In order to improve the accuracy of the dynamical model used in the orbit determination of the Lagrangian navigation satellites, the nonlinear perturbations acting on Lagrangian navigation satellites are estimated by a neural network. A neural network based state observer is applied to autonomously determine the orbits of Lagrangian navigation satellites using only satellite-to-satellite range. This autonomous orbit determination method does not require linearizing the dynamical mode. There is no need to calculate the transition matrix. It is proved that three satellite-to-satellite ranges are needed using this method; therefore, the navigation constellation should include four Lagrangian navigation satellites at least. Four satellites orbiting on the collinear libration orbits are chosen to construct a constellation which is used to demonstrate the utility of this method. Simulation results illustrate that the stable error of autonomous orbit determination is about 10 m. The perturbation can be estimated by the neural network.
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 1×10 8 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.
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