Observability analysis of autonomous navigation using inter-satellite range: An orbital dynamics perspective

Abstract

This paper focuses on the observability of the autonomous navigation for multi-satellite systems using only inter-satellite range (ISR), especially under complicated orbital dynamical model. According to previous studies, the autonomous is unobservable because the Right Ascension of Ascending Node (RAAN) can be determined, which is derived under reduced dynamics model only considering J2 non-spherical perturbation. In order to analyze this observability issue further, the ISR measurement model with respect to orbital elements and the orbital dynamical model considering several kinds of perturbations are built. Through calculating the value of the partial derivative of ISR with respect to the RAAN, we find that the RAAN is observable under complicated dynamical model considering the non-spherical, the solar pressure and third-body perturbations. This is because that the solar pressure and third-body perturbations make the RAAN change rates of satellites different, so the overall rotation does not exist. These conclusions are verified by simulation cases. Furthermore, the simulation results show that the perturbation model error has remarkable impact on the RAAN estimation accuracy.