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Multi-GNSS phase delay estimation and PPP ambiguity resolution: GPS, BDS, GLONASS, Galileo

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This paper focuses on the precise point positioning (PPP) ambiguity resolution (AR) using the observations acquired from four systems: GPS, BDS, GLONASS, and Galileo (GCRE). A GCRE four-system uncalibrated phase delay (UPD) estimation model and multi-GNSS undifferenced PPP AR method were developed in order to utilize the observations from all systems. For UPD estimation, the GCRE-combined PPP solutions of the globally distributed MGEX and IGS stations are performed to obtain four-system float ambiguities and then UPDs of GCRE satellites can be precisely estimated from these ambiguities. The quality of UPD products in terms of temporal stability and residual distributions is investigated for GPS, BDS, GLONASS, and Galileo satellites, respectively. The BDS satellite-induced code biases were corrected for GEO, IGSO, and MEO satellites before the UPD estimation. The UPD results of global and regional networks were also evaluated for Galileo and BDS, respectively. As a result of the frequency-division multiple-access strategy of GLONASS, the UPD estimation was performed using a network of homogeneous receivers including three commonly used GNSS receivers (TRIMBLE NETR9, JAVAD TRE_G3TH DELTA, and LEICA). Data recorded from 140 MGEX and IGS stations for a 30-day period in January in 2017 were used to validate the proposed GCRE UPD estimation and multi-GNSS dual-frequency PPP AR. Our results show that GCRE four-system PPP AR enables the fastest time to first fix (TTFF) solutions and the highest accuracy for all three coordinate components compared to the single and dual system. An average TTFF of 9.21 min with \(7{^{\circ }}\) cutoff elevation angle can be achieved for GCRE PPP AR, which is much shorter than that of GPS (18.07 min), GR (12.10 min), GE (15.36 min) and GC (13.21 min). With observations length of 10 min, the positioning accuracy of the GCRE fixed solution is 1.84, 1.11, and 1.53 cm, while the GPS-only result is 2.25, 1.29, and 9.73 cm for the east, north, and vertical components, respectively. When the cutoff elevation angle is increased to \(30{^{\circ }}\), the GPS-only PPP AR results are very unreliable, while 13.44 min of TTFF is still achievable for GCRE four-system solutions.

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Correspondence to Xingxing Li.



See Tables 7, 8, 9, 10, 11, 12, 13.

Table 7 Percentages of residuals within ± 0.15 cycles and ± 0.25 cycles of WL and NL UPDs before and after the code bias correction
Table 8 Percentages of residuals within ± 0.15 cycles and ± 0.25 cycles of WL and NL UPDs estimated from different types of receivers
Table 9 The average convergence time (min) of static PPP float solution under different cutoff elevation angles (from \(7{^{\circ }}\) to \(30{^{\circ }}\))
Table 10 The average TTFF (min) of static PPP AR solution under different cutoff elevation angles (from \(7{^{\circ }}\) to \(30{^{\circ }}\))
Table 11 RMS values of static PPP float solutions with different session lengths (10, 20, 30, 60, 120 min) in single-, dual- and four-system modes (Unit: cm)
Table 12 RMS values of static PPP AR solutions with different session lengths(10, 20, 30, 60, 120 min) in single-,dual- and four-system modes (Unit: cm)
Table 13 Fixing percentage with different session lengths for single-, dual- and four-system static PPP

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Li, X., Li, X., Yuan, Y. et al. Multi-GNSS phase delay estimation and PPP ambiguity resolution: GPS, BDS, GLONASS, Galileo. J Geod 92, 579–608 (2018).

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