# Precise Orbit Determination for GNSS Maneuvering Satellite with the Constraint of a Predicted Clock
## 3 Experiment Analysis
### Algorithm Validation with Normal Data  
It is hard to evaluate the proposed method during maneuvering, because the precise reference orbits are usually unavailable for maneuvering satellites. Therefore, the clock-constrained POD strategy is first evaluated using the normal observations during non-maneuvering periods when the dynamic orbits can be determined precisely and used as a reference in our evaluation. Specifically, the traditional dynamic POD method is employed to determine the 48-h reference orbits for all satellites during the whole experiment periods. Then, we assume a satellite experiences maneuver in the last 2 h of each POD arc when the POD processing is switched from the dynamic method to the RPPP method for the maneuvering satellite. For comparison, the clock constraining function is turned on and off to generate two orbit solutions during the maneuvering periods. The results are both compared to the reference orbits to generate the orbit differences in the along-track, cross-track and radial directions for the last 2 h of each POD arc. Figure 4 presents the RMS of orbit differences of each satellite in the along-track, cross-track and radial directions for the two RPPP orbit solutions. G04 satellite is excluded in the process because it is flagged as unhealthy for the whole period. As shown in the figure, when the constraints of predicted satellite clocks are not imposed, the average RMS of GPS satellites in the radial, cross-track and along-track directions is 69.3 cm, 5.4 cm and 5.7 cm and that of the BDS satellites is 153.9 cm, 12.8 cm and 10.0 cm, respectively. The GPS satellites exhibit higher orbit precision in all directions than the BDS satellites because of much better observation geometry. The RMS in the along-track and cross-track directions is comparable for each satellite, which is much smaller than that in the  
Figure 3: Distribution of stations used in the POD experiment (red: GPS + BDS stations, blue: GPS-only stations). radial direction. When the constraints of predicted satellite clocks are imposed, the average RMS in all directions is reduced, especially in the radial direction where the RMS is reduced by a factor of 7-11, with the value of 9.7 cm and 13.4 cm for GPS and BDS satellites. Equipped with Cs clocks, the G08 and G24 satellites exhibit obviously larger RMS in the radial direction than the other GPS satellites. Like the standard PPP, the precision of the RPPP POD method depends on the orbital dilution of precision (DOP) that reflects the observation geometry [9]. The DOP in the radial direction is donated as the RDOP and the HDOP represents the DOP in the plane orthogonal to the radial direction, which includes the along-track and cross-track directions. Table 2 lists the HDOP and RDOP for different satellites. Only two GPS satellites are listed as representative, because other GPS satellites have the similar DOP values. It can be seen that the HDOP is significantly smaller than the RDOP, which is consistent with the fact that the orbit accuracy in the along-track and cross-track directions is much better than in the radial direction, as shown in Figure 4. The DOPs of BDS satellites are larger than that of GPS satellites resulting in a much lower orbit accuracy of BDS as well. Figure 5 illustrates the orbit differences of the two solutions in the along-track, cross-track and radial directions from 22:00:00 to 24:00:00, DOY 124, 2017. As shown in this figure, the RPPP POD solution without clock-constraint exhibits dramatically larger orbit differences in the radial direction than the solution with the clock-constraint, while in the along-track and cross-track directions, both solutions have similar orbit differences whether the clock-constraint is imposed or not. Thus, a clock-constraint in RPPP POD can bring the orbit solution significant improvement in the radial direction but a few improvements in the along-track and cross-track directions.