Multipath effect on carrier-phase observation is one of the bottlenecks for mm-level applications when using precise point positioning (PPP). Hence, we extract the multipath directly from raw carrier-phase residuals of GPS, GLONASS, Galileo, and BDS, by using PPP technique. Although the residuals for one frequency assimilate the errors from other frequencies, which is caused by error adjustment by the least squares estimator, the primary component of residuals is multipath. The results indicate that the residuals between frequencies have a significant linear negative correlation and synchronous time lag for each system. Besides BDS Geostationary Earth Orbit satellites, the residuals for other satellites can establish accurate mathematic relationship between the frequencies. For GLONASS, the residuals of R1 frequency recovered from R2 frequency with the mathematical relationship are better than 0.1 mm accuracy, which means the effect of inter-frequency bias can be neglected. These regularities double-reduce the complexity of data processing. Based on the multipath distribution, we propose a modified Multipath Hemispherical Map model (M-MHM), which constructs grids from residuals and is divided into three equal-elevation angle parts with an optimal resolution 0.2° × 0.2° × 1° from numerous experiments. In addition, the multipath manifests great consistency among satellites for GPS, GLONASS, and Galileo systems when elevation angles are higher than 15°, while is more satellite dependent for BDS. Although GPS L1 frequency is identical to Galileo E1, the model still has some systematic bias between GPS and Galileo. Compared with sidereal filtering and original MHM model, the M-MHM brings the highest improvement in both residual variance reduction and positioning accuracy. The positioning accuracy is on average 12% improvement compared to MHM and 29% improvement compared to SF. For four systems combined solutions with the M-MHM model, can reach an accuracy of 0.75, 0.55, and 2.08 cm in the east, north, and up components.
Multipath model Multi-GNSS PPP Raw carrier-phase observation
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We gratefully acknowledge financial support from China Scholarship Council (CSC, file 201706270123). This work is funded by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 41721003), and The National Key Research and Development Program of China (Nos. 2016YFB0501803, 2017YFB0503402).
KZ conceived and designed the research and analyzed the data; KZ and PL performed the research; KZ wrote the paper; XZ and MG provided advice. The paper was modified by XZ, PL, XL, MG, FG, JS, and HS.
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