## 5 Conclusions  
Choosing an appropriate observation model is a critical prerequisite for positioning solutions. Adding a third frequency signal makes observation models diverse. With the introduction of a triple-frequency signal and multi-system, the IFB and ISB biases are proposed. In order to know how we can process the biases and how many benefits we can get from the new signal and multi-system, the below research was done. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**CEDU**} & \multicolumn{3}{c}{**DARW**} & \multicolumn{3}{c}{**JFNG**} & \multicolumn{3}{c}{**KARR**} & \multicolumn{3}{c}{**KZN2**} \\ \cline{2-13}  & **N** & **E** & **U** & **N** & **E** & **U** & **N** & **E** & **U** & **N** & **E** & **U** & **N** & **E** & **U** \\ \hline UC3-C & 9 & 10 & 18 & 4 & 12 & 27 & 6 & 9 & 22 & 8 & 22 & 20 & 64 & 13 & 31 \\ CIF3-C & 8 & 10 & 20 & 6 & 13 & 33 & 6 & 10 & 18 & 10 & 27 & 18 & 5 & 9 & 29 \\ ECIF2-C & 6 & 8 & 24 & 4 & 16 & 26 & 12 & 15 & 31 & 5 & 17 & 27 & 7 & 16 & 37 \\ CIF2-C & 5 & 9 & 36 & 3 & 9 & 23 & 8 & 7 & 20 & 4 & 10 & 33 & 7 & 8 & 34 \\ UC3-BDS & 13 & 17 & 22 & 10 & 17 & 34 & 6 & 12 & 60 & 15 & 11 & 21 & 9 & 20 & 9 \\ CIF3-BDS & 13 & 17 & 23 & 11 & 18 & 38 & 6 & 7 & 47 & 15 & 10 & 24 & 9 & 19 & 11 \\ CIF2-BDS & 13 & 17 & 23 & 10 & 18 & 37 & 6 & 7 & 46 & 15 & 10 & 24 & 9 & 20 & 11 \\ CIF2-GPS & 5 & 10 & 37 & 3 & 9 & 26 & 7 & 6 & 19 & 3 & 9 & 37 & 8 & 7 & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Precisions for different combined models with the daily solution in North, East, Up directions (mm). Figure 11: The convergence time for different combined models at different stations. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Accuracy (N,E,U) (mm)** & **Precision (N,E,U) (mm)** & **Mean CT (s)** & **Median CT (s)** \\ \hline UC3-C & (19, 38, 61) & (7, 13, 24) & 46.6 & 40 \\ CIF3-C & (18, 39, 58) & (7, 14, 23) & 54 & 55 \\ ECIF2-C & (15, 33, 72) & (7, 14, 29) & 58.9 & 55.5 \\ CIF2-C & (12, 33, 79) & (5, 8, 29) & 22.8 & 13.5 \\ UC3-BDS & (23, 37, 130) & (11, 15, 29) & 163.8 & 179.25 \\ CIF3-BDS & (23, 37, 124) & (10, 14, 28) & 190 & 196 \\ CIF2-BDS & (22, 37, 123) & (22, 37, 123) & 191 & 197.5 \\ CIF2-GPS & (12, 34, 86) & (5, 8, 30) & 16.4 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Mean accuracy, mean precision, mean convergence time, and median convergence time (CT) for different combined models with the daily solution at different stations. According to the first-order Taylor expansion of the general observation equations, the unified definitions and mathematical formulae of code biases (IFB and ISB) from receiver and satellites were respectively derived. ISB and IFB can be better understood and calculated for the future research on triple-frequency PPP or multi-system PPP. Subsequently, the uncombined observation model with triple-frequency and multi-system was presented. Compared with the conventional model, this model takes more advantage of ambiguity-fixed PPP. Thereafter, the characteristics of basic triple-frequency observation models were theoretically analyzed to shed light on the differences of observations, parameters, redundancies, and noises. Furthermore, the influences of ISB and IFB for positioning solution were analyzed by the PPP experiment in the CIF2-C, CIF3-C, UC3-BDS, and UC3-C at five stations. The results show that ignoring ISB can increase positioning errors in the decimeter range. While IFB does not cause many positioning errors, the ignored IFB can be absorbed by ambiguities. So ignoring IFB is not good for the fixed success rate of ambiguities. Therefore, neither IFB nor ISB could be omitted as a parameter to be solved in positioning solution. Finally, the PPP experiment with the eight observation models at five stations in DOY 100, 2018 was realized to analyze positioning performance of dual-frequency models and triple-frequency models.