# Advancing the Solar Radiation Pressure Model for BeiDou-3 IGSO Satellites
## 3 Results
### Performance of SRP Models for BeiDou-3 IGSO Satellites
#### 3.2.2 Orbit Assessment Based on Orbit Boundary Discontinuities  
The orbit DBD in the radial, along- and cross-track, and as well as three-dimension (3D) directions are defined as [35]:  
\[(\Delta R,\Delta A,\Delta C)^{T}=M\cdot(X_{i+1}-X_{i},Y_{i+1}-Y_{i},Z_{i+1}-Z_{ i})^{T} \tag{14}\]  
\[T_{3D}=\sqrt{\left(\Delta R\right)^{2}+\left(\Delta A\right)^{2}+\left(\Delta C \right)^{2}} \tag{15}\]  
where \(i\) and \(i+1\) refer to days. \((X_{i},Y_{i},Z_{i})\) and \((X_{i+1},Y_{i+1},Z_{i+1})\) are the geocentric satellite positions of the last epoch of day \(i\) and the first epoch of day \(i+1\), respectively. \(M\) is the rotation matrix converted from a geocentric terrestrial reference frame to an orbital frame. The terms \(\Delta R\), \(\Delta A\), \(\Delta C\) and \(T_{3D}\) are orbit DBDs in the radial, along- and cross-track as well as three-dimension (3D) directions, respectively. The mean values of 3D orbit DBDs of satellites C38, C39 and C40 for the solutions with ECOM1, ECOM2 and ECOM1 + BW models inside and outside eclipse seasons are listed in Table 6. For the non-eclipse periods, the ECOM1 + BW solution provides the best orbit quality in the three-dimension direction, followed by the ECOM2 and ECOM1  
Figure 9: Satellite C39 clock fitting residuals for the ECOM1 + BW (blue) and ECOM1D + BW (red) solutions on DOY 74–75, 2021(\(\beta\approx-1.8^{\circ}\)). solutions. Figure 10 shows the DBD \((|\Delta R|,|\Delta A|,|\Delta C|)\) statistics of BeiDou-3 ICSOs in the radial, along- and cross-track directions outside eclipse seasons. The ECOM1 + BW model shows the best performance, except that the satellite C39 cross-track orbit consistency for the ECOM1 + BW model is slightly worse than that of the ECOM2 model. The radial and 3D orbit consistency of BeiDou-3 ICSOs for the ECOM1 + BW solution improves by about 2.2 (32.7%) and 5.1 cm (29.5%), 1.2 (21.1%) and 2.6 cm (17.6%) relative to the solutions with the ECOM1 and ECOM2 models on average, respectively. To investigate whether orbit DBDs show \(\beta\) -dependent variations like daily clock residuals (Figure 4), the orbit DBD time series of BDS-3 ICSO C39 based on different SRP models in along-track, cross-track, and radial directions are given in Figure 11. It can be clearly seen that there are no \(\beta\) -dependent systematic variations in orbit DBDs. This should be due to the fact that the \(\beta\) -dependent systematic orbit errors are highly correlated from one day to the next and cannot be reflected in the overlap statistics. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**SRP Model**} & \multicolumn{2}{c}{**C38**} & \multicolumn{2}{c}{**C39**} & \multicolumn{2}{c}{**C40**} \\ \cline{2-7}  & **NE** & **E** & **NE** & **E** & **NE** & **E** \\ \hline ECOM1 & 19.1 & 67.3 & 14.9 & 58.8 & 17.8 & 90.0 (20.6) \\ ECOM2 & 16.7 & 66.5 & 12.4 & 57.8 & 15.2 & 90.8 (17.6) \\ ECOM1 + BW & 12.1 & 66.3 & 11.0 & 55.3 & 13.3 & 84.1 (16.7) \\ ECOM1D + BW & - & 17.7 & - & 11.3 & - & 13.3 (13.1) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Mean 3D orbit DBDs of BeiDou-3 ICSOs for the ECOM1, ECOM2, ECOM1 + BW and ECOM1D + BW solutions in cm. “NE” and “E” denotes the non-eclipse and eclipse seasons, respectively. For C40, values in and out of brackets were for the first two and third eclipse seasons, respectively. Figure 10: Mean orbit DBDs \((|\Delta R|,|\Delta A|,|\Delta C|)\) s for the ECOM1, ECOM2 and ECOM1 + BW solutions of BeiDou-3 ICSOs in along-track (A), cross-track (C), and radial (R) directions outside eclipse seasons. From Table 6 and Figure 11, the BeiDou-3 IGSO orbit consistency shows a significantly lower performance during eclipse seasons. The orbit 3D DBDs during eclipse seasons are 4-5 times larger than those in the non-eclipse seasons, except that C40 orbit 3D DBDs inside its first (1-23 January 2020) and second (28 June-22 July 2020) eclipse seasons during our experiment only increase by 15-20%.