# In-Orbit Attitude Determination of the UVSQ-SAT CubeSat Using TRIAD and MEKF Methods
## 5 Conclusions  
UVSQ-SAT CubeSat aims to validate innovative technologies in-orbit for a future constellation to study the Earth's energy imbalance. UVSQ-SAT has been in orbit since 24 January 2021. To improve the UVSQ-SAT's reflected solar radiation and outgoing long-wave radiation measurements at the top of the atmosphere, the UVSQ-SAT's attitude must be accurately known. Two different methods were implemented to determine the UVSQ-SAT CubeSat's attitude, and they are based on real data from space observations.  
The first method developed is based on the TRIAD algorithm. The accuracy of the UVSQ-SAT attitude knowledge obtained with the TRIAD method is close to \(\pm 3^{\circ}\) (at one \(\sigma\)) in sunlight. During eclipse periods, the accuracy of the UVSQ-SAT attitude knowledge is \(\pm 14^{\circ}\) (at one \(\sigma\)). In this observation phase, accurate knowledge of the CubeSat attitude is more difficult to obtain. This mode of operation with other sensors (Earth radiative sensors instead of solar visible photodiodes) brings limits. Moreover, the TRIAD method does not correct all measurement noises.  
The MEKF method allows us to estimate and correct instrument noise. It performs the real-time calibration of the UVSQ-SAT gyrometer. The MEKF method computes the UVSQ-SAT attitude knowledge with an accuracy similar to TRIAD in sunlight, but with an accuracy of \(\pm 10^{\circ}\) during eclipse periods (at one \(\sigma\)). There are limitations to the MEKF method, such as the lack of continuous data. This is a limiting factor since it leads to large divergence errors. The prediction becomes better when the time between two measurements is short. Then, the linearization becomes more realistic. Reducing the time-step could be beneficial for future CubeSats, and ground-based tests in near-space conditions would be recommended to optimize the various parameters.  
The methods presented on this manuscript are based on direct measurements (TRIAD) or Kalman filters (MEKF). Another approach would be to use neural networks to determine the UVSQ-SAT satellite's attitude as described in [31]. The neural network will be implemented and trained in-orbit in sunlight to improve the attitude determination accuracy during eclipse periods. The training will be based on the previously described methods, and the performance of the new method will be evaluated to assess the ability of the method to be implemented for the future satellites of the constellation.  
Conceptualization, A.F., C.D., T.B., M.M.; methodology, A.F., C.D., T.B. and M.M.; software, A.F., C.D.; validation, C.D.; resources, M.M.; writing--original draft preparation, A.F., C.D., T.B., M.M.; writing--review and editing, A.F., C.D., M.M., A.M., A.S., P.K. and T.B.; visualization, A.F., C.D., M.M.; supervision, M.M.; project administration, M.M.; funding acquisition, M.M. All authors have read and agreed to the published version of the manuscript.  
This research was mainly funded by Centre National de la Recherche Scientifique (CNRS, France), UVSQ (Universite de Versailles Saint-Quentin-en-Vleines, France), and Agence Nationale de La Recherche (ANR, France). This work was supported by the Programme National Soleil Terre (PNST) of CNRS/INSU (France) co-funded by CNES and Commissariat a l'energie atomique (CEA, France).  
Not applicable.  
The authors acknowledge support from the Centre National de la Recherche Scientifique (CNRS, France), the Centre National d'Etudes Spatiales (CNES, France), and Office National d'Etudes et de Recherches Aerospatiales (ONERA, France).