Galileo PPP rapid ambiguity resolution with five-frequency observations

Galileo, transmitting signals on the five frequencies E1, E5a, E5b, E5 and E6, has completed the fundamental constellation with 26 satellites and now can provide the global positioning service independently. Multi-frequency (triple-frequency or above) signals allow a variety of combinations on different frequencies, which has the potential to improve the performance of the precise point positioning (PPP) ambiguity resolution (AR). We developed a multi-frequency PPP AR method to make use of the Galileo five-frequency observations. The stable multi-frequency uncalibrated phase delay (UPD) products of Galileo were estimated first. It is interesting to find that the extra-wide-lane (EWL) UPDs on the E5a/E5b, E5a/E5 and E5/E5b combined frequencies are very close to zero. With the obtained UPD products, the Galileo triple-, quad- and five-frequency PPP AR was conducted. Triple-frequency PPP AR with different frequency combinations can improve the positioning accuracy of 30 min by 36.6-86.8% compared with float solutions, and 2.3-62.5% compared with dual-frequency PPP AR. Among the five types of frequency combinations, the triple-frequency PPP AR on E1/E5/E6 frequencies shows the best positioning performance with the averaged convergence time shortened to 16.9 min. Furthermore, the averaged convergence time is 15.3 min and 15.0 min for quad- and five-frequency PPP AR, respectively. Compared with the time to first fix (TTFF) of 19.9 min for narrow-lane ambiguity resolution with dual-frequency observations, the TTFF is only shortened by about 1 min with multi-frequency observations. It is beneficial that the EWL and wide-lane (WL) ambiguities can be fixed to integers instantaneously, and the decimeter-level positioning accuracy can be achieved within 0.5 min by utilizing triple-/quad-/five-frequency PPP wide-lane AR (WAR). Moreover, the positioning accuracy of the first epoch derived from Galileo five-frequency PPP WAR is (0.112, 0.144, 0.641) m in the east, north and up components, which has an improvement of 2.1-42.0% compared to triple-/quad-frequency PPP WAR.