## 3 Results
### Mixed Dual-/Triple-Frequency Performance Analysis  
The previous section showed the benefits of simultaneously processing and fixing dual- and triple-frequency satellites. The current section focuses on the dual- and triple-frequency solution and analyzes its convergence time and accuracy performance in more detail. The horizontal and vertical convergence time and rms (root mean square error) for the dual-/triple-frequency solution are summarized in Figure 7.  
As discussed in the previous section, looking at lower percentiles eliminates outlier solutions and gives a better idea on the distribution of the performance. For instance, the benefits of ambiguity resolution on up to three frequencies are clear on the horizontal convergence time. When fixing ambiguities, at the 1-sigma (67 th percentile), the solutions converge to and stay below one decimetre within 2 min, with a 73% improvement compared to that of the float solution. This result shows that it is possible to approach RTK levels of performance in terms of convergence time using only global corrections. Horizontal accuracy is also significantly improved as, at the 1-sigma (67 th percentile), the rms reaches 3.2 cm. Note that this rms value is computed over the whole hour of processing and that it includes the initial convergence period. The accuracies after convergence are below 1 cm. These results could be improved with the inclusion of BeiDou-3, as well as the fourth Galileo frequency. However, the effect of AR is limited when it comes to the vertical component when looking at the 100 th and 95 th percentiles, as the improvements to the convergence time and rms are not as significant as for the horizontal component. Though at the 67 th percentile, the vertical convergence time sees a 46% improvement to reach 3.5 min. Similar conclusions are valid for the vertical rms, as the vertical positions are not  
Figure 7: 100 th, 95 th, and 67 th percentile horizontal and vertical convergence times and rms for solution combining dual-frequency and triple-frequency satellites, with and without AR. as accurate as the horizontal ones. The better performance of the horizontal metrics is attributed to the fact that it is harder to estimate the vertical component due to the visible satellites all being distributed above the antenna (and the surface of the Earth). To understand the effect of AR and of the third frequency at the dataset level, Figure 8 shows the distribution of the convergence time based on all the datasets. Only one float histogram is shown, as the performance of both dual-frequency and mixed dual-/triple-frequency float solutions is very similar. Figure 8 shows clear improvements when fixing ambiguities compared to the float solution: the histograms get shifted to the left of the x-axis, with datasets converging sooner and with the mean of the histogram becoming smaller. A large portion of the fixed results converge within the first few minutes, as opposed to the float results, for which the majority converge within 10 min. More specifically, only 0.1% of float solutions converge instantaneously, compared to 7% for the fixed dual-frequency solutions, and 14% for the dual-/triple-frequency solutions. Similarly, only 0.2% of float solutions converge within a minute, as opposed to 12% for the fixed dual-frequency solutions, and 21% for the dual-/triple-frequency solutions. These results show that fixing ambiguities on as many frequencies as possible brings PPP closer to global instantaneous convergence, as fixing more frequencies leads to faster convergence at the dataset level. To further highlight the impact of the third frequency at the dataset level, one sample result is shown in Figure 9 for station GODS in Greenbelt, USA. First, Figure 9 shows the similar performance between both dual-frequency and dual-/triple-frequency float solutions. Both solutions are overlapping with minimal differences, as was noticed in the average results using all datasets. The triple-frequency solution appears to perform worse than its dual(/triple)-frequency counterpart.