# A BDGIM-Based Phase-Smoothed Pseudorange Algorithm for BDS-3 High-Precision Time Transfer
## 5 Conclusions  
SPP has been widely used in the field of civil time and frequency. However, SPP relies solely on pseudorange-only observations, which is not conducive to the improvement of SPP accuracy because pseudorange observation noise is rather high. The accuracy of pseudoranges can be increased by smoothing them with a high-precision phase. However, the classical phase-smoothed pseudorange method ignores the effect of ionosphere delay. In this study, we develop a BDGIM-based phase-smoothed pseudorange algorithm, and we investigate the contribution of the method to BDS-3 SF time transfer. First, to verify the feasibility of the BDGIM, we evaluated the accuracy of the BDGIM by comparing it with the Klobuchar model using the GIM product as the benchmark. Then, we evaluated the improved SPP time transfer performance using the observation data from six stations over five consecutive days. The following conclusions can be drawn from the experimental results:  
First, when comparing the broadcast ionosphere models, the VTEC error of the BDGIM fluctuates in a narrower range, with a peak-to-peak value within 10 TECU, while the peak-to-peak value of the VTEC error of the Klobuchar model is approximately 20 TECU. The RMS value of the BDGIM is 2.6 TECU, which is 1.7 TECU less than that of the Klobuchar model. The average CR value of the BDGIM is 75.5%, which is an improvement of 7.3%. Thus, the BDGIM outperforms the Klobuchar model.  
Second, the receiver clock error sequence after smoothing is relatively more concentrated, and its STD value is decreased by 13.6%, from 1.75 ns to 1.51 ns. Regarding time transfer, Type A uncertainty with the improved SPP time transfer is reduced from 2.34 ns to 2.08 ns, with a reduction of 11.1%. Regarding frequency stability, the frequency stability of the improved SPP time transfer is greatly improved. The MDEVs at 960 s and 61,440 s are 4.19 \(\times\) 10\({}^{-13}\) and 1.68 \(\times\) 10\({}^{-13}\), with an increase of 51.2% and 59.9%, respectively.  
Finally, we are aware that broadcast ephemeris and pseudorange observations are both used in SPP time transfer. Although the smoothed pseudorange helps to some extent with SPP time transfer accuracy, the quality of the satellite orbits and clock offsets provided by broadcast ephemeris is poor, which can potentially limit SPP time transfer performance. In order to further improve the capability of SPP time transfer, we will concentrate our efforts in the future on increasing the quality of broadcast ephemeris orbit and clock offsets.  
J.T.: conceptualization, methodology, software, validation, formal analysis, investigation, and writing--original draft preparation. D.L.: conceptualization, validation, resources, and writing--review and editing. F.Z.: validation, data curation, visualization, and supervision. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The datasets in this study are available by contacting the corresponding author.  
We greatly appreciate GFZ, CODE, and CSNO for providing BDS-3 observation data, ephemeris, and ionosphere products.  
The authors declare no conflict of interest.