Precision analysis of partial ambiguity resolution-enabled PPP using multi-GNSS and multi-frequency signals

A single-receiver integer ambiguity resolution-enabled precise point positioning (PPP-RTK) user experiences a long convergence time when the rather weak single-constellation dual-frequency ionosphere-float model is used. Nowadays, the rapid development of Global Navigation Satellite Systems (GNSS) provides a multitude of available satellites and frequencies that can serve in improving the user's model strength and, therefore, its ambiguity resolution and positioning capabilities. In this study, we provide insight into and analyze the global impact of a multi-GNSS (GPS, Galileo, BeiDou-3) multi-frequency integration on the expected ambiguity resolution and positioning performance of the ionosphere-float uncombined PPP-RTK user model, and demonstrate whether it is the increased number of satellites or frequencies, or a combination thereof, that speeds up ambiguity-resolved positioning. Moreover, we explore the capabilities of both full (FAR) and partial (PAR) ambiguity resolution, considering the full ambiguity information content with the LAMBDA method, and investigate whether PAR is an efficient solution to the multi-dimensional ambiguity case. The performance of our solutions is assessed in terms of the ambiguity success rate (ASR), the number of epochs (TTFA) to achieve both an ASR criterion and a horizontal positioning precision better than 10 cm, as well as the gain in precision improvement. Based on multi-system multi-frequency simulated data from nine globally distributed stations and a large number of kinematic solutions over a day, we found that the increase in number of frequencies enhances the ambiguity resolution performance, with PAR achieving a TTFA reduction of 70% when five instead of two Galileo frequencies are used, while the ambiguity-float solution is only slightly improved. Further, our numerical results demonstrated that the increase in number of satellites leads to an improvement in both the positioning and ambiguity resolution performance, due to the improved geometry strength. It is shown that the GPS+Galileo+BeiDou solutions can achieve a TTFA of 6.5 and 4.5 min (at 90%) on a global scale when two and three frequencies are used, respectively, without any a priori information on the ionospheric delays. Finally, we analyzed the sensitivity of the PPP-RTK user's performance to changes in the precision of the measurements.