Assessment of multi-frequency global navigation satellite system precise point positioning models using GPS, BeiDou, GLONASS, Galileo and QZSS

The development of a global navigation satellite system (GNSS) brings the benefit of positioning, navigation and timing (PNT) services with three or even more available frequency signals. This paper developed five-system multi-frequency precise point positioning (PPP) models based on mathematical and stochastic models. Static positioning performances were evaluated and analyzed with multi-GNSS experiment (MGEX) network datasets and a vehicle-borne kinematic experiment was conducted to verify the kinematic PPP performances. In addition, the receiver clock, zenith tropospheric delay (ZTD), inter-frequency bias (IFB) and differential code bias (DCB) estimates were discussed. Results show that the triple-frequency PPP performances perform slightly better than the dual-frequency solutions, apart from the GPS-related PPP models based on a single ionosphere-free (IF) combined measurement. By introducing the external ionospheric products, the mean convergence time is reduced. For instance, the mean convergence time of ionosphere-constrained (IC) multi-frequency PPP is reduced by 7.4% from 35.7 to 33.1 min and by 19.0% from 7.8 to 6.3 min, for Galileo-only and five-constellation solutions, respectively, compared with dual-frequency IF PPP models. Similarly, the kinematic PPP can also achieve improved performances with more frequency signals and multi-GNSS observations.