# Improving Short Term Clock Prediction for BDS-2 Real-Time Precise Point Positioning
## 5 Conclusions  
Driven by requirements of real-time GNSS precise positioning, short-term precise clock predictions are improved for BDS-2 satellites for possible applications where real-time clock corrections are not available. An improved model combing spectrum analysis and GRNN is proposed. Further, the periodic terms and GRNN related parameters including length and sampling interval of input data, as well as a smooth factor are optimized satellite by satellite to consider satellite-specific characteristics for all the fourteen BDS-2 satellites. For example, there exist some special periods, e.g., 1.3 h for C11, beyond our understanding that periodic terms are related to the orbit period. This noticeable period may be caused by the hardware of the atomic clock itself. The improved model with satellite-specific parameters is validated by comparing the predicted clocks of existing models and the improved model with precisely estimated ones. The clock accuracy of the improved model is generally better than that of the QP, SA, and GRNN model. The overall accuracy of predicted clocks is better than \(\pm\)1 ns within 3 h, which is significantly enhanced with respect to the ultra-rapid products and the accuracy is good enough for several real-time precise applications. The clock prediction is further evaluated by applying them to precise point positioning in both static and kinematic mode for eight IGS MGEX stations in the Asia-Pacific region. The position accuracies using predicted clocks obtained from QP, SA, GRNN models and the improved model are compared and their convergence times are also analyzed as well. In the static PPP, the improved model is validated to be effective, and helps to achieve more than 30.0% improvements on average for each component, which enables some stations to obtain sub-decimeter positioning accuracy. In the kinematic PPP, the improved model performs much better than the others in terms of both convergence time and position accuracy. The convergence time can be shortened from 1-2 h to 0.5-1 h, while the position accuracy is enhanced by 15.4%, 21.6%, and 19.3% on average in east, north and up component, respectively. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**DARW**} & \multicolumn{3}{c}{**MRO1**} \\ \cline{2-7}  & **E (m)** & **N (m)** & **U (m)** & **E (m)** & **N (m)** & **U (m)** \\ \hline
**GBU-P** & 0.131 & 0.127 & 0.176 & 0.140 & 0.135 & 0.161 \\
**SA 1** & 0.119 & 0.113 & 0.153 & 0.129 & 0.118 & 0.153 \\
**GRNN** & 0.117 & 0.110 & 0.142 & 0.123 & 0.109 & 0.149 \\
**IM 1** & 0.112 & 0.095 & 0.125 & 0.118 & 0.110 & 0.140 \\ \hline \hline \end{tabular}  
* SA means the spectrum analysis model, and IM means the improved model.  
\end{table} 
Table 6: The standard deviation (STD) values of DARW and MRO1 station in North (N), East (E), and Up (U) directions of the kinematic PPP solutions (after the initialization phase, with 5 min sample interval). Additionally, compared to the polynomial model, the improved model needs extra processing time in the GRNN network construction phase. Supposing that \(N\) is the number of the whole data, \(n\) is the number of the input data in an iteration that is small enough to be ignored when compared with \(N\), and \(L\) is the number of iterations. Therefore, the computational complexity of GRNN is _O(NL)_. However, the GRNN network construction is not a real-time task. Hence, the computing time of the improved model is almost at the same level as for the polynomial model in the clock prediction process. Furthermore, how to determine the smoothing factor value is a key issue. Generally, the Artificial Intelligence Community recommends the determination method of the smooth factor as the search method, which is an empirical method. A feasible way is determining the value of the smooth factor based on the relationship between the smooth factor and the clock quality determined by the Allan variance.