# Improving Short Term Clock Prediction for BDS-2 Real-Time Precise Point Positioning
## 4 Validation of the Predicted Clocks
### PPP Validation
#### 4.2.2 Kinematic PPP Validation  
The real-time kinematic PPP is realized for the abovementioned eight stations and position residuals of each station in east, north, and up component with respect to its IGS coordinates are calculated for evaluating the predicted clocks. Taking two stations DARW and MRO1 as examples,  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Solutions** & **Setting** \\ \hline Earth tides correction & Solid \\ Earth Rotation Parameters & Products by GFZ \\ Differential code biases & Products by CODE \\ Receiver clock & White noise parameter \\ Ambiguity & Real constants \\ Parameter estimator & Least square method and Kalman Filter \\ \hline \hline \end{tabular}
\end{table}
Table 4: _Cont._  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Station**} & \multicolumn{4}{c}{**E (m)**} & \multicolumn{4}{c}{**N (m)**} & \multicolumn{4}{c}{**U (m)**} \\ \cline{2-13}  & **GBU-P** & **SA\({}^{1}\)** & **GRNN** & **IM\({}^{1}\)** & **GBU-P** & **SA\({}^{1}\)** & **GRNN** & **IM\({}^{1}\)** & **GRU-P** & **SA\({}^{1}\)** & **GRNN** & **IM\({}^{1}\)** \\ \hline
**CEDU** & 0.132 & 0.130 & 0.103 & 0.094 & 0.120 & 0.122 & 0.110 & 0.092 & 0.147 & 0.144 & 0.135 & 0.130 \\
**COCO** & 0.135 & 0.133 & 0.110 & 0.083 & 0.132 & 0.131 & 0.132 & 0.086 & 0.184 & 0.190 & 0.175 & 0.162 \\
**DARW** & 0.097 & 0.089 & 0.092 & 0.084 & 0.095 & 0.107 & 0.099 & 0.076 & 0.115 & 0.082 & 0.088 & 0.095 \\
**HKSL** & 0.152 & 0.153 & 0.122 & 0.092 & 0.150 & 0.132 & 0.132 & 0.114 & 0.192 & 0.139 & 0.140 & 0.120 \\
**IISC** & 0.188 & 0.173 & 0.133 & 0.116 & 0.122 & 0.113 & 0.111 & 0.083 & 0.181 & 0.185 & 0.174 & 0.116 \\
**KRGG** & 0.150 & 0.138 & 0.108 & 0.105 & 0.162 & 0.151 & 0.136 & 0.112 & 0.166 & 0.154 & 0.133 & 0.101 \\
**LIHAZ** & 0.183 & 0.167 & 0.170 & 0.112 & 0.168 & 0.120 & 0.109 & 0.098 & 0.325 & 0.241 & 0.201 & 0.186 \\
**MRO1** & 0.132 & 0.125 & 0.118 & 0.098 & 0.120 & 0.121 & 0.094 & 0.088 & 0.172 & 0.146 & 0.133 & 0.135 \\ \hline \hline \end{tabular} \({}^{1}\): SA means the spectrum analysis model, and IM means the improved model.  
\end{table}
Table 5: The standard deviation (STD) values of each station in North (N), East (E), and Up (U) directions of the daily static PPP solutions (one position solution for each 24-h interval).  
Figures 10 and 11 intuitively demonstrate that the improved model provides better accuracy and shorter convergence time. As for GBU-P, position residuals converge after 1.5 h for DARW and 2 h for MRO1. Experiments results also show that the convergence time of the spectrum analysis model is shorter than that of GBU-P, and yet, GRNN achieves more stable position residuals for all three components after convergence. Comparatively speaking, position residuals obtained by the improved model converge rapidly within half an hour for DARW and one hour for MRO1 and keep within an accuracy level of \(\pm\)0.1 m in the rest of the time.  
Table 6 shows that improved model has the best positioning accuracy. As for DARW station, compared with the GBU-P, the spectrum analysis model increases the position accuracy of 9.1%, 11.0%, and 13.1% for east, north and up component, respectively, while GRNN achieves 10.7%, 13.3%, and 19.3% improvement. When the improved model is used, positioning accuracies are increased by 14.5%, 25.2%, and 28.9% for DARW station (15.7%, 18.5% and 13.0% for MRO1 station) in east, north and up component, respectively. Statistical results also show that the improved model achieves 15.4%, 21.6%, and 19.3% improvement on average in east, north and up component, respectively.