## 4 Experimental Analysis
### GNSS/LEO Combined POD during a Solar Storm
To better understand the influences of the spaceborne observational errors on the BDS POD, a purely geometrical approach was adopted here without considering any of the satellite dynamics. The orbit determination  
Figure 8: IF carrier-phase measurement residuals for the Swarm-A and GRACE-A spaceborne GPS observations. Figure 9: The number of tracked BDS C02 (left three subplots)/C06 (middle three subplots)/C11 (right three subplots) satellites by LEO satellites. The green, red, and blue dots represent the W2/1/0, W12/3/1, and W60/6/4 LEO constellation, respectively. results are shown in Figure 10. Figure 10 displays the POD error time series for the C02, C06, and C11 satellites. We can see from Figure 10 that the BDS orbits are severely affected by the spaceborne observational errors in the BDS/LEO combined POD mode. In the S2 scheme, each BDS satellite is observed by only one LEO satellite, as can be seen in Figure 9; therefore, the orbit of each BDS satellite is directly affected by the observational errors onboard this one LEO satellite. The 3D RMS values shown in Table 5 for the C02, C06, and C11 satellites are 1.18 m, 1.07 m, and 0.75 m, respectively. In the Walker 12/3/1 constellation, the BDS C02, C06, and C11 satellites are tracked simultaneously by two to five LEO satellites (Figure 9). Considering the times that the observational errors start to be added to each LEO satellite are different, the time that the  
Figure 10: Orbit differences between the estimated and the “references” of C02/C06/C11 satellites for scheme S2, S4, and S6, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**Item**} & \multirow{2}{*}{**Satellite**} & \multirow{2}{*}{**S2 (W2/1/0)**} & \multicolumn{4}{c}{**S4 (W/12/3/1)**} & \multicolumn{4}{c}{**S6 (60/6/4)**} \\ \cline{2-9}  & & & **C02** & & **C06** & **C11** & **C02** & **C06** & **C11** \\ \hline Mean ODOP & 297.5 & 237.5 & 203.1 & 84.0 & 96.4 & 72.6 & 40.2 & 38.8 & 18.7 \\ \hline \(\sigma_{0}^{2}\) [m\({}^{2}\)] & \multicolumn{4}{c}{\(1.12^{2}=1.25\)} & \multicolumn{4}{c}{\(1.83^{2}=3.35\)} & \multicolumn{4}{c}{\(0.88^{2}=0.77\)} \\ \hline \(\sigma_{0}^{2}\cdot ODOP_{mean}\) & 371.9 & 296.9 & 253.9 & 281.4 & 322.9 & 243.2 & 31.0 & 29.9 & 14.4 \\ \hline Orbital 3D RMS [m] & 1.18 & 1.07 & 0.75 & 1.10 & 1.15 & 0.69 & 0.60 & 0.43 & 0.44 \\ \hline \end{tabular}
\end{table} 
Table 5: Statistics of the ODOP and orbital 3D RMS values. POD starts to be impacted by large observational errors is different for each BDS satellite, resulting in different magnitude large POD errors and different impaction times. Even though part of the observational errors can be compensated for by a combined adjustment with different LEO satellites, they cannot be completely compensated for because of the small number of visible LEO satellites. The POD errors are nearly comparable to those in the S2 scheme, as can be seen in Figure 10.  
When the number of LEO satellites reaches 60, all the different types of BDS satellites can be tracked by 10-25 LEO satellites at the same time (see Figure 9). The fast change in the LEO geometric configuration, as well as the large number of LEO satellites involved in the adjustment of the combined POD, contribute to the improvement in the BDS orbit accuracy and the large observational errors are effectively reduced. The BDS orbit solutions are the best of the three schemes, as shown in Figure 10. The RMS values are 0.60 m, 0.43 m, and 0.44 m for the C02, C06, and C11 satellites, respectively (Table 5). There is another reason for the results shown in Figure 10. As explained before, the BDS POD results are associated with the ODOP value of the LEO constellation. However, they are also closely related to the spaceborne and ground-based observational errors. Note that more careful modeling or precise processing can be done to account for these observational errors. In this study, we do not try to eliminate these errors; instead, we attempt to weaken them by using a large LEO constellation.