## 4 Orbit-Tracking and -Determination Algorithm Simulation
### In-Orbit Measurement Results for Orbit Determination  
To better verify the unidirectional orbit-determination algorithm, the extended user conducted in-orbit validation. After the extended user was launched into orbit, an application for access to the inter-satellite link was made and planning for the link arc segment and time slot resources was carried out in advance. Both parties obtained each other's position and velocity information from the almanac, thereby obtaining the spatial coordinate pointing. Once the extended user entered the link mode, it utilized a wide-range capture capability to complete unidirectional link establishment and selected 5 min of 20 sets of unidirectional ranging data for clock adjustment and calculation. Under the condition of meeting the inter-satellite link's time and frequency precision constraints, bidirectional link communication was achieved. Based on the telemetry data received on the ground, measurements from universal time coordinated (UTC) 13 June 2022, to 16 June 2022, were selected. The extended user accessed the inter-satellite link for 1 h each day, establishing links with four different navigation satellites every minute within that hour. A 2 day sliding window of ranging values was used for orbit-determination calculation, with the results shown in Figure 9. Analysis indicates that the inter-satellite link's orbit-determination performance is stable, with a 100% availability rate for the determined orbit values and ranging precision better than 0.6 m. Here, R represents the radial component, T represents the component along the motion trajectory direction and N represents the normal component perpendicular to R and T.  
To further analyze the precision of the in-orbit orbit-determination results, a comparative analysis of the in-orbit orbit-determination accuracy was conducted using the satellite platform GNSS orbit-determination results and the ground orbit-determination results as \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & \multirow{2}{*}{**Data Arc Segment**} & **Time Slots** & **Time Slots** & **24 h** & **72 h** \\  & & **per Minute** & **Within 1 h** & **Where-Axis** & **Three-Axis** \\  & & & & & **Synthetic** \\  & & & & **Error (m)** & **Error (m)** \\ \hline
1 & 1 h each day & 8 & 480 & 1 day data processing & 1500 m & 5000 m \\
2 & 1 h each day & 4 & 240 & 2 day data processing & 80 m & 205 m \\
3 & 1 h each day & 3 & 180 & 2 day data processing & 140 m & 300 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Unidirectional orbit-determination result analysis. Figure 9: Extended user’s in-orbit orbit-determination results. benchmarks. The in-orbit orbit-determination results were compared by calculating the differences in velocity and position values with the control and satellite platform GNSS orbit-determination results. The precision analysis results are shown in Figure 10. Data from 13 June, after the GNSS orbit determination stabilized, were selected, showing an orbit-determination position error of 54 m and a velocity error of 0.035 m/s\({}^{2}\). By comparing the in-orbit orbit-determination results with the high-precision orbit-determination velocity and position values from the ground station, a precision analysis was conducted. The results are shown in Figure 11. The orbit-determination position error is within 20 m, and the velocity error is \(3\times 10^{-3}\) m/s\({}^{2}\). From the in-orbit measurement data, it can be seen that, with four time slots per minute and one hour of observation per day, the unidirectional orbit-determination results from a 2 day test are within 100 m of the GNSS results. Compared to the more precise ground high-precision orbit determination, the orbit-determination error is within 20 m. The results are on the same level as those of GNSS orbit determination and can surpass them under good error control conditions. Figure 11: Comparison of orbit-determination results with the orbit determination from the ground station.