## 5 Conclusions  
This paper focuses on establishing an a priori SRP model for the BDS-3's cuboid satellite body to reduce systematic errors in the radial direction. Given the enhancement in orbit accuracy through incorporating ISL observations, we tried to utilize 281-day ISL observation to refine the SRP model for BDS-3. The results are as follows:  
1. The correlation between the optical parameters of the +X/\(\pm\)Z panels cannot be significantly decreased even with the ISL observation, due to the parameter settings of the ABW model. Nonetheless, the ISL can still decrease the correlation between orbit parameters, thereby improving the orbit accuracy.
2. An a priori model established for the satellite body can reduce the systematic errors in ECOM orbits, and the model established using ISL observation demonstrates superior performance compared to solely using L-band observations. With the enhanced a priori model, the slopes in the SLR residual of CAST and SECM satellites are reduced from \(-0.097\) cm/deg and \(0.067\) cm/deg to \(-0.004\) cm/deg and \(-0.009\) cm/deg, respectively. The STD values are reduced with an improvement of 21.8% and 26.6%, respectively. Furthermore, a reduced \(\beta\)-dependent variation is observed in the OADEV of the corresponding clock offset. Nevertheless, systematic biases are still present in the SRL residual when using the a priori model. It is suspected that there are other effects that are yet to be properly accounted for.
3. The impact of self-shadowing from SAR-carrying satellites was considered. The systematic trends within the \(|\beta|<40^{\circ}\) decreased with the a priori model established by ISL observation. The orbit accuracy as indicated in the DBD and OADEV of clock offset exhibited a litter improvement. Because of the absence of SAR antenna geometric details from BDS authorities, we propose disregarding the SAR antennas' impact on the satellites in the current modeling phase.  
Conceptualization, Y.L.; methodology, Y.L.; software, Y.L.; validation, Y.L., Z.L. and R.J.; formal analysis, Y.L., Z.L. and R.J.; investigation, Y.L.; resources, X.X.; data curation, Y.L. and Z.L.; writing--original draft preparation, Y.L.; writing--review and editing, Z.L.; visualization, Y.L.; supervision, X.X.; project administration, Y.L. and X.X.; funding acquisition, Y.L. and X.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 42204029, 42204028, and the Startup Foundation for Introducing Talent of NUIST, grant number 2022r042.  
**Data Availability Statement:** BDS-3 L-band measurements, WUM precise orbits, and SLR measurements are publicly available from [[https://cddis.gsfc.nasa.gov/archive](https://cddis.gsfc.nasa.gov/archive)]([https://cddis.gsfc.nasa.gov/archive](https://cddis.gsfc.nasa.gov/archive)) (accessed on 1 May 2024), while K-band ISL measurements are accessible with permission from the China Satellite Navigation Office (CNSO).  
We gratefully acknowledge the IGS Multi-GNSS Experiment (MGEX) and the International GNSS Monitoring and Assessment System (iGMAS) for supplying BDS-3 observations, as well as the ILRS for providing SLR observations.  
**Conflicts of Interest:** The authors declare no conflicts of interest.