New Method and Accuracy Analysis for Medium and Long-term Orbit Prediction of BDS-3 Satellites

Long-term orbit prediction serves as an effective method to suppress the overall rotation of the inertial frame in autonomous navigation of satellite navigation systems, and the main factor influencing the accuracy of long-term orbit prediction is the uncertainty associated with the solar radiation pressure perturbation model. This paper proposes a method of modeling and updating the ECOM-5 solar radiation pressure model parameters for long-term orbit prediction, and evaluates its performance by fully utilizing the correlation between the solar radiation pressure coefficient and the solar altitude angle. Taking 24 Medium Earth Orbit (MEO) satellites and 2 Inclined Geosynchronous Orbit (IGSO) satellites of the Beidou-3 Global Navigation Satellite System (BDS-3) as examples, 18 groups of 90-day orbits were predicted from 1 January 2022 to 1 June 2023. Then the precise ephemeris of the Center for Orbit Determination in Europe (CODE) was used as the reference orbit to evaluate the performance of long-term orbit prediction. The experimental results indicate that when adopting the new orbit prediction method proposed in this paper for 90-day orbit prediction of navigation satellites, for MEO satellites, the average Root Mean Square (RMS) of the three-dimensional position error on the 30th, 60th, and 90th day is approximately 180, 650, 1400 m, respectively, and that of the average URE RMS of the orbit is 18.79, 61.43, 124.00 m, respectively. The RMS mean values of the orbital inclination angle error $\Delta i $ are 6.07, 9.76, 12.38 mas, respectively, and those of the right ascension of the ascending node error $\Delta \varOmega $ are 6.47, 11.24, 14.88 mas, respectively. For IGSO satellites, the average RMS of the three-dimensional position error on the 30th, 60th, and 90th day is approximately 260, 1000, 2200 m, respectively, while the prediction errors of i and Ω are comparable to those of MEO satellites. Therefore, it can be concluded that the method in this paper exhibits high accuracy in long-term orbital predicting positions and orbital orientation parameters i and Ω, which is expected to provide essential support for mitigating the overall rotation of autonomous navigation of navigation satellite constellations.