From network RTK to PPP-RTK, it is highly expected that high-precision positioning within a few minutes can be achieved with a sparse reference network. In this study, we investigate a rapid multi-frequency PPP convergence strategy based on Galileo E1/E5a/E6 and BeiDou-3 B1C/B2a/B3I signals, whose unambiguous wide-lane observables can efficiently assist in speeding up narrow-lane ambiguity resolution. Furthermore, frequency-specific biases existing on the third-frequency observables have been observed to slow down multi-frequency PPP-AR convergence. In this study, we partially mitigated their effects by estimating a second satellite clock for the third frequency of signals. We validated this approach with one month of data collected from 22 stations. On average, it took about 18 min for PPP wide-lane ambiguity resolution (PPP-WAR) to converge, while 32 min were required for ambiguity-float PPP. Compared with dual-frequency PPP-AR, which needed nearly 12 min to converge, multi-frequency PPP-AR required 6 min only. Once there were more than 10 satellites involved in PPP, the convergence could be achieved within 3 min on average. Meanwhile, 81% and 62% of multi-frequency PPP-AR solutions converged successfully within 5 and 1 min, respectively. Finally, we carried out a vehicle-borne experiment to validate this approach in a kinematic environment. Owing to frequent cycle slips during the movement of vehicle, it took 14 min for B1C/B2a/B3I and E1/E5a/E6 PPP-AR to obtain reliable positions, and 19 min for those using the other signal combinations B1C/B2a/B2b and E1/E5a/E5b, owning to higher noise. Overall, these results are promising for achieving high-precision PPP positioning globally within a few minutes if multi-frequency biases can be handled well in the data processing.

Precise point positioning with ambiguity resolution (PPP-AR) based on multiple global navigation satellite system (multi-GNSS) constellations is an important high-precision positioning tool. However, some unmodeled satellite and receiver biases (such as errors in satellite attitude) make it difficult to fix carrier-phase ambiguities. In order to fix ambiguities of eclipsing satellites, accurate integer clock and satellite attitude products (i.e., attitude quaternion) have been provided by the International GNSS Service (IGS). Nevertheless, the quality of these products and their positioning performance in multi-GNSS PPP-AR have not been investigated yet. Using the PRIDE PPP-AR II software associated with the corresponding rapid satellite orbit, integer clock and attitude quaternion products of Wuhan University (WUM), we carried out GPS/BDS PPP-AR using 30 days of data in an eclipsing season of 2020. We found that about 75% of GPS, 60% of BDS-2 and 57% of BDS-3 narrow-lane ambiguity residuals after integer clock corrections fall within ±0.1 cycles in the case of using nominal attitudes. However, when using attitude quaternions, these percentages will rise to 80% for GPS, 70% for BDS-2 and 60% for BDS-3. GPS/BDS daily kinematic PPP-AR after integer clock and nominal attitude corrections can usually achieve a positioning precision of about 10, 10 and 30 mm for the east, north and up components, respectively. In contrast, the counterparts are 8, 8 and 20 mm when using attitude quaternions. Compared with the case of using attitude quaternions only at the network end for the integer clock estimation, using attitude quaternions only at the user end shows a pronounced improvement of 15% in the east component and less than 10% in the north and up components. Therefore, we suggest PPP users apply integer clock and satellite attitude quaternion products to realize more efficient ambiguity fixing, especially in satellite eclipsing seasons.

Loading of the Earth’s crust due to variations in global atmospheric pressure can displace the position of geodetic stations. However, the station displacements induced by the diurnal and semidiurnal atmospheric tides (S₁-S₂) are often neglected during Global Positioning System (GPS) processing. We first studied the magnitudes of S₁-S₂ deformation in the Earth’s center of mass (CM) frame and compared the global S₁-S₂ grid models provided by the Global Geophysical Fluid Center (GGFC) and the Vienna Mapping Function (VMF) data server. The magnitude of S₁-S₂ tidal displacement can reach 1.5 mm in the Up component at low latitudes, approximately three times that of the horizontal components. The most significant difference between the GGFC and VMF grid models lies in the phase of S₂ in the horizontal components, with phase discrepancies of up to 180° observed at some stations. To investigate the effects of S₁-S₂ corrections on GPS coordinates, we then processed GPS data from 108 International GNSS Service (IGS) stations using the precise point positioning (PPP) method in two processing strategies, with and without the S₁-S₂ correction. We observed that the effects of S₁-S₂ on daily GPS coordinates are generally at the sub-millimeter level, with maximum root mean square (RMS) coordinate differences of 0.18, 0.08, and 0.51 mm in the East, North, and Up components, respectively. We confirmed that part of the GPS draconitic periodic signals was induced by unmodeled S₁-S₂ loading deformation, with the amplitudes of the first two draconitic harmonics induced by atmospheric tide loading reaching 0.2 mm in the Up component. Moreover, we recommend using the GGFC grid model for S₁-S₂ corrections in GPS data processing, as it reduced the weighted RMS of coordinate residuals for 45.37%, 46.30%, and 53.70% of stations in the East, North, and Up components, respectively, compared with 39.81%, 44.44%, and 50.00% for the VMF grid model. The effects of S₁-S₂ on linear velocities are very limited and remain within the Global Geodetic Observing System (GGOS) requirements for the future terrestrial reference frame at millimeter level.