Multi-frequency phase observable-specific signal bias estimation and its application in the precise point positioning with ambiguity resolution

Precise point positioning with ambiguity resolution (PPP AR) is a valuable tool for high-precision geodetic observations, while phase observable-specific signal bias (OSB) is critical to implementing PPP AR. We present a reliable approach to effectively estimate the multi-frequency phase OSB based on the triple-frequency phase geometry-free and ionospheric-free (GF–IF) combination. First, when the first- and second-frequency phase OSB (e.g., L1/L2 for GPS) and their undifferenced ambiguity have been resolved, we introduced them as known quantity into the phase GF–IF combination. Then, the third-frequency phase OSB is estimated as completely independent between epochs in the phase GF–IF combination. Finally, both the time-invariable and time-variable hardware biases will be absorbed into the third-frequency phase OSB. We used a global network of multi-frequency GPS/Galileo data over a month (January 2022) to verify this approach. The results demonstrated that such multi-frequency phase OSB is able to recover integer ambiguities with eligible frequency choices and observable combinations. In addition, after multi-frequency phase OSB corrections on the raw observation, the impact of large time-variable hardware biases of GPS IIF L5 could be mitigated at user. Regarding multi-frequency GPS/Galileo kinematic PPP AR with phase OSB, the positioning root mean square (RMS) of 1.0, 1.3 and 3.0 cm could be achieved in the east, north and up components with the 3-h observation session, respectively, while the corresponding positioning RMS without phase OSB was 2.9, 2.1 and 4.4 cm. Furthermore, when the multi-frequency phase OSB was applied, the horizontal positioning RMS of ambiguity-fixed solutions could achieve below the level of 10 cm within 4 min. Our multi-frequency phase OSB approach proves to be convenient and efficient in the multi-frequency PPP AR and can be flexibly generalized to five- or even more frequency phase OSB estimation.