## 7 Conclusions  
In our paper, the accuracy of instantaneous PPP employing a low-cost dual-frequency multi-constellation U-blox ZED-F9P receiver in precise positioning and tropospheric appli  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Product**} & \multicolumn{2}{c}{**GPS-PPP**} & \multicolumn{2}{c}{**GLONASS-PPP**} & \multicolumn{2}{c}{**Galileo-PPP**} & \multicolumn{2}{c}{**BeiDou-PPP**} \\ \cline{2-9}  & **Mean** & **RMSE** & **Mean** & **RMSE** & **Mean** & **RMSE** & **Mean** & **RMSE** \\ \hline BKG & 0.30 & 3.53 & 3.30 & 8.72 & 3.63 & 7.87 & – & – \\ \hline CNE & 1.53 & 3.47 & 1.11 & 9.24 & 3.57 & 7.60 & – & – \\ \hline GFZ & 3.55 & 3.38 & 3.10 & 9.95 & 3.52 & 3.98 & 5.75 & 9.45 \\ \hline IGS & 3.27 & 2.83 & 4.18 & 9.80 & 2.43 & 9.34 & 6.26 & 11.40 \\ \hline WHU & 1.75 & 2.78 & 3.86 & 10.32 & 2.74 & 5.37 & 3.42 & 10.90 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Real-time PWV statistics derived from PPP solutions (in mm).  
cations is investigated. Three-hour multi-GNSS static datasets over a reference station in Egypt spanning a period of three successive days were collected. The acquired datasets were processed by applying four real-time PPP models, which were GPS, GLONASS, Galileo, and BeiDou PPP. To adopt the real-time PPP mode, GNSS orbit and clock corrections products from five analysis centers were utilized, including BKG, CNE, GFZ, IGS, and WHU products. Our proposed solutions were explored in the static positioning and PWV domains. GNSS observations were acquired from the geodetic-grade Trimble R4s receiver and then processed in post-processed PPP mode to provide positioning and PWV reference solutions. The results demonstrated that decimeter-level 3D positional accuracy can be achieved by employing GPS and Galileo PPP solutions with significant superiority to the GPS PPP solution, while the 3D position of both the GLONASS and BeiDou solutions can reach the meter level. The GPS PPP's positioning accuracy ranged from 0.164 to 0.319 m, with WHU outperforming the other products, whereas the positioning accuracy of the Galileo PPP solution varied from 0.419 to 0.980 m, with superiority to BKG products. The BKG products showed the best performance for GLONASS scenarios compared with the other products, with 1.123 m 3D positioning accuracy; however, the WHU-based BeiDou PPP solution was better than the other solutions, with 1.402 m positioning accuracy. For the PWV domain, millimeter-level precision was attained using the four PPP models; moreover, WHU introduced more precise GPS-based PWV estimation than the others, with 2.78 mm precision. For GLONASS-derived PWV, an 8.72 mm PWV precision was attained utilizing BKG, which outperformed other products; on other hand, GFZ showed better precision than other products, with STD values of 3.98 mm and 9.45 mm for Galileo and BeiDou solutions, respectively. Consequently, the ultra-low-cost ZED-F9P module can be used in real-time atmospheric sounding applications.  
Conceptualization, M.A., A.A. and H.A.K.; methodology, M.A. and A.A.; software, A.A.; validation, M.A. and A.A.; formal analysis, A.A.; investigation, M.A.; resources, A.A. and H.A.K.; data curation, A.A.; writing--original draft preparation, M.A.; writing--review and editing, M.O.A.M.; visualization, M.A. and M.O.A.M.; supervision, M.A.; project administration, M.A.; funding acquisition, M.A. All authors have read and agreed to the published version of the manuscript.  
This project is sponsored by Prince Sattam Bin Abdulaziz University (PSAU) as part of funding for its SDG Roadmap Research Funding Program, project number PSAU-2023- SDG-43.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
This project is sponsored by Prince Sattam Bin Abdulaziz University (PSAU) as part of funding for its SDG Roadmap Research Funding Program, project number PSAU-2023- SDG-43.  
The authors declare no conflicts of interest.