## 4 Analysis And Assessment
### Results and Discussion of Single and Multi-GNSS PPP  
We will comment on the performance of positioning solutions in triple-frequency and dual-frequency models. Except for the above models (UC3-C, CIF3-C, CIF2-C, and UC3-BDS), we chose the other three models, which are the conventional ionosphere-free model with triple-frequency BDS-only (CIF3-BDS), the conventional ionosphere-free model with dual-frequency BDS-only (CIF2-BDS), and the conventional ionosphere-free model with dual-frequency GPS-only (CIF2-GPS). Furthermore, we present an extended CIF2-C model (ECIF2-C) to compare with triple-frequency models under the same satellites condition. The ECIF2-C is similar to CIF2-C, the only difference is the satellites in each epoch. The satellites, which can be used for positioning solution in CIF2-C, are determined by dual-frequency data in each epoch. Namely, for a satellite in an epoch, only if all the data in two frequencies exist, the satellite can be considered as an eligible satellite for positioning solution. The eligible satellites in ECIF2-C are determined based on triple-frequency data in each epoch. The number of the eligible satellites in ECIF2-C is less than that in CIF2-C, but the eligible satellites in ECIF2-C are the same with triple-frequency models. As shown in Figure 10, all eight models are used to compare positioning solution at different stations (CEDU, DARW, JFNG, KARK, KZN2). The results show that the positioning errors in different models are similar, except UC3-BDS and CIF3-BDS at KZN2. Because the number of visible BDS satellites at KZN2 is less than others stations in Figure 3.  
For analyzing the direction of positioning errors, Tables 5 and 6 respectively illustrate accuracies and precisions for different combined models with the daily solution in North, East, Up directions at different stations. The results show that horizontal components in positioning errors are similar, the vertical components in positioning errors have more deviations than horizontal components, especially UC3-BDS, CIF3-BDS and CIF2-BDS. [PERSON] et al. (2018) had concluded the horizontal positioning components are more accurate than the vertical component based on much research. And the positioning errors caused by lacking satellites are concentrated on vertical components, this is very well known in GPS analysis. The horizontal positioning errors in different models are similar. When the visible satellites are sufficient, all eight models give similar estimates for positioning solution, such as UC3-C, CIF3-C, and CIF2-C. Figure 11 shows the convergence time for different combined models at different stations. If the state that the positioning errors in three directions are less than 0.1 m can hold more than 20 epochs, positioning solution is considered to converge from the beginning of this state. The convergence time is the duration from the beginning epoch of positioning process to the beginning epoch of this state. Because the vertical positioning errors are larger than the horizontal positioning errors for each epoch, the convergence time is determined by the vertical positioning errors. Because the positioning errors of vertical components are quite different in different models, the convergence time for different models are widely different. The convergence time for UC3-BDS, CIF3-BDS and CIF2-BDS is longer than others, especially at KZN2. Figure 9: ISB at different stations in DOY 100, 2018.