resource constraints, necessitating efficient methods for selecting symmetric satellite subsets. This paper proposes a selection and reconfiguration framework based on 2D Necklace Flower Constellation (2DNFC) theory. By formulating the satellite selection problem as a number-theoretic “Necklace Problem” and solving linear congruence equations, the framework systematically identifies optimal subsets from large-scale parent constellations while preserving spatial geometric symmetry. Furthermore, leveraging the concept of “equivalent necklaces,” we propose a rapid reconfiguration mechanism that maintains monitoring performance without degradation in the event of satellite failures. Using the CENTISPACE LEO constellation as a candidate pool and full-arc monitoring of BeiDou-3 (BDS-3) as the objective, we compare the proposed method with conventional selection strategies. Results show that the 24-satellite subsets selected via the 2DNFC and double necklace methods achieve 100% four-fold coverage of the BDS-3 full arc, with significantly enhanced five-fold and six-fold coverage percentages. Moreover, in failure scenarios, subsets based on equivalent necklaces enable rapid reconfiguration without orbital maneuver and with no loss in monitoring performance. This study provides a theoretical foundation and empirical validation for constructing low-cost, efficient, and survivable GNSS space-based monitoring networks.