A Kalman filter-based online fractional cycle bias determination method for real-time ambiguity-fixing GPS satellite clock estimation

Integer ambiguity resolution (IAR) is one of the most powerful methods to improve the precision and the convergence of estimating real-time satellite clocks, which is an indispensable prerequisite to support the realtime precise point position (PPP) service. In this study, a Kalman filter-based online fractional cycle bias (FCB) determination method is proposed to facilitate the real-time IAR for satellite clock estimation. A real-time recursive algorithm for smoothing the average float wide-lane (WL) ambiguity is developed to mitigate the impact of pseudorange noise. Quality control procedures are established throughout the entire FCB filter process to remove low-quality observations and mitigate the impact of incorrect integer ambiguities. This method is designed as an embedded module in the clock estimation procedure to fix both integer WL and narrow-lane (NL) ambiguities in an epoch-by-epoch way for recovering the integer property of the undifferenced ionosphere-free (IF) ambiguities in real-time. The performance of the FCB filter and the ambiguity-fixing clock estimation is validated with a GPS network from the international GNSS service (IGS). Experiments show that the WL and NL FCB estimation accuracy reaches 0.004 cycles and 0.080 cycles for GPS satellites. The WL and NL residuals fit the normal distribution well after several minutes and 1.5 h, respectively, making the ambiguity-fixing clocks converge rapidly in about two hours. The online FCB filter method improves real-time ambiguity-fixing clock estimation accuracy significantly. Compared to the ambiguity-float solution, the STD of the ambiguity-fixing real-time satellite clocks is averagely improved by 31.0 % to 0.040 ns with the ultra-rapid orbits. The ambiguity-fixing satellite clocks can be applied in the real-time kinematic PPP ambiguity resolution, and the positioning accuracy is improved by 24.1 % to 51.7 % compared to that of using the ambiguity-float clock products.

Automated summary

This study proposes a Kalman filter-based online fractional cycle bias (FCB) determination method for real-time integer ambiguity resolution in satellite clock estimation. By smoothing the float wide-lane ambiguity and implementing quality control procedures, the method improves estimation accuracy and convergence. Validation results show significant improvement in real-time positioning accuracy.