Initial Results of Modeling and Improvement of BDS-2/GPS Broadcast Ephemeris Satellite Orbit Based on BP and PSO–BP Neural Networks

With the rapid development and gradual perfection of GNSS in recent years, improving the real-time service performance of GNSS has become a research hotspot. In GNSS single-point positioning, broadcast ephemeris is used to provide a space–time reference. However, the orbit parameters of broadcast ephemeris have meter-level errors, and no mathematical model can simulate the variation of this, which restricts the real-time positioning accuracy of GNSS. Based on this research background, this paper uses a BP (Back Propagation) neural network and a PSO (Particle Swarm Optimization)–BP neural network to model the variation in the orbit error of GPS and BDS broadcast ephemeris to improve the accuracy of broadcast ephemeris. The experimental results showed that the two neural network models in GPS can model the broadcast ephemeris orbit errors, and the results of the two models were roughly the same. The one-day and three-day improvement rates of RMS(3D) were 30–50%, but the PSO–BP neural network model was better able to model the trend of errors and effectively improve the broadcast ephemeris orbit accuracy. In BDS, both of the neural network models were able to model the broadcast ephemeris orbit errors; however, the PSO–BP neural network model results were better than those of the BP neural network. In the GEO satellite outcome of the PSO–BP neural network, the STD and RMS of the orbit error in three directions were reduced by 20–70%, with a 20–30% improvement over the BP neural network results. The IGSO satellite results showed that the PSO–BP neural network model output accuracy of the along- and radial-track directions experienced a 70–80% improvement in one and three days. The one- and three-day RMS(3D) of the MEO satellites showed that the PSO–BP neural network has a greater ability to resist gross errors than that of the BP neural network for modeling the changing trend of the broadcast ephemeris orbit errors. These results demonstrate that using neural networks to model the orbit error of broadcast ephemeris is of great significance to improving the orbit accuracy of broadcast ephemeris.