# Improving GNSS PPP Convergence: The Case of Atmospheric-Constrained, Multi-GNSS PPP-AR
## 6 Conclusions and Future Work  
Using GIM and tropospheric zenith delay corrections, a progression of improvements has been shown. Position accuracy and solution convergence were the key performance criteria assessed. By resolving ambiguities while constraining atmospheric parameters, it was observed that the multi-GNSS PPP solutions converged to a decimetre-level in less than 2 min for the horizontal components. Comparing the atmospheric constrained multi-GNSS PPP-AR to the unconstrained solution, a significant level of improvement was noticed which addressed the importance and efficacy of the constraints applied. The atmospheric constrained PPP solutions for triple-frequency PPP solutions showed more than 60% improvement in the position accuracy as compared to dual-frequency solutions. Using a strict convergence threshold of 10 min for the PPP solution to be steady under a horizontal error of 10 cm, the significance of atmospheric constraints in PPP-AR was shown. The realism of the GIM and estimated slant delays was also investigated which informs on the need to be cautious of either under or over constraining the PPP solutions. In summary, to address the original questions posed at the introduction of this contribution, here are the brief conclusions:  
1. What is the magnitude of improvements observed from the usage of traditional dual-frequency measurements to triple-frequency PPP processing with atmospheric constraints? Results presented show a significant level of improvement of more than 60% from atmospheric constrained dual- to triple-frequency multi-GNSS PPP in terms of the reduction in convergence time. Figure 11: 95 th percentile time series showing horizontal positional error (hourly) based on 24 hourly solutions for 40 stations for dual-frequency GREC with GPS-AR processing mode. Blue dotted line represents the 10 cm convergence threshold. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Processing Modes** & \
\begin{tabular}{c} **Convergence in** \\ **Minutes (Typical)** \\ \end{tabular} &
\begin{tabular}{c} **Convergence in** \\ **Minutes (Achieved)** \\ \end{tabular} \\ \hline Dual-frequency PPP & 20 & 15 [9; 42] \\ Triple-frequency PPP & 20 & 18 [9] \\ Dual-frequency atmospheric-constrained PPP & \(\sim\) & 6 \\ Triple-frequency atmospheric-constrained PPP & \(\sim\) & 2 \\ Dual-frequency PPP-AR & 15 & 11 [43] \\ Dual-frequency atmospheric-constrained PPP-AR & \(\sim\) & \textless{}2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Improvements in convergence time achieved in comparison to typical convergence periods (to 10 cm horizontal) defined by the mode of PPP processing. What are the inherent challenges when constraining PPP solutions with atmospheric corrections either functionally or stochastically? It was shown that caution needs to be taken when considering using GIM estimates and their uncertainties to constrain. To avoid under or over constraining, there is the need for, e.g., an adaptive method in the application of the constraints. * What is the significance of PPP-AR in multi-GNSS PPP atmospheric constrained solution? PPP-AR plays a vital role and enables an improved atmospheric-constrained solution. Results presented in this paper with GPS-AR show the greatest improvement at the 95 th percentile. * Finally, what are the key challenges left in obtaining near-instantaneous PPP convergence akin to RTK data processing? With typical RTK convergence of 10 min, results presented show how close we are to near-instantaneous convergence. With improved atmospheric products, as well as orbits, clocks and bias estimation, PPP solution accuracy is bound to improve. Future work would involve resolving ambiguities on GPS, Galileo and BeiDou in both dual- and triple-frequency modes while constraining the atmospheric parameters. Given the additional frequencies being transmitted due to modernization and new satellite launches, ambiguity resolution with extra-widelane combinations of multi-frequency observables will also be investigated.