# Advancing the Solar Radiation Pressure Model for BeiDou-3 IGSO Satellites
## 3 Results  
In this study, 15 months of GNSS data from 1 January 2020 to 31 March 2021, collected by 21 iGMAS (International GNSS Monitoring and Assessment Service) stations [28] and 34 Multi-GNSS Experiment (MGEX) stations [29], were selected to determine precise orbits  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Panel** & **Area** & \(\alpha\) & \(\delta\) & \(\rho\) \\ \hline +\(X\) & 8.496 & 0.350 & 0 & 0.650 \\ +\(Z\) & 20.871 (4.956) & 0.870 & 0 & 0.130 \\ \(-Z\) & 20.871 (4.956) & 0.870 & 0 & 0.130 \\ SPs & 17.700 & 0.920 & 0 & 0.080 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Reference values of optical absorption \(\alpha\), reflectivity \(\delta\), and diffusion \(\rho\) as well as geometrical dimensions of satellite bus and solar panels (SPs) for BeiDou-3 IGSOs. Values in brackets were the areas of \(\pm Z\) panels without considering communication payloads. The unit of Area is m\({}^{2}\).  
and clocks, and their distribution is illustrated in Figure 2. The data processing was divided into the following two steps. In the first step, a static GPS/Galileo precise point positioning (PPP) solution is conducted for each station using the GFZ (GeoForschungsZentrum) MGEX products including precise orbits, 30-s clocks and Earth orientation parameters. In the second step, the station coordinates, zenith troposphere delays and receiver clock parameters obtained in the first step are kept fixed to determine BeiDou-3 IGSO orbits and clocks, ambiguities and inter-system bias (ISB) as well as SRP parameters. In data processing, the ionospheric-free combination of BeiDou-3 B1I/B3I, GPS L1/L2 and Galileo E1/E5a dual-frequency observations are used. Due to the sparse BeiDou-3 IGSO tracking network, data of a 2-day arc is computed to strengthen the solution. The first day of 2-day-arc solutions is extracted as the final daily solution in this study. General data processing settings are listed in Table 2.  
There are various SRP models involved in data processing. The ABW model is employed to estimate the surface optical coefficients, which are either not yet available or are inaccurate, but definitely needed for establishing a proper BW model for BeiDou  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Item** & **Description** \\ \hline Software & PANDA [30] \\ Orbits & Initial positions and velocities \\ Clocks & Estimated as white noise \\ Elevation cutoff & 5\({}^{\circ}\) \\ Sampling & 5 min \\ Weight & Elevation-dependent weighting: \(\sin(E)\) \\ Initial standard deviations & 10 mm and 1 m for ionospheric-free combination carrier phase \\  & and pseudo-range, respectively \\ Gravitational forces & Earth, Sun/Moon/Planets (DE405), solid earth, ocean and \\  & pole tides \\ Relativistic effects & IERS conventions 2010 [31] \\ Attitude model & GPS/Galileo [32], BeiDou-3 IGSOs [33] \\ Antenna thrust & igs\_metadata\_2081.snx \\ Ambiguity & Fixed for BeiDou-3 IGSOs [34] \\ Receiver ISB & Estimated as constants for each receiver \\  & Satellite antenna PCOs and PCVs of GPS L1/L2, Galileo \\  & E1/E5a and BeiDou B1I/B3I from jsg14\_2097.atx. For BeiDou \\ Antenna phase center model & and Galileo receiver antenna, the corrections for GPS L1/L2 \\  & are used for the BeiDou B1I/B3I and Galileo E1/E5a as their \\  & calibrations are unavailable in the jsg14\_2097.atx \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of precise orbit determination strategies.  
Figure 2: Distribution of GNSS tracking stations used for the BeiDou-3 IGSO POD. Red circles are iGMAS stations, and blue triangles represent MGEX stations.  
3 IGSOs. The ECOM1 and ECOM2 models are used to demonstrate their insufficiency for BeilDou-3 IGSOs, and the impact of the BW model is shown by the comparison of the ECOM1/ECOM2 and ECOM1 with the developed BW model. The ECOM1D + BW model suggested in the study shows a significant improvement in orbit quality during eclipse seasons.