# Improved Short-Term Clock Prediction Method for Real-Time Positioning
## 3 Experiment Results
### Accuracy Verification of Short-Term Clock Prediction
#### 3.1.1 Experiment Using IGS Final Product  
The use of IGS clock final products with 0.075 ns precision provides PPP results at centimeter-level application [18]. These products refer to the IGS timescale [19]. The accuracy of PPP solutions of a single day in E, N, and U directions is about 5, 3, and 9 mm, respectively [20]. We use IGS precision clock products obtained from the IGS website to improve the prediction method and analyze the high-precision real-time clock prediction [21]. The time span of clock correction is from day 120 to day 151 in 2016, which entails a total of 30 days of IGS precision clock products tabulated at 30-s intervals [22]. Table 3 indicates that the prediction results of cesium AFS are not ideal when the linear or quadratic model is used. Therefore, only rubidium AFS is discussed in the next part of this paper. During real-time prediction, only a few hours of short-term data are selected to ensure the accuracy of the clock error of adjacent epochs. A prediction workflow-diagram for one single epoch \(m_{i}\) (\(i=1,\ 2,\ 3,\cdots\)) is depicted in Figure 4. The processing method is as follows. First, \(n\) hours clock data are used for the linear sliding prediction of clock correction after \(m_{i}\). Second, when the prediction is accumulated to \(k\) hours, the residuals between the prediction and estimation are fitted by the periodic terms obtained through FFT to estimate the coefficients and corresponding time reference. Finally, when the periodic term is added to the subsequent sliding prediction, the prediction accuracy is greatly improved. Figure 3 indicates that the periodic signals of 12 and 6 h are stronger than those of the 4-h variation. Thus, we let the value of N be 2. Figure 5 shows the prediction accuracy of the improved model (blue) and the general linear model (yellow) to intuitively compare the improvement degree. We use 2 h of observation to fit the trend term, forecast the 2-h clock correction, and simulate the real-time clock for 30 days with a continuous 30-day IGS final clock product. The difference is that the improved model is added with the periodic term correction using the residuals of the previous day forecast. All of the satellite clock prediction accuracy depicted in Figure 5 improves. In particular, Block IIF satellites are generally better than 0.3 ns due to their high accuracy. The remaining types of satellites also improve significantly, and several of them, such as G16, exhibit improved accuracy by nearly half. Satellite type does not affect the improvement in model accuracy, and the previous periodic signal model can be applied to the current prediction. Part of the results of 1-h (blue), 2-h (green), and 3-h (yellow) clock prediction depicted in Figure 6 is used to determine how much observation is suitable for short-term prediction. Figure 6a indicates  
Figure 4: Workflow-diagram for one single epoch \(m_{i}\). Figure 5: Comparison of 2-h results obtained with improved and linear models. that precision is concentrated in two ranges. The first range is the rest of the Block IIF satellites. The accuracy of their on-board atomic clocks is better than 0.2 ns, and the length of time required for modeling data exerts a minimal effect on the final results. However, when the linear model is used to forecast 1 h only, the accuracy of using 3-h observation is worse than that of using 1-h observation. In other words, the performance of using 1-h observation shown in Figure 6a is less accurate than that of the two other plans, which demonstrates the effectiveness of the improved model. The second range is the Block IIR and Block IIR-M satellites with precision concentrations between 0.2 and 0.35 ns. Modeling them with 2-h or 3-h observation is better than using the 1-h model, which also confirms that the periodic signal model established with the previous 24-h forecast residuals is suitable for 2-h or 3-h prediction. As for G13, the clock aging should be responsible for the worse accuracy.