Implicit UKF and its observability analysis of satellite stellar refraction navigation system

Satellite autonomous navigation by stellar refraction is a type of autonomous celestial navigation method that uses high-accuracy star sensors instead of Earth sensors to provide information regarding Earth's horizon. There are two kinds of measurements of satellite stellar refraction navigation. They are the apparent height and the stellar refraction angle. A better navigation performance can be achieved by the stellar refraction angle rather than the refraction apparent height. However, the measurement model of the stellar refraction angle is an implicit function. The traditional UKF and observability analysis methods are not applicable to the system with an implicit measurement model. The implicit UKF (IUKF) and its observability analysis method are proposed in this paper. The equivalent observability matrix is constructed based on the IUKF algorithm. Furthermore, the best scheme for observation of the stellar refraction angle is studied using this new IUKF and its observability analysis. Both the observability analysis and simulation results show that a significant improvement in navigation performance can be achieved by the rotating observation of the stellar refraction angle.