## 3 Results
### Performance Comparison with Dual-, Triple-, and Mixed Dual-/Triple-Frequency Processing  
To assess the impact of the frequency combinations on the PPP and PPP-AR results, the 100 th, 95 th, and 67 th percentiles are computed for both float and fixed horizontal and vertical errors. The results are presented in Figure 4 in the form of time series. The horizontal dashed lines refer to the convergence threshold defined in this work as the time it takes to reach and settle below a 10 cm horizontal error for the rest of the dataset. The horizontal convergence times corresponding to Figure 4 are summarized in Figure 5.  
Multiple observations can be made from Figures 4 and 5. Firstly, let us discuss the triple-frequency results to highlight the importance of processing and fixing a combination of dual- and triple-frequency satellites. The triple-frequency results appear to perform worse than dual-frequency and dual-/triple-frequency results, for both float and fixed solutions. The reason behind this behaviour is that the triple-frequency result excludes any satellite that does not have measurements on all three frequencies simultaneously. This exclusion means that only GPS-IIF and GPS-III satellites are processed for example, and GLONASS is not included in the processing as all of its satellites are dual-frequency. The histogram of the number of satellites for all three frequency combinations is shown in Figure 6. The graph is based on all epochs from all datasets, and indicates the distribution of the number of satellites overall. Given that the dual-/triple-frequency processing mode includes both dual- and triple-frequency satellites, the number of satellites distributions between the dual-frequency mode and dual-/triple-frequency mode are completely overlapping. On average, there are 13 satellites being processed in the triple-frequency mode, as opposed to 23 satellites in dual-(/triple-)frequency mode. This discrepancy in the number of satellites explains the worse performance in the triple-frequency-only results. The triple-frequency results show worse performance from the AR solution at the 100 th and 95 th percentiles. The reason is that there are certain datasets for which a very low number of satellites is being tracked on all three frequencies simultaneously, leading to poor satellite geometry as well. Some of the problematic datasets are removed in the 95 th percentile results, while most are removed when looking at the 67 th percentile. The latter shows a decrease in the horizontal convergence time from 11 min for the float solution to 8 min for the fixed solution. The convergence time of the vertical solution was not impacted by AR, owing to the limited impact of AR on the vertical component. Figure 4: Time series comparison of 100 th, 95 th, and 67 th percentile horizontal and vertical errors for dual-frequency, triple-frequency, and mixed dual-/triple-frequency combinations both with and without ambiguity resolution. Horizontal dashed lines represent convergence threshold. Figure 5: Horizontal convergence time for dual-frequency, triple-frequency, and mixed dual-/triple-frequency results with and without AR at 100 th, 95 th, and 67 th percentiles. Convergence time statistics correspond to results in Figure 4.  
When comparing the dual-frequency and mixed dual-/triple-frequency results, the addition of the third frequency does not seem to have any significant impact on the float solutions. Indeed, when comparing the dual-frequency and dual-/triple-frequency results, both float solutions have centimetre or even millimetre-level differences at all percentiles for both the horizontal and vertical components. This observation hints that the additional pseudorange and carrier-phase measurements do not provide significantly new information that would help the estimation of the various PPP states, as opposed to, e.g., adding a satellite to the processing, which would improve the satellite geometry and provide a new set of independent measurements.