The new generations of global navigation satellite system (GNSS) space vehicles can transmit three or more frequency signals. Multi-frequency observations bring a significant improvement to precise point positioning ambiguity resolution (PPP AR). However, the multi-frequency satellite code and phase biases need to be properly handled before conducting PPP AR. The traditional satellite bias correction methods, for example, the commonly used differential code biases (DCB), are limited to the dual-frequency ionosphere-free (IF) case and become more and more difficult to extend to multi-GNSS and multi-frequency cases. In this contribution, we propose the observable-specific signal bias (OSB) correction method for un-differenced and uncombined (UDUC) PPP AR. The OSB correction method, which includes observable-specific satellite code and phase bias correction, can directly apply kinds of OSBs to GNSS original observation data, thus, it is more appropriate for multi-GNSS and multi-frequency cases. In order to verify the performance of multi-frequency UDUC-PPP AR based on the OSB correction method, triple-frequency GPS observation data provided by 142 Multi-GNSS Experiment (MGEX) stations were used to estimate observable-specific satellite phase biases at the PPP service end and some of them were also used to conduct AR at the PPP user end. The experiment results showed: the averaged time-to-first-fix (TTFF) of triple-frequency GPS kinematic UDUC-PPP AR with observable-specific satellite code bias (SCB) corrections could reach about 22 min with about 29% improvement, compared with that without observable-specific SCB corrections; TTFF of triple-frequency static UDUC-PPP AR with observable-specific phase-specific time-variant inter-frequency clock bias (IFCB) corrections took about 15.6 min with about 64.3% improvement, compared with that without observable-specific IFCB corrections.

The emerging BeiDou navigation satellite system has contributed to global precise positioning and has recently moved toward space-borne applications. However, the contribution of BeiDou on LEO orbit determination applications is limited by the poor precision of the GEO satellite orbit and clock products. Current researches suggest that BeiDou GEO satellites should not be included in LEO precise orbit determination. Based on analyzing the characteristics of errors existing in BeiDou GEO orbit products, we propose a feasible method to mitigate the offsets in BeiDou GEO orbit errors by in-flight calibration of the systematic daily constant biases in the along-track and cross-track of BeiDou GEO satellites. The proposed method is investigated and validated using one entire month of onboard BDS data from the Chinese FY-3C satellite. The average daily RMS compared with the GPS-derived orbit indicates that our method achieves 6.2 cm three-dimensional precision. When compared to the solutions that disregard the GEO orbit errors scheme and roughly exclude the GEO scheme, the FY-3C orbit precision has been improved by 89.1% and 20.2%, respectively. The average daily RMS values of phase residuals are about one centimeter for solutions that exclude GEO and that estimate systematic biases in GEO orbits. The calibrated orbits of GEO with the decimeter level in along-track and cross-track can be reconstructed by correcting the orbit biases estimated in the FY-3C precise orbit determination. Statistics of the FY-3C orbit quality, observation residuals, and precision of the recovered GEO orbits demonstrate that calibration of daily orbit biases in GEO can improve the precision of LEO orbit determination and enhance the reliability of the solution.