# Modelling and Assessment of a New Triple-Frequency IF1213 PPP with BDS/GPS
## 4 Conclusions  
This study focuses on the precision modeling of the dual-system triple-frequency IF1213 PPP based on BDS/GPS triple-frequency observations. The TF-C model is able to estimate the IFCB. This was deduced by considering the time-varying part of the phase hardware bias of the receiver and satellite. The TF-CF model is able to estimate the IFCB of the first GNSS. This was deduced by considering that the time-varying part of the phase bias of the receiver and the satellite in the first system, and the second one can be ignored. The advantage of the TF-C model is that it does not require the DCB product and IFCB product to correct the corresponding deviation terms. The disadvantage is that it has a large number of parameters to be estimated, which can reduce the degrees of freedom of the observation equation and lead to an increased convergence time when applied to GPS. The reliability of the deduced models was demonstrated using static PPP experiments for a single system. GPS PPP experiments demonstrated the reliability of the models, except for the TF-CF model, and the fact that GPS PIFCB has a bad influence on the GPS PPP. The BDS PPP experiments demonstrated the reliability of the TF-CF model and the negligible effect of the BDS-2 PIFCB when BDS-2 and BDS-3 are used as the BDS. Using one week of observation from 60 stations provided by the MGEX of the IGS organization, we conducted a BDS/GPS dual-system static and kinematic experiment. The results show that the GPS PIFCB had less of an influence in the static experiment, while the influence was greater in the kinematic experiment. The performance of the DF, TF-C and TF-CF models is similar; the positioning accuracy is better than 1.0 cm in the three directions in the static experiment, and in the kinematic experiment, the horizontal positioning accuracy is better than 2.0 cm, while the U directional positioning accuracy is better than 4.0 cm. The addition of third-frequency data does not significantly improve the positioning accuracy [34], but the convergence time is reduced. Compared with the DF model, the TF-C model improves the convergence time by approximately 23.5%, 13.6% and 19.8% in the E, N and U directions, respectively, and the TF-CF model improves \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**Convergence Accuracy (CM)**} & \multicolumn{3}{c}{**Convergence Time (Min)**} \\ \cline{2-7}  & **E** & **N** & **U** & **E** & **N** & **U** \\ \hline DF & 1.23 & 1.01 & 2.93 & 31.24 & 13.33 & 18.39 \\ TF-F & 2.75 & 2.08 & 5.17 & 23.07 & 12.13 & 17.47 \\ TF-C & 1.75 & 1.29 & 3.37 & 20.02 & 8.93 & 13.50 \\ TF-CF & 1.79 & 1.31 & 3.53 & 18.74 & 9.08 & 13.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Statistics on the positioning results of the four BDS/GPS kinematic PPP models. Figure 10: Positioning accuracy and convergence time distribution of the four BDS/GPS kinematic PPP models. (**a**) Convergence accuracy. (**b**) Convergence time. by approximately 18.1%, 9.7% and 12.1%, respectively, in the static experiment. In the kinematic experiment, the TF-C model improves by approximately 46.2%, 33.5% and 35.1% in the E, N and U directions, respectively, and the TF-CF model improves by approximately 49.6%, 32.4% and 36.1%, respectively. The positioning performance of the TF-C model is slightly better than that of the TF-CF model, probably because the IFCB parameters in the TF-C model can absorb the residuals. However, one should be aware that the positioning performance of IF1213 PPP models is limited due to the limitations of the float ambiguity solution. Therefore, we will focus on finding a multi-frequency solution to integer ambiguity in the future. For dual-system PPP based on BDS/GPS observations, the TF-C model is the most rigorous; therefore, the TF-C model is recommended. Conceptualization, Z.W. and R.W. ; methodology, R.W. ; software, R.W. ; validation, Z.W., R.W. and Y.W. ; formal analysis, R.W. ; investigation, Z.W. and Y.W. ; resources, Z.W. and C.H. ; data curation, C.H.