A GNSS-aid star camera fusion approach towards statistically optimal attitude determination of ll-SST missions

Accurate attitude determination is crucial for orbit determination and time-varying gravity field recovery in low-low Satellite-to-Satellite Tracking (ll-SST) missions, such as GRACE and its successor GRACE-FO. The acquisition of attitude information largely depends on the fusion of data from multiple star cameras (SCs) on board, where the covariance (i.e., noise) along each axis of each SC must be well known. Additionally, the covariance information is also vital for the subsequent reprocessing of the fused attitude. However, previous studies have assumed that the covariance is fixed and diagonal, which may not be realistic. Inspired by noise methods based on relative comparison analysis and combined with GNSS-based attitude determination performance research, considering GNSS-based attitude as an independent reference for spacecraft attitude helps quantify the SC's covariance matrix. Based on this, we propose a GNSS-aided Star Camera Fusion (GSCF) approach based on the quaternion-based generalized least squares principle for statistically optimal attitude determination in ll-SST missions. This method allows for the construction of dynamic noise models for attitude sensors and the acquisition of fused attitude covariance information, while also revealing the strong negative correlation between short-term covariance and solar angle during blind events, along with SC anomaly detection parameter. The study finds that, for daily GRACE-FO operations, compared to traditional methods, GSCF achieves an average improvement of 10 arcseconds in attitude determination, especially in the spectrum of the one Cycle -Per-Revolution (CPR) frequency and its harmonics. In terms of inter-satellite pointing variations, GSCF shows improvements in the pitch angle (maximum improvement of 1.1 arcseconds) and yaw angle (maximum improvement of 0.3 arcseconds). Additionally, GSCF has an impact on along-track measurements of up to 0.02 um/s. While these effects may be negligible for the current GRACE-FO mission, next-generation ll-SST gravity missions with ultra-high-precision payloads will be extremely sensitive to attitude determination, and the proposed GSCF method is expected to provide significant benefits in such missions.