The Effectiveness of Solution Technique on the Autonomous Orbit Determination Accuracy of Lagrangian Navigation Constellation

Abstract

The accuracy of autonomous orbit determination of Lagrangian navigation constellation will affect the navigation accuracy for the deep space probes. Because of the special dynamical characteristics of Lagrangian navigation satellite, the error caused by different solution technique will cause totally different orbit prediction accuracy. We apply the RKF78 and RK4 to solve the motion equation of Lagrangian navigation satellites. There is no obvious difference when these two methods are used to calculate the orbits around the Earth-Moon triangular libration points. However the calculation error increases when RKF78 and RK4 are used to calculate the orbits around the Earth-Moon collinear libration points. Although the calculation error will be the order of 1×10⁸ meter, it doesn't cause big difference on the AOD with an AOD step of 1 hour. If the AOD step is bigger than 10 hour, the accuracy of autonomous orbit determination using RKF78 is better than the autonomous orbit determination accuracy using RK4.