## 4 Experimental Analysis
### GNSS/LEO Combined POD during a Solar Storm  
A geomagnetic storm, which was triggered by a coronal mass ejection that broke out on 7-8 September 2017, was analyzed to investigate the impact of spaceborne observational errors on the BDS POD [35]. Studies show that the quality of the LEO constellations, i.e., the Swarm constellation, are severally degraded during the main phases of storms and that the maximum degradation of the orbit accuracy can be over 10 cm [18]. The main reason for the Swarm orbit accuracy degradation is the enhanced thermospheric mass density at the Swarm altitude, which increased the atmospheric drag for the LEO satellites. In addition, high-order ionospheric residual errors negatively affect the BDS/LEO combined POD. In the POD processing, if most observational errors have been carefully corrected by modeling or precise data processing strategies, the residuals will be in a normal distribution and close to the measurement noise level. Therefore, residuals are important indicators to assess the positioning or orbit determination errors. In this study, the Swarm-A and GRACE-A satellite POD residuals calculated with the geometric approach were first analyzed during the 7-9 September 2017 geomagnetic storm. The IF carrier-phase residuals of the Swarm-A and GRACE-A spaceborne GPS observations for days 007-009 are shown in Figure 8. The carrier-phase residuals of GRACE-A are much lower than those of Swarm-A, likely as a result of the much smaller carrier-phase measurement noise of GRACE-A, as seen in Figure 5. Therefore, considering the worst case, the Swarm-A observation residuals were used and applied in the observation simulation. In addition, the impaction times of the solar storm on the Swarm-A POD were 2:00-10:00 Universal Time (UT) and 15:20-23:00 UT, while the impaction times were 04:00-14:00 UT and 18:00-09:00 UT (+24 h) on 8 September 2017 for the GRACE-A POD. The initial impaction times are different for the two LEO satellites primarily because they are located on different orbital planes and at different altitudes. Therefore, it is necessary to consider the differences in the initial impaction times for the designed LEO satellites when adding the actual-observed residuals to the simulated spaceborne observations. Here, we first selected an LEO satellite on each orbital plane and then added the actual residuals calculated from the data on 8 September. The residuals added to the other satellites in this plane were lagged for a period of time depending on the specific satellite. For example, in the Walker 12/3/1 constellation, it takes 84 min for an LEO satellite to circle the Earth; the lag time for two adjacent satellites on each orbital plane is therefore 84 min/4 = 21 min. For the Walker  
Figure 7: The ODOP values of G05/G10/C02/C03/C06/C11 satellites with respect to the regional ground stations; the regional network and W2/1/0 LEOs; the regional network and W6/2/1 LEOs; the regional network and W12/3/1 LEOs; the regional network and W24/4/2 LEOs; and the regional network and W60/6/4 LEOs, which are shown from subplots left to right. The epoch time interval is 10 s.  
2/1/0 constellation, according to the number of LEO satellites tracking the BDS satellites, which is shown in Figure 9, only one LEO satellite at most simultaneously tracks each BDS satellite. The observation residuals of Swarm-A at 00:00 UT on 8 September start to be added to an LEO satellite when it flies over 30\({}^{\circ}\) E longitude and the observation residuals 49 min later are added to the next LEO satellite according to the lag time. Note that the actual effect of the solar storm on the BDS/LEO combined POD is very difficult to simulate because the impaction time and magnitude are very irregular and almost impossible to accurately simulate. This study makes an approximate simulation and the only certainty is that the initial impaction times for the LEO satellites in different orbital planes or at different altitudes are different.