# Estimation and Evaluation of Zenith Tropospheric Delay from Single and Multiple GNSS Observations
## 6 Conclusions  
In this study, zenith tropospheric delay is estimated using the single-, dual-, triple-, or four-GNSS PPP techniques. The multi-GNSS observations of 55 globally distributed MGEX stations were used in single- and multiple-system solutions during the year 2019. The ZTD results are evaluated and compared with IGS products, radiosonde, and ERA5 data. The results show that, in general, the ZTD results of BDS, Galileo, and GLONASS are close to those of GPS. The RMS of the ZTD differences is about 4.3-12.2 mm between GPS-only and Galileo-only solutions, and about 2.5-7.9 mm between GPS-only and GLONASS-only solutions. The ZTD difference is not significant. Additionally, in the combined solutions, some outliers that appeared in single-GNSS solutions could be eliminated. With the increasing number  
Figure 13: Geographical distribution of RMS values of ZTD differences for the multi-system solutions with respect to the ERA5 data at GNSS stations. (**a**) G. (**b**) GR. (**c**) GER. (**d**) GCER. of satellites, ZTDs of the four-system solutions are more stable and consistent than those of the single-GNSS solutions. The ZTD results from multi-GNSS combined solutions exhibit great consistency with IGS products. An improvement of 13.8%, 42.8%, 27.6%, and 22.9% in accuracy was achieved when compared to the GPS-only, BDS-only, Galileo-only, and GLONASS-only solutions by utilizing the multi-GNSS processing. The RMSs of the four-system solution are 5.5 mm with respect to IGS final products. The ZTD results from the four-system solution show a little deviation of a few millimeters with radiosonde data. This deviation in accuracy can be compensated for through the multi-GNSS solutions. The RMS of the GPS-only solution is 10.6 mm, whereas that of the four-system is 7.8 mm with respect to ERA5 data. Therefore, multi-GNSS-based tropospheric products with enhanced precision and dependability will greatly contribute to weather and climate change. By validating multiple GNSS ZTD through multiple data sources, the accuracy of ZTD has been greatly improved from single-system to multi-system solutions. However, for some stations with good observations, the accuracy of ZTD is only slightly improved from two-system to four-system by adding more observations. The increase in observation redundancy, especially the establishment of BDS-3, will inevitably bring great convenience to improving the accuracy of positioning and atmospheric parameter estimation, which will also lead to problems such as longer data processing time and more costs. Therefore, it should improve the accuracy and efficiency of ZTD estimation from multi-GNSS observations together in the future. Conceptualization, S.J. ; methodology, S.X. and S.J. ; software, S.X. ; validation, S.X. and S.J. ; formal analysis, S.X. ; investigation, S.X. and S.J. ; resources, S.X. ; data curation, S.X. ; writing--original draft preparation, S.X., S.J. and X.J. ; writing--review and editing, S.X., S.J. and X.J. ; visualization, S.X. and S.J. ; supervision, S.J. ; funding acquisition, S.J. All authors have read and agreed to the published version of the manuscript. This work was supported by the Open Fund Project of the Tianjing Key Laboratory for Rail Tranzit Navigation Positioning and Spatial-Temporal Big Data Technology (Grant No. : TKL2023A01). The GNSS observations and IGS final products can be obtained from [[https://cddis.nasa.gov/archive/gnss/](https://cddis.nasa.gov/archive/gnss/)]([https://cddis.nasa.gov/archive/gnss/](https://cddis.nasa.gov/archive/gnss/)) (accessed on 12 November 2022); the radiosonde data can be obtained from NOAA/GSL-RAOB (accessed on 15 December 2022); the ERA5 data can be obtained from [[https://cds.climate.copernicus.eu/cdsapp#/dataset/](https://cds.climate.copernicus.eu/cdsapp#/dataset/)]([https://cds.climate.copernicus.eu/cdsapp#/dataset/](https://cds.climate.copernicus.eu/cdsapp#/dataset/)) (accessed on 2 February 2023); the ZTD products can be obtained from the authors.