# A Short-Term Forecasting Method of Inter-Frequency Clock Bias for GPS Block IIF Satellites
## 3 Results
### Time-Varying Characteristics of the IFCB
This indicates that the period of the IFCB time series had good consistency in the short term for modeling prediction. Figure 4: Autocorrelation coefficients of the GPS Block IIF satellites. The top and bottom panels in Figure 6 exhibit the epoch moments corresponding to the peaks of the time series of the autocorrelation coefficient for the GPS Block IIF satellite IFCBs, respectively. As the lag time increased, the epoch moments were not constant but presented an approximately linear decrease in regularity. The reason for this phenomenon is that the GPS IFCB sequence period is not a complete 24 h, and the changing characteristics of the IFCB time series are related to the relative position of the satellite-Earth-Sun. To analyze the reduction characteristics in detail, the epoch moments corresponding to the primary and secondary peaks were fitted by linear functions according to the change characteristics of peak moments for all GPS satellites. As shown in the black, solid lines in Figure 6, there was excellent agreement between the epoch moments and the linear function. According to the slope of the fitting function, the mean difference of the peaks over the adjacent days was approximately 2.62 min for all satellites. Figure 5: Hypothesis test \(t\) values of the IFCB. Figure 6: Epoch moments corresponding to the primary peak (top) and secondary peak (bottom) of the autocorrelation coefficients. In order to realize accurate IFCB short-term prediction, a least squares linear fitting function was performed for each satellite based on the epoch moments corresponding to the primary and secondary peaks. The primary and secondary peaks were the largest and second largest places in the time series of the correlation coefficients in one day, respectively. The fitting results of the primary period and secondary period are shown in Table 2, where \(a\) and \(b\) represent the first-order term coefficient and the constant term of the linear function, and the root mean square (RMS) was calculated by the fitting values and the real values corresponding to the epoch moments. It is worth mentioning that the primary period and secondary periods were the epoch intervals corresponding to two adjacent primary peaks and secondary peaks. The primary and secondary periods are equal in the theory. However, due to the error, there were small differences between them; thus, we first calculated the fitting coefficient of each peak moment and then calculated the average to establish the prediction model. Taking the G01 satellite as an example, when the lag days were \(n\), the difference of the peak moment was approximately \(3.04n\) min compared to the first day. Therefore, the differences in the initial moment caused by lagging days need to be fully taken into account for IFCB prediction. In fact, the periodic features presented by the GPS Block IIF satellite IFCB basically coincide with the satellite's own orbital motion period, which is related to the bias between the solar day and sidereal day and the influence of other satellite dynamics factors. [PERSON] et al. used the IFCB of the previous day to forecast the current day, and the prediction accuracy of IFCB was 0.6 cm, which indicated that the IFCBs on different days were highly related in terms of fluctuation size and periodicity [14]. From the above analysis, the initial moments of the IFCB time series on different days did not strictly correspond with the increase in lag time, and there was a regularity bias. When the observation data used to estimate IFCB were not available in time, it was necessary to implement short-term modeling forecasts for the IFCB in the current time period. Considering that the release time of IGS final precision ephemeris products generally lags by 7 days, we used IFCB on day \(n\) to predict IFCB on day \(n+7\) in view of the periodic regularity changes of the IFCB time series.