# Analysis of Precise Orbit Determination for the HY2D Satellite Using Onboard GPS/BDS Observations
## 4 Results and Discussion
### POD Precision Analysis for HY2D  
In this study, we also compare the calculated orbit using spaceborne BDS and GPS data with the precise Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS)-derived orbits provided by CNES. Figures 6 and 7, respectively, show the position differences in Radial (R), Tangential (T), and Normal (N) directions between the calculated orbit and the precise orbit.  
Figure 5: Variation of residuals in the POD for HY2D using spaceborne GPS data.  
Figure 6: The variation in errors for the HY2D satellite using spaceborne BDS data compared with CNES orbit.  
As can be seen from Figures 6 and 7, the variations in the radial direction have smaller fluctuation, which are basically located within \(\pm\)0.03 m. However, the fluctuation in the tangential direction is relatively bigger, and this may be related to the used models of atmospheric drag and solar pressure, which are hard to estimate exactly. It should be noted that the normal fluctuations of GPS are relatively smaller than BDS; this is related to the number of GPS satellites, which are more than the BDS satellites and the orbit precision of GEO and IGSO satellites is lower. To analyze the precision visually, Table 5 gives the accuracy statistics of the HY2D satellite using spaceborne BDS and GPS data. We can find that the mean values are close to zero, which illustrate that these error values are basically unbiased and have no obvious systematic errors. For spaceborne BDS data, the radial, tangential, normal and 3D accuracy can achieve 1.5 cm, 4.1 cm, 3.0 cm, and 5.3 cm, respectively, and the radial, tangential, normal and 3D accuracy are, respectively 1.5 cm, 3.5 cm, 2.0 cm, and 4.3 cm for spaceborne GPS data. However, because of the fewer satellites available, the consistency the BDS-derived orbits are slightly worse than the GPS-derived orbits.  
For validating the reliability of the used method and model strategies, we also utilize more spaceborne BDS and GPS data to conduct POD solutions for HY2D satellite, and the results of comparison with precise orbit provided by CNES are shown in Figures 8 and 9 in radial, tangential, normal and 3D directions.  
Figure 7: The variation in errors for the HY2D satellite using spaceborne GPS data compared with CNES orbit.  
\begin{table}
\begin{tabular}{c c c c} \hline  & & **Mean** & **RMS** \\ \hline  & Radial & 0.4 & 1.5 \\ BDS & Tangential & \(-\)0.8 & 4.1 \\  & Normal & 0.1 & 3.0 \\  & 3 DRMS & & 5.3 \\ \hline  & Radial & \(-\)0.1 & 1.5 \\ GPS & Tangential & 0.8 & 3.5 \\  & Normal & \(-\)0.5 & 2.0 \\  & 3 DRMS & & 4.3 \\ \hline \end{tabular}
\end{table}
Table 5: Accuracy statistics of POD for HY2D using spaceborne BDS and GPS data (unit: cm).  
As can be shown from Figures 8 and 9, the radial RMS values are basically 1.4\(\sim\)1.5 cm for BDS and GPS data, and the tangential and normal accuracies are slightly poorer compared to the radial direction. Overall, the precision based on spaceborne GPS data are slightly better than that of spaceborne BDS data, and the results are in agreement with the previous analysis, which shows that the used method and model strategies have a certain reliability. Moreover, Tables 6 and 7 show the accuracy statistics of HY2D. As can be shown from Tables 6 and 7, the average radial accuracy based on spaceborne BDS and GPS data are, respectively, 1.5 cm and 1.4 cm, the average three-dimensional accuracy are 5.3 cm and 4.3 cm, respectively. These results illustrate that the HY2D satellite, using spaceborne BDS and GPS data, can achieve the radial precision of 1.4\(\sim\)1.5 cm, the 3D position precision better than 5.5 cm, and the radial precision can satisfy high-precision altimetry applications.  
Figure 8: The RMS values for HY2D satellite using spaceborne BDS data.  
Figure 9: The RMS values for HY2D satellite using spaceborne GPS data.