Realizing rapid re-convergence in multi-GNSS real-time satellite clock offset estimation with dual-thread integer ambiguity resolution

Real-time satellite clock offsets are key in realizing real-time precise point positioning (PPP). Typically, tens of minutes are required for re-convergence because many tropospheric and ambiguity parameters are estimated in the clock offset estimation when the interruption of observation data occasionally occurs. This contribution proposes a rapid re-convergence method for multi-global navigation satellite system (GNSS) real-time satellite clock offset estimation. In case of a few seconds of interruption, the dual-thread integer ambiguity resolution method is proposed. The float clock offset, uncalibrated phase delay, fixed and float ambiguities, clock offset with IAR, zenith wet delay (ZWD) and inter-system bias (ISB) are generated in a slow thread, in which the fixed and float ambiguities, ZWD and ISB are used in a quick thread to achieve rapid re-convergence. Observations from 60 globally distributed stations were processed using the proposed method. The experimental results show that rapid re-convergence, fast estimation and high-precision clock offsets can be achieved. The re-convergence time of clock offset estimation was 0.14, 0.15, 0.74, 0.36 and 2.48 min for the GPS, Galileo, BDS-2, BDS-3 and GLONASS, respectively. Most satellite clock offsets can realize instantaneous re-convergence. The clock offset standard deviations are 0.028, 0.024, 0.069, 0.043 and 0.125 ns, respectively. The computation times were 21.4 and 1.7 s for the slow and quick threads, respectively. Compared to the float PPP solutions, the positioning accuracy of the PPP-AR was improved by 53.9, 29.9 and 18.2% from 1.80 to 0.83 cm, 1.57 to 1.10 cm and 3.63 to 2.97 cm for the east, north and up components, respectively. In case of interruptions lasting from a few minutes to tens of minutes, the ZWD, ambiguities and ISB information before interruption are used in the clock offset estimation, and a strong constraint is imposed on the normal equation, i.e., a large value (e.g., 10 5 ) is used instead of the diagonal value of the normal equation matrix corresponding to each estimated parameter. Experimental results show that rapid re-convergence can be achieved for GPS and Galileo with an interruption of 10 min, whereas the rapid re-convergence cannot be achieved for BDS-2, BDS-3 and GLONASS because of the impact of satellite orbit accuracy, error model, and neglection of the inter-frequency bias, respectively.