# A Short-Term Forecasting Method of Inter-Frequency Clock Bias for GPS Block IIF Satellites
###### Abstract  
The time-varying biases within carrier phase observations are integrated into satellite clock offset parameters for precise clock estimation. Consequently, when the precise satellite clock bias is applied to the third frequency observation for precise point positioning (PPP), a new type of inter-frequency clock bias (IFCB) with satellite dependence should be noticed. If the IFCB is estimated together with the receiver coordinates, tropospheric wet delay, ambiguity and other parameters, it will increase the computational burden and lead to more time consumption. In order to solve this problem, the IFCB of GPS Block IIF satellites were estimated using 162 global uniformly distributed Multi-GNSS Experiment (MGEX) stations. By analyzing the time-varying characteristic of each satellite IFCB and combining the lag characteristics of the final ephemeris products, a modeling method of short-term IFCB prediction based on the epoch-by-epoch sliding Pearson autocorrelation function is proposed. The feasibility of this method was verified through the Student's \(t\)-distribution, comparison with the measured IFCB, the posteriori residual of the third frequency carrier phase and the kinematic/static PPP solutions. The results showed that since the IFCB period was not a complete 24 h, the difference in the IFCDs time series on different days was increasingly significant with the passage of lag time, and the correlation constantly decreased. The peak-to-peak amplitudes of the IFCB difference reached 1.13, 3.44, 6.86 and 11.25 cm when the lag time was 1, 9, 19 and 29 days, respectively. In addition, based on the lag characteristic of final precise ephemerides released by the International GNSS Service (IGS) analysis centers, the prediction accuracy of the IFCB was evaluated with a time lag of 7 days. The root mean square of the posteriori residuals at the third-frequency observation decreased by approximately 51.3% compared to that without considering for IFCB correction. The triple-frequency uncombined PPP in the horizontal and vertical directions improved by approximately 33.2% and 17.2% for the static PPP solutions and 50.2% and 39.7% for the kinematic PPP solutions, respectively. In general, the accuracy and convergence time of the triple-frequency uncombined PPP were equivalently improved when the predicted IFCB and the measured IFCB were used. inter-frequency clock bias; triple-frequency; precise point positioning; prediction method +
Footnote †: journal:  
0000-0002-4130-3330]Y.Y. fact that the current GNSS satellite clock products are generated based on specific measurements, such as L1/L2 ionospheric-free (IF) combined observations for GPS, resulting in IF time-varying phase hardware delays in parts of the satellite terminal that are contained in satellite clock products. When this type of clock product is applied to the third-frequency observations or more for PPP, the posterior residues on the corresponding frequency show large fluctuations, namely, inconsistency between the first two frequencies (i.e., L1/L2) and the third-frequency or more observations. That is, an additional bias on the third-, quad-, or more frequency observations need to be processed, which is called the inter-frequency clock bias (IFCB) [13; 14]. [PERSON] et al. found that the changing characteristics of the GPS IFCB time series were related to the relative position of the satellite-Earth-Sun by analyzing the law of period changes of the GPS IFCB, and the peak amplitudes reached over a dozen centimeters [13; 15]. As for BeiDou-2, small bias variations were also recognized, but they were generally confined to peak amplitudes of approximately 2 cm. In contrast, the QZSS, BDS-3, and Galileo were shown to exhibit good consistency with different frequency carriers [16; 17; 18; 19]. In the process of multi-frequency PPP resolution, in order to reduce the computational burden and avoid the problem of the overestimation of the parameter to be examined, three methods are traditionally used for GPS IFCB.