A Statistically Optimized Star Camera Fusion Approach for the Attitude Determination of Low-Low Satellite-to-Satellite Tracking Mission

Precise attitude determination is essential for orbit determination as well as time-variable gravity field recovery from low-low Satellite-to-Satellite Tracking (ll-SST) missions, e.g., GRACE and its successor, GRACE-FO. The acquisition of attitude information relies on the fusion of multiple onboard star cameras (SC), where a precise estimation of noise covariance (between three axes and between SCs) is required. However, the previous assumption of noise may be unrealistic. In this study, we used the GNSS-orbit to benchmark SC and obtained dynamic, non-homogeneous, and robust noise covariances for the first time. Furthermore, these realistic covariances enable a quaternion-based generalized least squares solution towards a statistically optimal attitude determination. This novel framework, which makes use of GNSS as ’prior’ information to establish a Bayesian-like fusion, is referred to as the GNSS-aided Star Camera Fusion (GSCF) approach. It is used for GRACE-FO attitude determination throughout 2020 for demonstration purposes. Compared to the traditional method that assumes empirical covariance matrices, GSCF has a major impact on a cycle per revolution (CPR) frequency and its harmonics with a magnitude of [-9.6, 8.5] arcsec at the confidence level 99%. Further tests in terms of inter-satellite pointing analysis confirm the improvement of GSCF over the traditional method, i.e., with a long-term mean reduction of pointing variation by 0.037 mrad in roll and 0.046 mrad in pitch direction. In addition, our approach has shown a consistent improvement in the daily mean range AOC (antenna offset correction), i.e., up to 18.40 nm, and the range rate AOC standard deviation has also been consistently reduced, up to 1.17 nm/s. Finally, the main impact on the inter-satellite ranging rate is within 2 nm/s. While these effects are likely marginal for current GRACE-FO, the next-generation ll-SST gravity missions with ultra-high-precision payloads (e.g., laser ranging system with nanometer-level accuracy) that will be extremely sensitive to the attitude determination can benefit from the proposed GSCF method.