Observability analysis and autonomous navigation for two satellites with relative position measurements

The autonomous navigation of multi-satellite systems using only on-board measurements is a fundamental task in many space missions. The main purpose of this study is to establish new methods for the autonomous orbit determination of a dual satellite system using relative position measurements only. A novel concept, k-order local weak observability, is proposed. Based on unperturbed Kepler orbit dynamics and J(2)-perturbed orbit dynamics respectively, sufficient and necessary conditions of k-order local weak observability are mathematically proved for the autonomous navigation system. Observability-based modified EKF, modified UKF, and modified SDREF are presented and used as navigation algorithms. Simulation results illustrate the performance of the developed navigation algorithms in comparison with the traditional EKF, UKF, and SDREF.