# Estimation and Evaluation of Zenith Tropospheric Delay from Single and Multiple GNSS Observations
## 4 Results and Analysis
### Evaluation by IGS Final Products  
To evaluate the precision of ZTD obtained from different solutions, we use three different types of reference data: IGS final troposphere products, radiosonde data, and ERA5 data. The sample interval of the three different independent validation data types differs, and therefore temporal and spatial matching are required and the amount of data is sufficient to ensure that interpolation on results of the evaluation is not needed. The time series of ZTD obtained from single-system and multi-system solutions, so as to compare with IGS final troposphere products at stations DGAR and PTGG, are shown in Figure 7. The ZTD values of the BDS-only solution present larger values, relatively, and those of multi-system solutions agree very well with those from IGS tropospheric products (within several millimeters). The ZTD differences of single- and multi-system solutions with respect to IGS products at stations DGAR and PTGG, are shown in Figure 8. At DGAR, ZTD differences of BDS-only are mostly above 0 mm, and those of other solutions appear stable with few fluctuations. At PTGG, the ZTD differences of the BDS-only solution are mostly below 0 mm, and those of the GLONASS-only solution present a significant fluctuation. It is worth noting that there are few large fluctuations in the multi-system combined solutions. The differences of single-system solutions mainly range from \(-\)20 to 20 mm and those of multi-system combined solutions are smaller than 10 mm. Figure 7: ZTD derived from single-system and multi-system solutions and IGS final troposphere products during DOY 140–150, 2019 (**top panel**: DGAR; **bottom panel**: PTGG). Figure 9 displays the RMS and mean absolute bias values for ZTD differences of single-system and multi-system solutions with respect to IGS products at three stations, including DGAR, PTGG, and AREG. Other stations equipped with four-system GNSS receivers and IGS products are also considered. For the four-system solution, the RMS values are about 3.9-6.3 mm and for the single-GNSS solutions (G, C, E, R), the values are about 4.7-9.1 mm, 5.6-12.8 mm, and 4.9-12.1 mm, respectively. The absolute bias values are also reduced by about 1-3 mm. The difference between two-system and three-system solutions is small, which can also be seen in Figure 6. In other words, the degree of accuracy improvement is not as good as that between single-system and two-system solutions. The possible reason is that the observations reach a certain number, and the accuracy improvement of the unknown parameters' estimation is basically not significant. In order to obtain a higher accuracy estimation, increasing the number of observations will also lead to longer data processing time. Taking the IGS products as a reference, the RMS values for the two-, three-, and four-system solutions are reduced by 2.8%, 5.3%, and 13.8% respectively, compared to the GPS-only solution when including GPS observations in the PPP solution. Similarly, RMSs of the two-, three-, and four-system solutions fall by 35.1%, 37.2%, and 42.8% respectively, compared to the BDS-only solution when including BDS observations in the PPP solution. RMSs of the two-, three-, and four-system solutions are also decreased by 17.5%, 20.1%, and 27.6% respectively, compared to the Galileo-only solution when including Galileo observations in the PPP solution. The RMS values fall by 14.4%, 15.5%, and 22.9% compared to the GLONASS-only solution when including GLONASS observations in the PPP solution. The ZTD values produced for the GPS-only solution are the ones that are closest to IGS products from the standpoint of single-system solutions. From the perspective of the two-system solutions, the ZTD values obtained for the GPS/GLOAASS combined solution are the most accurate. The ZTD values obtained for the GPS, Galileo, and GLONASS combined solution are the most precise in terms of three-system solutions.