## 4 Orbit Determination Results
### Analysis of Experimental Results
However, the margin of error for each satellite after correction was inconsistent, which affected the integrity of the constellation as a rigid body. The algorithm for global constraints on satellites corrected the \(i\) and \(\Omega\) well, and the errors after correction were basically consistent, which did not affect the integrity of the constellation as a rigid body. Without any correction, the average RMS of the \(i\) prediction errors for the entire constellation on the 30 th day was 2.11 \(\times\) 10\({}^{-7}\)/rad, and the average RMS of the \(\Omega\) prediction errors was 2.25 \(\times\) 10\({}^{-7}\)/rad. After adopting the algorithm for independent satellite constraints, the \(i\) prediction error was 5.43 \(\times\) 10\({}^{-8}\)/rad, and the \(\Omega\) prediction error was 2.03 \(\times\) 10\({}^{-7}\)/rad. When the algorithm for global satellite constraints was applied, the average \(i\) prediction error was 5.31 \(\times\) 10\({}^{-8}\)/rad, and the average \(\Omega\) prediction error was 1.95 \(\times\) 10\({}^{-7}\)/rad. The two constraint algorithms could weaken the \(i\) and \(\Omega\) prediction errors of the constellation to some extent, and the algorithm for global satellite constraints achieved the best performance. Figure 6: 30-day prediction errors of UTI-UTC in EOP. Figure 7: The \(i\) angle and \(\Omega\) angle errors of PRN37 under different cases for autonomous orbit determination. The differences between the autonomous orbit determination results and the reference orbits were analyzed, and the radial errors (RERR), tangential errors (TERR), normal  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{3}{c}{_i/rad_} & \multicolumn{3}{c}{_f_**rad**} \\ \cline{2-7}
**PRN** & **Case 1** & **Case 2** & **Case 3** & **Case 1** & **Case 2** & **Case 3** \\ \hline
25 & \(1. For the 24 BDS-3 MEO satellites, the orbit-only URE is expressed as:  
\[URE=\sqrt{0.96\;*\;\text{RERR}^{2}+0.04\;*\;\left(\text{TERR}^{2}+\text{NERR}^{2} \right)} \tag{23}\]  
As can be seen, without rotation correction, the average RMS of the RERRs for the entire constellation in 30 days was approximately 0.17 m, the TERR was 4.70 m, the NERR was 4.55m, and the orbit accuracy was approximately 1.41 m. After adopting the algorithm for independent satellite constraints to carry out rotation correction, the average RMS of RERR was 0.54 m, the RMS of TERR was 2.21 m, the RMS of NERR was 4.07 m, and the orbit accuracy of was 1.09 m. By adopting the algorithm for global satellite constraints, the average RMS of RERR was 0.17 m, and the NERR and TERR were 2.14 m and 4.02 m, respectively, and the accuracy of orbit determination for the entire constellation was 0.72 m. Among them, the 30-day accuracy in autonomous orbit determination of without rotation correction was the worst, and the accuracy under the algorithm for global constraints on satellites was the best. The orbit accuracy of the three cases of autonomous orbit determination deteriorated with time gradually, because the errors created by UT1-UTC prediction in autonomous orbit determination cannot be eliminated relying on only the observed values of inter-satellite links but without external reference constraints. The orbit error trend was basically consistent with the prediction errors of UT1-UTC in Figure 4.  
Compared with Case 1, the algorithm for independent satellite constraints significantly decreased TERR and NERR in the orbit determination. However, the RERR showed an increasing trend. The reason is that the rotation parameters of each satellite in the independent constraint algorithm are calculated separately, which caused variations in the geometry configuration of the inter-satellite ranging network [11]. When the \(\Omega\) variations of two satellites were the same, the inter-satellite distance was not to be changed. Conversely, a change in the inter-satellite distance was unavoidable. Table 4 shows the \(\Omega\) error of the predicted orbit for each satellite.