## 3 Experiments and Analysis
### The Influence of STD on PPP Accuracy  
In order to evaluate the marginal effects of STD modeling on the convergence of PPP float solutions, observations from eight GNSS reference stations located in European region during 149 to 159 in 2013 were used. The distribution of the eight stations from the European Permanent Network (EPN) is presented in Figure 2. The corresponding ZTD, horizontal gradients, and precise STD products were calculated and applied for kinematic PPP. Four different positioning modes were considered, as illustrated in Table 2. Note that the external zenith tropospheric and horizontal gradient corrections were estimated with the G-Nut/Tefnut software with backward smoothing [16; 17; 18].  
Figure 3 illustrates the statistical RMS on the N/E/U direction calculated by different tropospheric correction strategies. The precision of simulated real-time kinematic PPP was calculated after a given convergence period. There were eight stations lasting 11 days for observation during the experimental period, thus 88 PPP solutions were obtained in total. In general, the positioning accuracy on the north direction was better than that on the east and up directions. With the increase of convergence time, the accuracy of PPP was improved; however, minor accuracy improvement could be observed after 30 min. Obvious precision improvement could be observed in the U direction when the \"fix-ZTD\" and \"fix-ZTDG\" strategies were used, whereas the effects on tropospheric gradient parameters were minor. The positioning accuracy in N/E/U reached 1.5 cm/1.8 cm/2.6 cm for the strategy \"fix-ZTD\", whereas the positioning accuracy in N/E/U direction was 0.5 cm/1 cm/1.2 cm for the \"fix-STD\" strategy. Precision improvements could be observed in all directions when adopting the \"fix-STD\" strategy, of which the improvement in the U direction was significant.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Strategy** & **Positioning Modes** \\ \hline est-ZTD & troposphere is modeled as a parameter \\ fix-ZTD & external zenith tropospheric correction products \\ fix-ZTDG & external zenith tropospheric and horizontal gradient correction products \\ fix-STD & STD correction products considering residuals \\ \hline \hline \end{tabular}
\end{table}
Table 2: The positioning modes and their corresponding abbreviations.  
Figure 2: Distribution of stations.  
Figure 4 illustrates the positioning error series of the CFRM station which suffered large tropospheric variations. It was observed that the positioning accuracy in the east direction is significantly improved with the help of the horizontal gradient (the \"fix-ZTDG\" strategy) during the convergence period. In the case of the STD augmentation (the \"fix-STD\" strategy), the convergence and accuracy were further improved, which was obvious in the north and up directions. Since the observation noise was not eliminated in the STD modeling based on Equation (3), the observations in PPP processing were smoothed when applying the STD corrections. Therefore, that the positioning errors series for the \"fix-STD\" strategy is rather smooth. The results also demonstrated that the elimination of multipath and observations noise in the \"fix-STD\" strategy could improve the convergence and positioning accuracy.  
Figure 3: Coordinate precision statistical results after different convergence periods with four different tropospheric correction strategies. The \(x\) axis represents the convergence time used for the precision statistics of PPP. (**a**) North. (**b**) East. (**c**) Up.