# Orbit Determination Method for BDS-3 MEO Satellites Based on Multi-Source Observation Links
## 2 Orbit Determination Method
### Construction of Multi-Source Observation Equations  
According to the multi-source observation links mentioned above, three kinds of observation equations can be constructed:  
For the satellite-to-ground observation equation, the pseudo-distance and phase undifferenced data should be combined and linearized by the ionosphere-free method. Various system errors should be corrected. These errors mainly include the satellite clock error, differential code bias (DCB), relativistic effect, tropospheric delay, antenna phase center bias, Earth tide and multipath effect error. For the inter-satellite observation equation, the characteristics of the Ka-phased array time division system should be considered. When the sending time and the receiving time are reduced to the same observation time, bidirectional observation equations can be established, with various errors corrected. These errors mainly include relativity errors, antenna phase center correction and the inter-satellite link device delay. For the satellite-based observation equation, the method is basically the same as the satellite-to-ground observation equation. Compared with the satellite-to-ground observation model equation, the influence of tropospheric errors can be ignored, as the orbit of  
Figure 1: Multi-source observation network. LEO satellites is above the troposphere, but antenna phase winding and cycle slip repair should be considered. For the multi-source observation equations, differences in spatiotemporal reference and DCB should be fully considered, as they could be seen as inter-system bias (ISB). If there is a tight coupling relationship between the BDS-3 satellites and LEO satellites, the parameter adjustment method (PAM) can be applied to calibrate the ISB. The processing chart of the multi-source observation equations is shown in Figure 2 and the correction methods for observation errors are shown in Table 1.  
In conclusion, the multi-source observation equations can be described as follows: \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type** & **Error** & \begin{tabular}{c} **Satellite-to-** \\ **Ground** \\ \end{tabular} & \begin{tabular}{c} **Inter-** \\ **Satellite** \\ \end{tabular} & \begin{tabular}{c} **Satellite-** \\ **Based** \\ \end{tabular} & **Correction Method** \\ \hline \multirow{4}{*}{Satellite correlation} & Antenna phase center bias & \(\surd\) & \(\surd\) & \(\surd\) & Model correction \\ \cline{2-6}  & Antenna phase winding & \(\surd\) & \(\surd\) & \(\surd\) & Model correction \\ \cline{2-6}  & Relativistic effect & \(\surd\) & \(\times\) & \(\surd\) & Model correction \\ \cline{2-6}  & Earth tide & \(\surd\) & \(\times\) & \(\times\) & Model correction \\ \hline \multirow{4}{*}{Broadcasting path correlation} & \multirow{4}{*}{Ionospheric delay} & \multirow{4}{*}{\(\surd\)} & \multirow{4}{*}{\(\times\)} & \multirow{4}{*}{\(\surd\)} & \begin{tabular}{c} Model correction + \\ parameter \\ estimation \\ \end{tabular} \\ \cline{2-6}  & & & & & \\ \cline{1-1} \cline{2-6}  & Ionospheric delay & \(\surd\) & \(\times\) & \(\surd\) & \
\begin{tabular}{c} Ionosphere-free \\ combination \\ \end{tabular} \\ \cline{1-1} \cline{2-6}  & Multi-path effect & \(\surd\) & \(\times\) & \(\times\) & Model correction \\ \cline{1-1} \cline{2-6}  & Atmospheric drag & \(\times\) & \(\times\) & \(\surd\) & Model correction \\ \hline \multirow{4}{*}{Measurement correlation} & \multirow{4}{*}{Phase ambiguity} & \multirow{4}{*}{\(\surd\)} & \multirow{4}{*}{\(\times\)} & \multirow{4}{*}{\(\surd\)} &
\begin{tabular}{c} Model correction + \\ cycle slip correction \\ \end{tabular} \\ \cline{2-6}  & DCB & \(\surd\) & \(\surd\) & \(\surd\) & Fixed value \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Correction methods for observation errors. Figure 2: Processing chart of multi-source observation equations. \[\left\{