A Multi-Frequency Galileo PPP-RTK Convergence Analysis with an Emphasis on the Role of Frequency Spacing

Abstract

The single-receiver integer ambiguity resolution-enabled variant of precise point positioning (PPP), namely PPP-RTK, has proven to be crucial in reducing the long convergence time of PPP solutions through the recovery of the integerness of the user-ambiguities. The proliferation of global navigation satellite systems (GNSS) supports various improvements in this regard through the availability of more satellites and frequencies. The increased availability of the Galileo E6 signal from GNSS receivers paves the way for speeding up integer ambiguity resolution, as more frequencies provide for a stronger model. In this contribution, the Galileo-based PPP-RTK ambiguity resolution and positioning convergence capabilities are studied and numerically demonstrated as a function of the number and spacing of frequencies, aiming to shed light on which frequencies should be used to obtain optimal performance. Through a formal analysis, we provide insight into the pivotal role of frequency separation in ambiguity resolution. Using real Galileo data on up to five frequencies and our estimated PPP-RTK corrections, representative kinematic user convergence results with partial ambiguity resolution are presented and discussed. Compared to the achieved performance of dual-frequency fixed solutions, it is found that the contribution of multi-frequency observations is significant and largely driven by frequency separation. When using all five available frequencies, it is shown that the kinematic user can achieve a sub-decimeter level convergence in 15.0 min (90% percentile). In our analysis, we also show to what extent the provision of the estimable satellite code biases as standard PPP-RTK corrections accelerates convergence. Finally, we numerically demonstrate that, when integrated with GPS, the kinematic user solution achieves convergence in 3.0 and 5.0 min on average and at 90%, respectively, in the presence of ionospheric delays, thereby indicating the single-receiver user’s fast-convergence capabilities.

Review of PPP–RTK: achievements, challenges, and opportunities

“…Since the concept of PPP-RTK was first proposed by Wübbena et al (2005), many researchers implemented the PPP-RTK method and carried out several experimental verifications (Li et al, 2011(Li et al, , 2014Oliveira et al 2017;Psychas et al, 2021;Teunissen et al, 2010;Zhang et al, 2022). The flow of PPP-RTK generally goes through two major phases: the server phase which is to derive the precise orbit, clock, UPD, and atmospheric corrections based on the observations at network stations, and the user phase, where the corrections derived from network enable the fast AR of absolute positioning.…”

“…For better positioning performance, the research on bias estimation, atmospheric correction modeling, and rapid ambiguity resolution were conducted (Li et al, 2020a;Nadarajah et al, 2018;Wang et al, 2020b). With the advancement of multi-GNSS, the research of PPP-RTK experienced the developments from an ionosphere-free model to an undifferenced and uncombined model (Li et al, 2014;Odijk et al, 2016;Zhang et al, 2018a), single system to multi-system Li et al, 2021a;Ma et al, 2020), and dual-frequency to multi-frequency (Li et al, 2022d;Psychas et al, 2021). Following the advancement of the theoretical study, the PPP-RTK service systems have been developed by several research institutions and commercial companies to provide real-time precise positioning services around the world.…”

Improving the precision and accuracy of wildlife monitoring with multi‐constellation, multi‐frequency GNSS collars

“…In addition, the availability of a greater number of satellites allows the GNSS receiver to choose the best geometrically distributed subset to obtain a highly accurate solution (Weiss 2021). Furthermore, multi‐frequency data integration leads to higher accuracy, shorter convergence time, and improved ambiguity resolution performance (Geng and Guo 2020, Xin et al 2020, Psychas et al 2021).…”

PPP-RTK considering the ionosphere uncertainty with cross-validation

“…Integrating the observations of multiple frequencies provides a stronger positioning model, potentially resulting in the faster PPP-RTK ambiguity resolution. The studies on investigating the PPP AR with multi-GNSS and multi-frequency observations have demonstrated that the horizontal convergence of the kinematic Galileo + GPS multi-frequency PPP AR needs 3.0 min on average and 5.0 min in the 90% of cases (Psychas et al 2021), and the convergence can be achieved within 3 min on average if there are more than 10 Galileo + BeiDou satellites involved in PPP AR without any ionospheric corrections (Guo et al 2021). These results imply that the rapid convergence of a few minutes is achievable by multi-GNSS and multi-frequency PPP AR even without the a priori ionospheric constraints.…”