A Novel Navigation Approach of Low Earth Orbit Satellites Formation Based on Reduced Relative Orbital Elements

Since the consumption of energy is the foundation of satellite’s life-span, an energy-saving relative dynamic model was introduced in the first decade of 21 century which is based on the Eccentricity/Inclination (E/I) vectors. In the new relative dynamic model, the variables are relative orbital elements. Later, navigation algorithms of guidance, navigation and control (GNC) system were designed for autonomous formation flying. Commonly, the observation inputs of the formation navigation algorithm are the relative position detected by spaceborne GPS receivers. In the navigation algorithm, the relative orbital elements (ROE) are transformed into the relative position by measuring equation. However, the measuring matrix has a strong nonlinearity. In this paper, an improved navigation approach is suggested based on the analysis of linearization errors, which is caused by the measuring equation. In our suggested approach, deviation of semi-major axis is computed based on the along-track excursion. The reduced relative orbital elements (RROE) are applied in EKF filter instead of ROE. The suggested navigation approach can well recognize the deviation of semi-major axis between satellites which is mainly caused by the air drag, resulting in a long-term stable and high-precision navigation algorithm.