Real-time estimation of multi-GNSS and multi-frequency integer recovery clock with undifferenced ambiguity resolution

Precise clock product of global navigation satellite systems (GNSS) is an important prerequisite to support real-time precise positioning service. The developments of multi-constellation and multi-frequency GNSS open new requirements for real-time clock estimation. In this contribution, the estimation model of multi-GNSS and multi-frequency integer recovery clock (IRC) is developed to improve both the accuracy and efficiency of real-time clock estimates. In the proposed method, the undifferenced ambiguities are fixed to integers, thus the integer properties of the ambiguities are recovered and the accuracy of the clock estimates is also improved. Moreover, benefitting from the removal of large quantities of ambiguity parameters, the computation time is greatly reduced which can guarantee high processing efficiency of real-time clock estimates. Multi-GNSS observations from 150 globally distributed Multi-GNSS Experiment (MGEX) tracking stations were processed with the proposed model. Compared to the float satellite clocks, the precision of the real-time IRC with respect to CODE 30 s final multi-GNSS satellite clock products were improved by 53.0%, 42.7%, 63.7% and 33.9% for GPS, BDS, Galileo and GLONASS, respectively. The average computation time per epoch with multi-GNSS observations was improved by 97.1% compared to that of standard float clock estimation. Kinematic precise point positioning (PPP) ambiguity resolution was also performed with the derived real-time IRC products. Compared to the float PPP solutions, the position accuracy of the multi-GNSS IRC-based fixed solutions was improved by 77.2%, 49.7% and 52.7% from 24.2, 13.3 and 30.7 mm to 5.5, 6.7 and 14.5 mm for the east, north and up components, respectively. The results indicate that ambiguity fixing can be successfully achieved by using the derived the IRC products. In addition, the estimation model of multi-frequency IRC products is also investigated to promote the capability and application of real-time PPP AR under multi-frequency signals.