## 4 Results
### Performance Analysis of PPP-RTK
#### 4.2.1 Medium-Scale Networks  
The accuracy of SD ionospheric delay interpolation in scenario A was analyzed as described in Section 4.1. The average RMS of the residuals was 0.014 m for GPS and 0.012 m for Galileo using DSM. The interpolation accuracy of the two systems was similar. The RMS of the residuals for both GPS and Galileo was 0.018 m using DIM. The mean squared error of the SD ionospheric delays of 2.8 cm by experience is slightly larger than the situation. It is because the quality of the corrections of the surrounding reference stations should be much better than that of the single base station. Considering that too tight constraints will reduce the accuracy of the results, we think the empirical value that was used is appropriate, but it may not be optimal for all periods. Table 3 summarizes the convergence of the two models in the horizontal and three-dimensional directions. The horizontal success rate of DSM was approximately 95%, and the average convergence time was 14.5 s. Compared with DIM, the ambiguity fixation with DSM increased, but there was no significant difference in either TTFF or the percentage of convergence time. In the three-dimensional direction, 90% of  
Figure 3: Percentage of interpolation accuracy improvement of DSM compared with USM and DIM in different scenarios. the periods converge within 1 min, 95% within 2 min, and all periods within 3 min using DSM. The convergence speeds of the two models in the horizontal direction were similar to those in the three-dimensional direction. To show convergence throughout the day, taking the DSM as an example, Figure 4 shows a time series diagram of TTFF in all periods and the number of satellites participating in ambiguity fixing at TTFF. When not converging, TTFF was set to \(-1\). It can be seen that most of the periods with poor convergence are concentrated in the period with large ionospheric residuals in Figure 2. Except for the period with more ionosphere activity, during periods of the low number of satellites, the time that was required to fix the ambiguity was also longer. If the observation conditions were poor or the atmospheric delay products that were provided by the server were few, the number of satellites will be less, and the geometry of the satellite network will be poor. This will lead to poor solutions and ambiguity fixation failure. Therefore, multi-GNSS and multi-frequency observation data can be used to improve the performance of PPP-RTK, especially in urban areas with poor observation environments. To explore the positioning accuracy after the ambiguity is successfully fixed, Figure 5 shows the positioning bias of the three directions (east, north, and up) at the TTFF. The horizontal bias of the DSM was concentrated within 2 cm, and the vertical bias was concentrated within 10 cm, while the DIM was less accurate than the DSM in the N direction. Figures 6 and 7 show the RMS value and its distribution of the positioning bias after the successful fixation in each period. The RMS was within 5 cm in the horizontal direction and within 10 cm in the vertical direction for all periods after convergence using the two models. However, the RMS values that were obtained using DSM of more than 90% and 98% of the horizontal bias were less than 2 cm and 3 cm, respectively. Approximately 66% and 93% of the vertical bias was less than 3 cm and 5 cm, respectively, and 98% was less than 10 cm, which was better than the results that were obtained using DIM. According to statistics, the average RMS values of the DSM in the three directions (E, N, U) were 0.80,