## 4 Orbit Determination Results
### Analysis of Experimental Results  
To verify the effect of the aforementioned rotation correction methods on the accuracy of autonomous orbit determination solutions, the following three kinds of a priori constraint information were adopted in data filtering processing. Case 1: No rotation correction. Case 2: Adoption of an algorithm for independent constraints to correct the rotation. Case 3: Adoption of an algorithm for overall constraints onboard the satellite to correct the rotation. A priori constraint information was generated for the three aforementioned cases, respectively, and autonomous orbit determination simulation processing was carried out with inter-satellite ranging data from 16 October 2020 to 14 November 2020 of 24 MEO satellites of BDS-3. Figure 3: AOD data processing flowchart. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Model** \\ \hline Observed values & Observation data of inter-satellite links \\ \hline Observation interval & 1 min \\ \hline Satellite transceiver delay & Not estimated, calibrated numerical values are adopted \\ \hline Gravity field model & Earth Gravitational Model 2008 (EGM2008) model to the 8 th order \\ \hline Tidal correction & Only solid tides are considered \\ \hline Solar radiation pressure model & ECOM model, parameters not estimated \\ \hline EOP &
\begin{tabular}{c} International Earth Rotation and Reference Systems \\ Service (IERS) prediction of EOP (Bulletin A) \\ \end{tabular} \\ \hline Gravitational force of N body & Considers the gravitational forces of the sun and moon \\ \hline Parameters of the initial orbit & Broadcast ephemeris orbit \\ \hline Parameters of the initial clock offset & Broadcast ephemeris clock offset \\ \hline Estimator & Extended Kalman filter (EKF) \\ \hline Parameters to be estimated & Only the position and velocity parameters of each satellite are estimated \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Processing strategies of autonomous orbit determination (AOD). Using the satellite-ground and inter-satellite joint orbit determination results as reference, the rotation errors acquired by Case 1, Case 2, and Case 3 were analyzed. The three Euler angles (\(\alpha\), \(\beta\), \(\gamma\)) of the constellation rotation parameters were calculated, and the results are presented in Figure 4. Figure 5 shows the prediction errors of UT1-UTC in EOP. Compared with the no-rotation-correction case, both the algorithm for independent constraints and the algorithm for global constraints could constrain the constellation rotation on the X and Y axes better, while no significant improvement was shown on the \(Z\)-axis. Moreover, the errors were basically consistent with the prediction errors of UT1-UTC in EOP given in Figure 6, which occurred because the errors on the \(Z\)-axis in the overall rotation of the constellation were mainly caused by the prediction errors of UT1-UTC, and the errors could not be eliminated without external reference input. Furthermore, the orbit inclination angle \(i\) (iot) and right ascension of the ascending point \(\Omega\) (Omega) under the three cases were calculated. Using the post-processed precise orbits of satellite-ground and inter-satellite joint orbit determination as references, the angle errors relative to the precise ephemeris error were obtained. Due to the space limitations of the article, only the time series of the PRN25 and PRN37 satellites are given here, as shown in Figures 5 and 7. Table 4 shows the prediction errors in the \(i\) and \(\Omega\) for each satellite on the 30 th day under the different cases. It can be seen from Figures 7 and 8, when the rotation was not corrected, the \(i\) and \(\Omega\) of PRN25 and PRN37 became divergent gradually, and the trends of the two satellites were basically consistent. After adopting the algorithm for independent satellite constraints, the \(i\) errors of the two satellites could be better constrained, and there was also a correction effect on \(\Omega\).