## 4 Satellite Precision Orbit Determination and Accuracy Analysis
### Influence of PCV on HY-2B/C/D Satellite Orbit Determination  
While it is possible to measure a priori PCV values for LEO satellites prior to launch, the satellite's flight environment, influenced by factors such as atmospheric pressure and temperature, significantly deviates from the ground environment. This leads to notable disparities between the actual PCV values in orbit and the a priori PCV values determined on the ground. Consequently, in-orbit PCV estimation holds pivotal significance for achieving precise orbit determination of the satellite. The main estimation methods of the LEO satellite antenna PCV model include the direct method and residual method [39]. The direct method of estimation is to add the unknown parameter PCV into the observation equation and solve it together with other parameters to be solved. Although the physical meaning is clear, the data calculation is large. In the process of orbit determination, the residual method uses the carrier phase residual under different azimuth and elevation angles to model, and builds the final PCV model by several iterations. Although PCV will be affected by other parameters in the orbit determination process, most of the PCV errors will be reflected in the carrier phase residual. The LEO antenna is divided into a different resolution (n\({}^{\circ}\)\(\times\) n\({}^{\circ}\)) grid space, and the average value of phase residual in the range of \(\pm\)n\({}^{\circ}\)/2 is calculated with the grid node as the center. Because the data are not evenly distributed in the grid space, there is no residual value in some areas, and the PCV value of the grid point cannot be obtained. In order to avoid the \"void\" phenomenon, the PCV of this part of grid points is assigned a value of 0, and the complete PCV model can be obtained. The observed residual is affected by the clock offset, and the influence of this error is mitigated through multiple iterations, typically requiring 3-5 iterations to achieve convergence. The satellite-borne GPS data from the HY-2B and HY-2C satellites collected between 14 and 20 December 2020, as well as data from HY-2D satellite from 20 to 26 September 2021, were used to estimate the PCV model by using the direct method and residual method, and the results are shown in Figure 6. Upon comparing the PCV models derived from these two different methods, it becomes apparent that they exhibit similar distribution characteristics, yet some differences are discernible. The direct method involves solving for the PCV at individual grid points as unknown parameters, leading to a more precise estimation of PCV. Consequently, the PCV map resulting from this method displays a speckled distribution. On the other hand, the residual method for PCV estimation entails averaging the residual errors across the grid space. As a result, the PCV values at adjacent grid points tend to be more similar, and the PCV map is characterized by a striped distribution. \begin{table}
\begin{tabular}{c c} \hline
**Model/Parameters** & **Description** \\ \hline Global Gravity Field Model & XGM2019 [36] \\ N-body & JPL DE405 [37] \\ Solid-earth tides & TIDE2000 \\ GPS antenna phase center variation & PCV.I14 \\ Ocean Tides & FES2014 [38] \\ Elevation cutoff & 5\({}^{\circ}\) \\ Sampling interval & 1 s \\ GPS orbit & CODE precision orbit (15 min) \\ GPS precise clock offset & CODE precise clock offset (30 s) \\ \hline \end{tabular}
\end{table} 
Table 4: Reduced-dynamic orbit determination strategy of HY-2B/2C/2D satellites. As shown in Table 5, after adding the PCV model, the orbit determination accuracy is improved. The carrier phase residual is reduced by 0.4\(\sim\)0.6 mm, and the 3D RMS of the reduced-dynamic orbit to CNES orbit intercomparison was reduced by 0.2\(\sim\)0.3 cm. The direct estimation method is to solve the PCV value of each grid. When the PCV model with a higher resolution is estimated, the calculation is large and the time required is long.