Research on empirical correction models of GPS Block IIF and BDS satellite inter-frequency clock bias

Triple-frequency observations will introduce an inter-frequency clock bias (IFCB) between the new frequency and the original dual-frequency observations. It has been verified that satellite IFCB can reach dozens of centimeters and several centimeters for GPS Block IIF satellite and BDS satellite, respectively. The existence of satellite IFCB will significantly affect undifferenced triple-frequency data processing. Based on 4-year data collected from 80 globally distributed stations, the long-term characteristics of IFCB coefficients obtained by using harmonic analysis have been studied. The results demonstrate that the coefficients of IFCB periodic model cannot be well fitted only by using sun elevation angle. Also, coefficients have obvious periodic characteristics and their periods differ among different satellites. Thus, a new linear-plus-periodic model is proposed to fit the long-term coefficients. Then, IFCB empirical correction models for 12 GPS Block IIF satellites and BDS GEO and IGSO satellites are built. In order to validate the correction model, IFCB standard deviation (STD), triple-frequency precise point positioning (PPP) and undifferenced extra-wide-lane (EWL) ambiguity resolution are employed. The results based on more than 4-year observations show that, with correction model applied, the average IFCB STD decreases by about 65.5% and 45.5% for GPS and BDS satellites, respectively. Compared to triple-frequency PPP without IFCB correction, triple-frequency PPP results with IFCB correction show that Up, North and East components accuracy are improved by 12.3%, 16.0% and 13.2%, respectively. Besides, IFCB correction will greatly improve the consistence of EWL fractional cycle bias among different stations and improve the success rate of EWL ambiguity resolution.