A unified model of GNSS phase/code bias calibration for PPP ambiguity resolution with GPS, BDS, Galileo and GLONASS multi-frequency observations

The performance of high-precision Global Navigation Satellite System (GNSS) positioning in multi-frequency and multi-constellation environments strongly depends on the understanding and handling the biases that inevitably exist between the different systems and signals. The usage of observable-specific signal bias (OSB), allowing to map biases to each individual observation type involved, provides full flexibility for the multi-GNSS bias processing. In this contribution, the OSB estimation model is extended from the traditional dual-frequency model to multi-frequency and multi-GNSS one to provide GPS/GLONASS triple-frequency, Galileo five-frequency, BDS six-frequency phase/code bias products for precise point positioning (PPP) ambiguity resolution (AR). Results indicate that the code bias products exhibit high stability with average standard deviations (STDs) of 0.06-0.10 ns for GPS and 0.16-0.33 ns for BDS/Galileo/GLONASS. Likewise, the daily phase bias is extremely stable, with average STDs of 0.01-0.02 ns for GPS and Galileo, 0.03-0.05 ns for BDS and 0.05-0.07 ns for GLONASS. Particularly, for the modernized binary offset carrier signals of Galileo E5 and BDS-3 B2, their phase/code biases present relatively high consistency between the different tracking modes and different frequencies. In addition, obvious differences in the range of 10.92-28.58 ns can be noted between the receiver-specific code bias of BDS-2 and BDS-3 for their common frequency signals. Based on the observable-specific phase and code biases, a multi-frequency PPP cascade integer resolution model is developed to make full use of all available observations from different GNSSs. After applying these bias products, PPP AR with GPS, BDS, Galileo and GLONASS multi-frequency observations is achieved with an average convergence time of 4.44 min, showing remarkable improvements of 56.8% and 16.8% compared to dual-frequency PPP float and fixed solutions, respectively.