Constraining Constellation Rotation in BDS-3 Autonomous Navigation: Analytical and Simulation Studies of Intersatellite Directional Observations

The BeiDou navigation satellite system (BDS-3) has achieved global coverage and its autonomous navigation (AutoNav) capability is crucial for ensuring system autonomy and reliability. However, AutoNav systems relying solely on inter-satellite links (ISLs) face the challenge of constellation rotation, where the entire satellite constellation gradually drifts relative to an inertial reference frame due to cumulative orbit determination errors. This study investigates the impact of inter-satellite directional observations (ISDOs) on enhancing the AutoNav performance of the BDS-3 through theoretical analysis and numerical simulations. Through rigorous mathematical derivation and analysis of AutoNav covariance matrix, we have demonstrated that ISDOs exhibit sensitivity to satellite rotational errors, whereas ISLs lack this capability. The simulation results show that incorporating ISDOs effectively constrains the drift of satellite orbit inclination and right ascension of the ascending node (RAAN), thereby reducing horizontal orbit errors and user range errors (URE). This ensures stable long-term AutoNav performance. The 2-h predictions of satellite orbit and clock also demonstrate stability and accuracy, providing reliable real-time navigation services. We explore various ISDO topologies and frequencies, finding that simplified configurations, such as equipping only a single satellite with ISDOs capability or establishing a single ISDO link once a day, offer a cost-effective solution while maintaining acceptable performance. This study establishes ISDOs as a viable solution to constellation rotation while providing actionable recommendations for topology design and frequency management in future deployments.