## 5 Conclusions  
In our work, GLONASS inter-frequency code biases (IFCBs) for GLONASS PPP-based international time transfer is modeled through a reparameterization process. Three different GLONASS IFCB handling schemes, which neglect IFCBs (IFCB0), estimate IFCBs for each GLONASS frequency number (IFCB1), and estimate each GLONASS satellite (IFCB2), were proposed for ionosphere-free GLONASS-only PPP. Seventy days of observation data from DOY 227-297 in 2017 from 36 stations of IGS network and three stations of time a keeping laboratory were selected to assess the model, and preliminary international time transfer results have been concluded. For the comparison, the GPS-only PPP solutions using IGS final products are regarded as reference. Clock differences between GPS- and GLONASS-only PPP solutions are then analyzed.  
The quality of the IFCBs estimated for IFCB1 and IFCB2 are not equal. The bias is approximately 0.5 ns. The numerical results showed that for GLONASS PPP, considering the IFCBs can significantly reduce the STD of the clock difference for identical receivers (the reductions from 3.0% to 49%) or mixed receivers (the reductions from 3.3% to 62.6%). IFCB0 performs worst in the time transfer performance, while IFCB2 performs best for identical receivers or mixed receivers. Furthermore, the uncertainty (STD) of different end users, which include the exact coordinate of the station as known and unknown values, for example, time keeping laboratories and time users, shown a similar characteristic. Compared with neglecting IFCBs, the STDs of end users with coordinate-fixed were reduced by more than 30% from 0.3 to 0.2 ns, and 10% from 0.40 to 0.35 ns, at the one-day arc solutions and ten-days arc solutions, respectively, when estimating the IFCBs for each GLONASS satellite. The STDs of end users without coordinate-fixed improved by 30.59% going from 0.304 to 0.211 ns, and by 10.46% going from 0.411 to 0.368 ns in one-day arc solutions and ten-day arc solutions at the 95% level, respectively. Moreover, different precise products from the three IGS ACs were adopted for analysis. Even though different IFCBs handling strategies were adopted during their GLONASS satellite clock estimation, our numerical analysis showed that GLONASS-only PPP-based international time transfer achieved better performance when estimating IFCBs for each GLONASS satellite among using the three GLONASS final products.  
Generally, estimating the IFCBs for each GLONASS satellite is superior for GLONASS PPP time transfer uncertainty improvement. The results suggest that, GLONASS IFCBs may not be strict for each satellite frequency. Therefore, it is recommended that this scheme can be utilized to handle GLONASS IFCBs in the PPP international time transfer processing for GLONASS observations.  
[PERSON] and [PERSON] designed the experiments. [PERSON] contributed to the tests and analyzed the data. [PERSON], [PERSON], [PERSON] and [PERSON] validated the experimental results and reviewed the paper. [PERSON] wrote the paper. Funding supports from the National Natural Science Foundation of China (Nos. 41104021, 11173026 and 11703033) and the National R&D Infrastructure and Facility Development Program of China, \"Fundamental Science Data Sharing Platform\" (DKA2017-12-02-24). The authors would like to acknowledge iGMAS for providing funding. Many thanks go to the IGS MGEX for providing precise orbit and clock products, and MGEX, PTB for providing data. The authors declare no conflict of interest.