Relative orbit determination for formation flying spacecraft using differenced BeiDou carrier phase

A reduced-dynamic approach is developed for precise formation flying relative orbit determination using the double-differenced carrier phase of China's Bei-Dou navigation system as the main observable. The reduced dynamic technique combines the benefits of kinematic positioning techniques with those of a fully dynamic trajectory modeling to determinate the relative orbit using an extended Kalman filter, where the empirical accelerations are estimated using a first-order Gauss-Markov process noise model. In addition, the augmented filter state is estimated to compensate the incomplete dynamic model for better precision of the orbit solution. A simulated LEO scenario is established to investigate the performance of the proposed filtering schemes. The relative navigation results indicate that the filter provides accurate and compatible solution, which match an external reference solution to millimeter level when using the single-frequency measurements.