## 5 Conclusions  
In this paper, the models for constellation rotation errors during autonomous orbit determination were analyzed theoretically. Aiming at the drawbacks of the algorithm for independent satellite constraints in distributed autonomous orbit determination, an algorithm for global satellite constraints was proposed. Based on the inter-satellite observation data for the 24 MEOs in the BDS-3, BDS-3 autonomous orbit determination experiments were designed under three schemes for correcting the rotation and the orbit determination results were assessed. The results are described as follows:  
1. The BDS-3 inter-satellite ranging data show satisfactory continuity, and the average number of established links for a single satellite was approximately 14.4. The geometric configuration of inter-satellite link establishment was good, with an average PDOP of approximately 0.99.  
Among three rotation-correction cases, the algorithm for independent satellite constraints and the global satellite constraints constrained the constellation rotation on the X and the Y axes better. However, this method did not improve the \(Z\)-axis rotation errors caused by the prediction errors in UT1-UTC.
3. Under the three rotation-correction schemes, distributed autonomous orbit determination processing can be carried out. Compared with precise ephemeris, it shows that without external constraints, the accuracy of autonomous orbit determination deteriorates with time. With no correction algorithm applied, the average RMS of the 30-day orbit URE of autonomous orbit determination was 1.41 m. Using the algorithm for independent satellite constraints, the average RMS of the 30-day orbit URE was 1.09 m. Using the algorithm for global satellite constraints, the average RMS of the 30-day orbital URE was 0.94 m, and this scheme achieves stable and reliable autonomous orbit determination results.
4. Both the algorithm for independent satellite constraints and the algorithm for global satellite constraints can weaken the influence of the overall constellation rotation. The former will affect the integrity of the constellation configuration as a rigid body to a certain extent, while the later solves this problem perfectly. Among the three schemes, the 30-day accuracy of autonomous orbit determination using the algorithm for global constraints on satellites was the best.  
The work conducted and the conclusions obtained in this paper provide some reference for improving the accuracy of autonomous orbit determination. However, in a case where the ground reference benchmarks are missing, the constellation rotation errors of autonomous orbit determination caused by UT1-UTC predictions using the inter-satellite link ranging data cannot be eliminated. To follow up, further research and performance analysis on autonomous orbit determination technology for the navigation constellation based on anchoring support should be carried out.  
[PERSON], [PERSON] and [PERSON] conceived and designed the experiments; [PERSON], [PERSON] and [PERSON] performed the experiments and analyzed the data; [PERSON], [PERSON] and [PERSON] wrote the paper; [PERSON], [PERSON] and [PERSON] reviewed the paper. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The data presented in this study are available on request from Beijing Institute of Tracking and Telecommunications Technology (BITTT). The data are not publicly available due to the confidentiality of the data.  
The authors declare no conflict of interest.