# Improving Short Term Clock Prediction for BDS-2 Real-Time Precise Point Positioning
## 3 Realization of the Improved Model
### Impact of the Length of Input Data  
The performance of the GRNN network differs in different sample datasets. Meanwhile, to build a suitable GRNN network, a sample dataset is required to be divided into input data and output data in an appropriate way. In this experiment, the remaining clock residues after the removal of trend and periodic terms are used, including all fourteen BDS-2 satellites. In the GRNN network construction phase, the length of input data successively increases from 1 h to 9 h to investigate how the length of input data affects the GRNN network performance. As an example, the length of input data is 5 h, in the first iteration, the GRNN network is constructed based on data of 1-5 h as input and with data 2-6 h as output. By analogy, in the second iteration, the GRNN network is optimized based on data of 2-6 h as input and with data 3-7 h as output. After completion of the (N-5)-th iteration (assuming there are N hour data), the GRNN network is employed for prediction.  
Now, we can judge which sample length is the best for each BDS-2 satellite, including 5 GEOs, 6 IGSOs, and 3 MEOs, by checking the agreement of true (GFZ precise clock products) and prediction with different length of input data. Figure 5 gives clock difference results for each satellite type, and they are on the sub-nanosecond level when the prediction time is less than 1 h, no matter the length of input data raises from 1 h to 9 h. The clock differences for all fourteen BDS-2 satellites increase along with prediction time increasing, but are still within \(\pm\)2 ns for most satellites, when the prediction time is not more than 3 h. Figure 5 also shows when a short length of input data is employed, i.e., 1-2 h, the characteristics of the satellite clock cannot be fitted properly. On the other hand, when the length of input data is up to 8-9 h, the clock differences are not the smallest, since too much perturbation information is introduced. After numerous experiments, when the prediction time is less than 3 h, the recommended length of input data is 3 h for most satellites as the best compromise between prediction accuracy and computational complexity. Additionally, it should be noted that the clock differences for all satellite clocks start from zero since the fitting ability of the GRNN is extremely strong and the training set and the test set are continuous.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **Satellite** & **Main Period (h)** & **Secondary Period (h)** \\ \hline \multirow{6}{*}{GEO} & C01 & 5.9850 & 24.0059 \\  & C02 & 7.9727 & 12.0029 \\  & C03 & 23.7449 & 11.8725 \\  & C04 & 11.9373 & 23.2397 \\  & C05 & 11.9700 & 5.9850 \\ \hline \multirow{6}{*}{IGSO} & C06 & 11.9373 & 23.6166 \\  & C07 & 23.8747 & 11.9700 \\  & C08 & 11.9700 & 23.8747 \\  & C09 & 23.8747 & 11.9373 \\  & C10 & 11.9373 & 23.8747 \\  & C13 & 11.9700 & 23.8747 \\ \hline \multirow{2}{*}{MEO} & C11 & 12.8125 & 1.2922 \\  & C12 & 12.8502 & 6.4157 \\ \cline{1-1}  & C14 & 6.4063 & 12.8125 \\ \hline \hline \end{tabular}
\end{table}
Table 1: BDS-2 satellite clock periodic terms analysis.