In precise satellite clock estimation, the satellite clock offsets absorb the pseudorange and carrier phase time-variant hardware delays. The dissimilarity of the satellite clock estimated with observations at different frequencies is termed the inter-frequency clock bias (IFCB). The bias inconsistency suggests that the simple ionospheric-free satellite clock cannot directly be applied to the multi-frequency carrier phase observations in multi-frequency precise point positioning (PPP). We propose the carrier phase time-variant observable-specific signal bias (OSB) concept and the corresponding estimation approach to solve this. The definition, rationality, reliability and validity of the carrier phase time-variant OSB are clarified. The new concept advantage is that a set of the carrier phase time-variant OSB values can directly amend on the carrier phase observations, and thereafter, the IFCB effect can be eliminated, which provides the flexibilities for the GNSS carrier phase observation handing. Datasets collected from 144 Multi-GNSS Experiment (MGEX) stations are adopted for the carrier phase time-variant OSB estimation and an analysis of its effect on the GNSS multi-frequency PPP performance. The various multi-frequency PPP models are tested and evaluated considering the carrier phase time-variant OSB correction. The results indicate that the GPS, BDS-2 and BDS-3 carrier phase time-variant OSB time series have the obvious amplitudes and the amplitudes of the Galileo and QZSS carrier phase time-variant OSB are small. The GPS and BDS-2 multi-frequency PPP performance is significantly enhanced when correcting the carrier phase time-variant OSB. The GPS-only kinematic ionospheric-float PPP exhibits the positioning accuracy of 1.0 cm, 2.2 cm and 2.6 cm in the north, east and up components when correcting the carrier phase time-variant OSB, whereas the positioning accuracy of the case without the correction is 1.4 cm, 2.8 cm and 3.7 cm in three directions, respectively. The mean convergence time of two dual-frequency and three triple-frequency BDS-2-only kinematic PPP is reduced by 5.0%, 4.9%, 5.4%, 4.7% and 4.6%, respectively, with the carrier phase time-variant OSB correction. The carrier phase time-variant OSB improvement on BDS-3-only multi-frequency PPP is not obvious owing to the relatively few available and stable carrier phase time-variant OSB values. The reliability, suitability and effectiveness of the GNSS carrier phase time-variant OSB are demonstrated.
In precise satellite clock estimation, the satellite clock offsets absorb the pseudorange and carrier phase time-variant hardware delays. The dissimilarity of the satellite clock estimated with observations at different frequencies is termed the inter-frequency clock bias (IFCB). The bias inconsistency suggests that the simple ionospheric-free satellite clock cannot directly be applied to the multi-frequency carrier phase observations in multi-frequency precise point positioning (PPP). We propose the carrier phase time-variant observable-specific signal bias (OSB) concept and the corresponding estimation approach to solve this. The definition, rationality, reliability and validity of the carrier phase time-variant OSB are clarified. The new concept advantage is that a set of the carrier phase time-variant OSB values can directly amend on the carrier phase observations, and thereafter, the IFCB effect can be eliminated, which provides the flexibilities for the GNSS carrier phase observation handing. Datasets collected from 144 Multi-GNSS Experiment (MGEX) stations are adopted for the carrier phase time-variant OSB estimation and an analysis of its effect on the GNSS multi-frequency PPP performance. The various multi-frequency PPP models are tested and evaluated considering the carrier phase time-variant OSB correction. The results indicate that the GPS, BDS-2 and BDS-3 carrier phase time-variant OSB time series have the obvious amplitudes and the amplitudes of the Galileo and QZSS carrier phase time-variant OSB are small. The GPS and BDS-2 multi-frequency PPP performance is significantly enhanced when correcting the carrier phase time-variant OSB. The GPS-only kinematic ionospheric-float PPP exhibits the positioning accuracy of 1.0 cm, 2.2 cm and 2.6 cm in the north, east and up components when correcting the carrier phase time-variant OSB, whereas the positioning accuracy of the case without the correction is 1.4 cm, 2.8 cm and 3.7 cm in three directions, respectively. The mean convergence time of two dual-frequency and three triple-frequency BDS-2-only kinematic PPP is reduced by 5.0%, 4.9%, 5.4%, 4.7% and 4.6%, respectively, with the carrier phase time-variant OSB correction. The carrier phase time-variant OSB improvement on BDS-3-only multi-frequency PPP is not obvious owing to the relatively few available and stable carrier phase time-variant OSB values. The reliability, suitability and effectiveness of the GNSS carrier phase time-variant OSB are demonstrated.