# Assessment of BeiDou-3 and Multi-GNSS Precise Point Positioning Performance
## 5 Data Tests and Results Analysis
### ZTD Accuracy  
When considering that GNSS plays an important role in atmospheric science and ZTD is important to PPP solutions [31; 32; 33; 34]. It is meaningful to assess the performance of the GPS, BDS-2, BDS-2/BDS-3, GLONASS, Galileo, and multi-GNSS PPP in terms of ZTD accuracy. We use conventional methods that ZTD is estimated together with the positioning error parameters in an epoch in order to intuitively illustrate the differences of GPS, BDS-2, BDS-2/BDS-3, GLONASS, Galileo, and multi-GNSS in solving ZTD. Figure 9 shows the solutions of ZTD at BRCH for 12 different processing cases on DOY 024 in 2019. The solutions of ZTD for 12 different processing cases are relatively stable, there are no significant anomaly distortion, and no significant differences between the different systems, except BDS-2. Due to the less of number of BDS-2 available satellites at BRCH, there is a slight difference between the ZTD solutions of BDS-2 and those of other navigation systems. However, adding BDS-3 observations significantly reduces the difference, and the ZTD solutions of BDS-2/BDS-3 are as good as those of other navigation systems. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & **G** & **C2** & **C** & **R** & **E** & **G + C** \\ \hline \multirow{4}{*}{Accuracy (cm)} & North & 4.40 & 7.98 & 5.88 & 4.99 & 5.46 & 3.45 \\  & East & 5.61 & 11.61 & 7.43 & 6.14 & 6.06 & 4.63 \\  & Up & 7.12 & 15.50 & 9.50 & 9.51 & 8.45 & 6.04 \\  & 3 – D & 10.08 & 20.95 & 13.42 & 12.37 & 11.74 & 8.36 \\ \hline \multirow{4}{*}{Time (min)} & North & 56.15 & 76.80 & 61.96 & 58.15 & 56.57 & 36.42 \\  & East & 65.98 & 90.43 & 77.71 & 67.66 & 68.51 & 60.22 \\  & Up & 71.24 & 121.98 & 97.75 & 95.57 & 92.40 & 58.07 \\ \hline \multirow{4}{*}{Accuracy (cm)} & North & 3.20 & 3.24 & 3.50 & 3.59 & 3.45 & 2.68 \\  & East & 4.20 & 4.37 & 4.74 & 5.79 & 5.13 & 3.28 \\ \cline{1-1}  & Up & 5.61 & 5.54 & 5.74 & 6.18 & 5.89 & 5.14 \\ \cline{1-1}  & 3 – D & 7.70 & 7.76 & 8.23 & 9.20 & 8.54 & 6.66 \\ \hline \multirow{4}{*}{Time (min)} & North & 33.15 & 38.11 & 35.86 & 40.97 & 38.91 & 30.05 \\ \cline{1-1}  & East & 45.23 & 49.70 & 53.60 & 46.28 & 45.91 & 34.05 \\ \cline{1-1}  & Up & 55.91 & 52.58 & 66.93 & 61.57 & 67.32 & 41.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Kinematic PPP accuracy and convergence time. The ZTD in the tropospheric products provided by iGMAS ([[http://112.65.161.230/download/](http://112.65.161.230/download/)]([http://112.65.161.230/download/](http://112.65.161.230/download/)); [[ftp://222.240.181.170/products/](ftp://222.240.181.170/products/)]([ftp://222.240.181.170/products/](ftp://222.240.181.170/products/))) is used to assess the accuracy of ZTD estimated by PPP, since IGS has not yet provided ZTD data for iGMAS stations. In order to verify the accuracy of iGMAS tropospheric products, we counted the RMS of 130 global IGS stations between iGMAS and IGS ZTD products from 2 January 2019 to 31 January 2019. The calculation method of RMS between iGMAS ZTD and IGS ZTD can be expressed as  
\[RMS=\sqrt{\frac{\sum\limits_{i=1}^{N}\left(ZTD_{i}^{iGMAS}-ZTD_{i}^{IGS} \right)^{2}}{N}} \tag{8}\]  
Figure 10 depicts the distribution and 30-day \(RMS\) between \(iGMAS\) and \(IGS\)\(ZTD\) products of 130 \(IGS\) stations. It is obvious from Figure 10 that the 30-day \(RMS\) of 130 \(IGS\) stations are all below 5 mm, and the 30-day \(RMS\) of most \(IGS\) stations ranges from 0 to 3.5 mm. From Figure 11, we can find that the stability of the time series of \(RMS\) and the accuracy of \(iGMAS\)\(ZTD\) products are very good. The average \(RMS\) of 130 \(IGS\) stations for 30 days is 2.98 mm. The \(IGS\)\(ZTD\) products are synthesized from the results of several analysis centers, and their accuracy is 1.5 to 5 mm [35]; the difference between \(iGMAS\) and \(IGS\)\(ZTD\) products are in millimeter level. Therefore, the millimeter accuracies of \(iGMAS\)\(ZTD\) products are sufficient to assess the accuracy of \(ZTD\) estimated by PPP.