Objectives Multipath effect is one of the main factors that affect the convergence time and positioning accuracy of precise point positioning (PPP). For multi-frequency GNSS undifferenced and uncombined PPP, it is necessary to establish a multipath correction model for each frequency, which increases the complexity of data processing. We evaluate the effectiveness of multipath correction in undifferenced and uncombined PPP using multi-frequency GNSS observation data from 12 International GNSS（global navigation satellite system） Service stations.

Methods We extract the raw phase residuals based on GPS/Galileo/BDS（BeiDou satellite navigation system） multi-frequency undifferenced and uncombined PPP, and use multiple linear regression to construct a correlation model of inter-frequency phase residuals. The sidereal filtering is used to establish a multipath model for the phase residuals of some frequencies, combined with the residual correlation model to recover the full-frequency multipath correction.

Results The results show that the phase residuals of any frequency can be fitted by the phase residuals of other frequency points, with a fitting accuracy of 91% or more. In static conditions, it leads to an average decrease of 19.2% in the GPS convergence time. In contrast, for Galileo systems employing dual-frequency, triple-frequency, and five-frequency PPP positioning, the convergence time is reduced by 31.2%, 42.8%, and 32.9%, respectively. Similarly, for BDS dual-frequency and triple-frequency positioning, the convergence time shortened by 16.4% and 17.0%, stabilizing around 28 min. The kinematic results also showed significant improvement. Additionally, for GPS/Galileo/BDS combination, the average convergence time was shortened from 15 min to about 13 min with multipath correction in static mode, the resulting positioning accuracies in the east, north, and up directions reached 0.27 cm, 0.24 cm, and 0.80 cm, respectively. Under kinematic conditions, the average convergence time of GPS/Galileo/BDS was decreased from 17 min to about 16 min. Furthermore, the positioning accuracies of GPS/Galileo/BDS in the east, north, and up directions reached 0.82 cm, 0.68 cm, and 2.40 cm, respectively.

Conclusions Therefore, studying the inter-frequency phase multipath correlation and obtaining a comprehensive multipath correction model is of significant importance for improving the efficiency of multi-frequency GNSS multipath mitigation and positioning accuracy.