Only recently, fast convergence of PPP-RTK solutions depended on the proximity of users to a regional network of ground stations. Obtaining quasi-instantaneous cm-level accuracies worldwide seemed like a utopic goal. But two weeks ago, Hexagon's Autonomy and Positioning division announced “RTK From the SkyTM”, a technology that enables such positioning feat. In this blog post, I offer insights into what it takes to achieve rapid PPP convergence at a global level.
As described in the Hexagon press release and white paper, the development of “RTK From the Sky” is the result of advancements in the whole positioning ecosystem. It leverages the modernization of GNSS constellations and, in particular, the availability of three or four frequencies broadcast by most constellations. The plots below, from the white paper, show the horizontal error (95%) after a PPP reset, based on one week of data reset every 10 minutes for six globally distributed stations. To achieve this level of performance, the rover exploited the L1/E1/B1, L2, L5/E5/B2 and E6/B3 bands. As you can see, convergence happens within seconds, just like RTK. Impressive!
Figure 1 Horizontal error (95%) after a PPP reset, based on one week of data reset every 10 minutes (courtesy of Hexagon)
Is it really possible to obtain global instantaneous cm-level accuracies from PPP, i.e., without using nearby base stations? As Denis Laurichesse and myself explained in this GPS World article, using the Galileo E6 signal provides significant benefits in terms of convergence time. Following the publication of this article in 2018, I was expecting many papers replicating our results. Interestingly, these papers never materialized. We have seen multi-GNSS, multi-frequency positioning being presented in several manuscripts, but none (to my knowledge) clearly demonstrating instantaneous convergence. Why?
A possible explanation could be that researchers only focused on the big picture: using all GNSS constellations and frequencies. But the devil is in the details. In the GPS World article, we used the best integer equivariant (BIE) ambiguity estimator. This approach computes a weighted average of integer vectors instead of performing ambiguity validation using other popular methods (success rate, ratio test, etc.). A benefit of BIE is that it converges gradually, and often quite rapidly, to a fixed solution. Still, BIE is a double-edged sword: if your stochastic model is incorrect, your solution can quickly converge to the wrong position! In the paper, we “solved” this issue by using single-epoch PPP solutions and, therefore, cleverly avoided modelling the impact of time-correlated errors. I am not claiming that BIE itself is essential to fast PPP convergence, but adequate stochastic modelling and an efficient ambiguity validation strategy are certainly critical.
While the GPS World article defined a path forward for global (quasi-) instantaneous convergence, there were still a lot of details to figure out to bring this method into a usable technology in the field. There are still issues that I would not personally know how to address. As the Hexagon press release emphasized, the whole positioning ecosystem must be mastered to achieve these results. For this reason, I have great respect for the team of researchers and engineers at Hexagon. Kudos!