# Solar Radiation Pressure Models for BeiDou-3 I2-S Satellite: Comparison and Augmentation
## 6 Conclusions  
Similar to Galileo satellites, deficiency in ECOM1 orbit solution for BeiDou-3 I2-S satellites was identified, in which a marked \(\varepsilon\)-angle-dependent radial error exists. The standalone ECOM1 fail to properly describe the acceleration acting on an extended body shape with a large area-to-mass ratio. Through the comparisons of the widely used SRP models i.e., ECOM1, ECOM2, and ABW, we found that all of them showed similar orbit accuracy of approximately 50 cm revealed by OBDs, but SLR validation results of ECOM1 confirmed larger \(\varepsilon\)-angle-dependent error, as well as a bias of nearly \(-17\) cm. Although the \(\varepsilon\)-angle-dependent errors in SLR residuals can be reduced by ECOM2, there was still a large bias. Fortunately, the ABW model can be used to overcome the issues.  
We established an analytical a priori cuboid model from coarse information of BeiDou-3 I2-S satellite. In addition, the empirical FFT model was obtained with accuracy of around 1 nm/s\({}^{2}\). By augmenting the ECOM1 with the a priori models, radial orbit accuracy was improved by approximately 35% w.r.t the ECOM1 solution. More importantly, the \(\varepsilon\)-angle-dependent error of SLR residuals was almost eliminated.  
Though the success of the applications of those priori models, further efforts should be performed for the orbit dynamics in eclipse seasons. Yaw attitude is another point to be carefully considered to model SRP. In addition, relevant modeling of SRP by ray-tracking method ([PERSON] et al., 2016) is in need for the detailed structure and the additional effects of shadowing and secondary intersections.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Solution** & **Along-Track** & **Cross-Track** & **Radial** & **3D** \\ \hline Cuboid + ECOM1 & 42.4 (43.5) & 22.5 (22.1) & 11.0 (12.1) & 49.3 (50.3) \\ FFT + ECOM1 & 42.6 (43.5) & 21.5 (17.0) & 11.8 (12.4) & 49.1 (48.4) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Mean value of OBDs in Along-track, Cross-track, radial, and three-dimensional (3D) for BeiDou-3 I2-S solutions with cuboid and priori model to argument ECOM1. Values in brackets was for eclipse season (unit: cm).  
Figure 7: Time series of OBDs for solutions using the a priori (**a**) cuboid model and (**b**) FFT model for BeiDou-3 I2-S. The red, green and blue curves represent OBDs in along-track, cross-track and radial direction, respectively.  
**Acknowledgments:** The IGS MGEX (Multi-GNSS Experiment), iGMAS (International GNSS Monitoring and Assessment System), and ILRS (International Laser Ranging Service) are greatly acknowledged for providing the multi-GNSS and SLR tracking data. The research is partially supported by the National Natural Science Foundation of China (Grant No. 41504009, 41574030).  
**Author Contributions:** [PERSON], [PERSON] and [PERSON] provided the initial idea for this study. [PERSON] designed the experiments. [PERSON] performed the experiments. [PERSON] and [PERSON] analyzed the data; [PERSON] contributed to the analysis tools. [PERSON] and [PERSON] gave valuable advice on the paper writing.  
**Conflicts of Interest:** The authors declare no conflict of interest.