## 3 Improvements in HY-2B POD
### GPS Antenna Offset Calibration  
For a high-quality determination of the LEO orbit, the additional in-flight calibration of the LEO GPS antenna is essential [25; 49]; the impact of unmodeled systematic errors on the HY-2B orbit is discussed. The validity of the GPS receiver antenna phase center for the HY-2B and a correction value are assessed in this section. The generation of the HY-2B GPS antenna phase center's location was based on the PCO vectors, (e.g., from the ground calibration), and no additional PCO was provided. As a starting point, the reduced-dynamic POD as well as an estimation of the PCO's z-component (i.e., the direction of the upward-facing antenna's boresight) were obtained for a 420-day period. A 20 mm systematic discrepancy in the modeled antenna phase center could be observed for the HY-2B (see Table 4). A 20 mm correction in the PCO z-component was adopted for further study, and the phase residual from POD was obviously improved, as shown in Figure 6. The negative residuals in the low-elevation area near the azimuth (0 degand 180 deg) were significantly reduced; Figure 6 shows a typical example for this situation. \begin{table}
\begin{tabular}{c c c} \hline
**Item** & **Reference (v, y, z) (mm)** & **Notes** \\ \hline CoM location & (+1332.000, \(-\)8.600, +3.400) & Nov. 2018 \\ \hline GPS antenna location & (+347.290, \(-\)175.140, \(-\)1372.680) & Main antenna (GPS a) \\ \hline GPS antenna PCO & (+0.0, +0.0, +20.0) & Estimated PCO-offset valid for ionosphere-free L1/L2 \\ \hline \end{tabular}
\end{table} 
Table 4: Coordinates for the GPS receiver and CoM in the body-fixed coordinate system. Figure 6: Sky plot of the residuals of the ionosphere-free L1/L2 carrier phase combination for HY-2B on 1 January 2019. The azimuth 0° of the antenna frame coincides with the +x-axis of the spacecraft’s body, which points into the flight direction. The residual approach [25; 50] was used to obtain the phase map (see Figure 7) from the ionosphere-free carrier phase residuals over a 420-day data span. The PCV map describes the empirical phase pattern corrections around the given phase center. The static multipath or other near-field effects caused by satellite components near the GPS antenna are potential sources of these variations. Similar to other missions, flight calibration for the GPS antenna and estimation of the PCV map from actual observations have been a standard practice for POD [16; 26; 49]. Considering fuel loss and deformation caused by in-flight temperature variations, a long-term analysis of the locations of the GPS antenna phase center was carried out. Table 4 shows the average value of the PCO z-component estimation, and the change in daily estimation is discussed (see Figure 8). The offset deviation of the PCO z-component fluctuated by about 21 mm since the start of the mission, while its offset changed by around 18 mm one year after the launch. The trend of 2-3 mm in the z-direction can be observed in Figure 8. Regular updates of the PCO of onboard receivers are indispensable to ensure high-precision orbit determination. Figure 8: Estimation of the PCO z-component (red triangle) for HY-2B at the beginning of the satellite’s mission (**left**) and one year later (**right**). The black line is the trend line fitted by least squares. Figure 7: Estimated azimuth elevation diagrams of the \(5^{\circ}\times 5^{\circ}\) PCV patterns for the HY-2B satellite. For an assessment of the HY-2B POD solutions with PCO/PCV correction, the uncorrected and newly corrected orbits were compared against the SLR observations. Figure 9 shows the SLR residuals of the two orbit solutions from 11 high-performance stations. It is clear that the PCO/PCV correction improved the overall accuracy of the POD solution for HY-2B. SLR validation demonstrated a 26% improvement for the orbit solution with PCO/PCV correction, and a 1.57 cm RMS of SLR residuals for the reduced-dynamic orbits was obtained. This means that the HY-2B POD product is of high quality, which is extremely important for an altimetry satellite.