Instantaneous PPP convergence

When I first got involved in GNSS, more than a decade ago, my objective was to reduce the convergence time of PPP solutions. In the past few years, I witnessed this methodology evolve and fast convergence became possible using ambiguity resolution and external atmospheric data. The upcoming years will be a game changer in this area: with GNSS modernization, instantaneous PPP convergence will be possible even without any reference stations nearby.

 

In March 2018, the European Union decided to open the Commercial Service (CS), making available the E6 signal at no cost to users. As a result, modern receivers can currently track a total of five frequencies (E1, E5, E5a, E5b, E6) on 14 Galileo satellites. With three or more frequencies, a series of widelane ambiguities can be resolved in a cascading scheme. These unambiguous widelane signals can be used to form an ionosphere-free phase measurement with lower noise than code measurements, but typically still at the decimeter level. This concept has already been exploited to obtain a position error of a couple of decimeters within 5 minutes (see, for example, Laurichesse [2015]).

 

The availability of the Galileo E6 signal provides a significant step forward for PPP-AR: as a result of frequency separation, fixing widelane signals on Galileo allows for the instantaneous determination of an unambiguous ionosphere-free range having a precision of 19 cm. This is a significant improvement over code measurements (78 cm) and GPS triple-frequency widelane fixing (30 cm). This means that, with resolved Galileo widelane ambiguities and a PDOP equal to 1, we would be getting a 3D position error of about 20 cm. Already impressive, but can we do better?

 

While fixing widelane ambiguities can often be achieved within a single epoch, it is more complex to reliably resolve the remaining ambiguities (the narrowlanes). This is where the best integer equivariant (BIE) approach to ambiguity resolution comes in handy. Rather than using a simple binary outcome to ambiguity resolution (pass vs fail), BIE computes a weighted average of integer vectors. The resulting BIE estimates are thus typically an improved version of the float estimates: even if they are not integers, they are closer to integers than the float solution. As a result, the position estimates lie somewhere between the float and the fixed solutions.

 

My friend Denis Laurichesse (CNES) and myself applied these concepts to a network of stations in Australia, using 6 reference stations and 1 PPP user. (Note that only few receivers within the IGS currently track the E6 signal, so we had to restrict our study to a wide-area network rather than a global network.)  Denis estimated uncombined Galileo satellite phase biases on the E1, E5a, E5b and E6 signals. These phase biases enable ambiguity resolution for Galileo and, combined with the CNES orbit and clock products (GRM), we were able to estimate both GPS and Galileo ambiguities as integers. The next figure shows the convergence of the GPS + Galileo solution using BIE, where each line represents a different (independent) session:

 

Fig 1 Convergence of GPS + Galileo PPP-AR solution

 

As we can see, a (few) centimeter-level horizontal accuracy is possible instantaneously, and the solution converges very quickly. Remember that this is only the beginning: with more satellites tracking several frequencies (a full constellation of GPS, Galileo, BeiDou and QZSS), the reliability of the approach will greatly improve.

 

This blog post is a short summary of our paper published in the Innovation column of GPS World. Please refer to the article for more details on our methodology and our results. At the time of writing this blog post, there is an important screw up in the online version of the paper as Denis is missing from the author list! Before this is fixed, let me stress that this project was Denis’ idea and I simply added my little personal touch to it! 😉

 

Reference

Laurichesse D (2015) Carrier-phase Ambiguity Resolution: Handling the Biases for Improved Triple-frequency PPP Convergence. GPS World, Vol. 26, No. 4, April 2015, pp. 49-54.



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