###### Abstract  
The autonomous orbit determination of the navigation constellation uses only bidirectional ranging data of the inter-satellite link for data processing. The lack of space-time benchmark information related to the Earth inevitably causes overall rotational uncertainty in the constellation, leading to a decrease in orbit accuracy and affecting user positioning accuracy. This study (1) introduces a method for rotation correction in distributed autonomous orbit determination based on inter-satellite bidirectional ranging; (2) conducts constellation autonomous orbit determination and time synchronization processing experiments based on inter-satellite ranging data for the 24 medium Earth orbit (MEO) satellites in the Beidou-3 global satellite navigation system (BDS-3); and (3) makes comparative analyses on the accuracy of autonomous orbit determination based on three rotation correction cases, including a no-rotation-correction case, independent satellite constraints case, and global satellite constraints case. The experimental results are described as follows. For the no-rotation-correction case, the prediction error of the orbital inclination angle (iot, _i_) for the entire constellation on the 30 th day was 2.11 \(\times\) 10\({}^{-7}\)/rad, the prediction error of the right ascension of the ascending point (Omega, _f_) was 2.25 \(\times\) 10\({}^{-7}\)/rad, and the average root mean square (RMS) of the user range error (URE) for the entire constellation orbit was 1.41 m. In the autonomous orbit determination experiment with independent constraints on satellites, the prediction error of \(i\) for the entire constellation on the 30 th day was 5.43 \(\times\) 10\({}^{-7}\)/rad, the prediction error of \(f\) was 2.03 \(\times\) 10\({}^{-7}\)/rad, and the average RMS of the orbital URE for the entire constellation was 1.09 m. In the autonomous orbit determination experiment with global satellite constraints, the prediction error of \(f\) for the entire constellation on the 30 th day was 5.31 \(\times\) 10\({}^{-7}\)/rad, the prediction error of \(f\) was 1.95 \(\times\) 10\({}^{-7}\)/rad, and the RMS of the orbital URE for the entire constellation was 0.94 m. According to the analysis of the above experimental results, compared with the autonomous orbit determination under the no-rotation-correction case, the adoption of an algorithm for independent satellite constraints to correct the overall constellation rotation weakens the constellation rotation influence; however, it may destroy the overall constellation configuration, which affects the stability of autonomous orbit determination. Finally, the algorithm based on global satellite constraints both impairs the influence of constellation rotation and maintains the overall constellation configuration. Beidou satellite navigation system; distributed autonomous orbit determination; inter-satellite link; overall constellation rotation; algorithm for the correction of independent satellite constraints; algorithm for the correction of global satellite constraints  
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autonomous, and stable operation and service capabilities of a navigation system, based on the distance measurement and communication functions of the inter-satellite link through the autonomous operation of the constellation and on-orbit ephemeris updates during long-term absence of ground system support. Subsequently, the initial theory, design, and data research work on autonomous orbit determination was conducted in June 1990 [2]. In July 2020, the Beidou-3 global satellite navigation system (BDS-3) began to operate and provide global service. The Ka-band inter-satellite link payload carried by the BDS-3 satellites can realize inter-satellite pseudorange measurement and inter-satellite communication, which enables research on the autonomous orbit determination of the constellation [3]. Autonomous navigation is first introduced for GPS Block IIR satellites and its design index requirement is that the user range error (URE) is less than 6 m within 180 days [4].