Algorithms for precise point positioning with ambiguity resolution (PPP-AR) were developed over a decade ago. Since then, techniques have matured and most analysis centres (ACs) of the International GNSS Service (IGS) now produce products enabling PPP-AR. The IGS PPP-AR working group, created during the 2018 IGS workshop in Wuhan, investigated the interoperability of such products and recently published a paper on this topic in the Journal of Geodesy.
Until recently, CNES/CLS was the only AC openly sharing phase-bias products enabling PPP-AR. In the last year, both the Center for Orbit Determination in Europe (CODE) and Wuhan University also made their products publicly available. Other ACs, such as NRCan and ESA, compute experimental PPP-AR products that they shared for the purpose of the experiment. Finally, Graz University of Technology participated in this study by providing code and phase biases obtained from undifferenced and uncombined observations. Hence, in total, PPP-AR solutions were available from six ACs: CNES/CLS (GRG), CODE, ESA, Graz University of Technology (TUG), NRCan (EMR), and Wuhan University (WHU).
With the Bias SINEX format, ACs have a mean of exchanging observable-specific biases (OSBs) for both code and carrier-phase observables. However, the format is yet to be adopted by all ACs and many of them (CNES/CLS, ESA and NRCan) provided biases in different formats: the CNES/CLS distributed widelane biases in the clock file header, ESA shared widelane and narrowlane uncalibrated phase delays (UPDs), and NRCan provided time-varying widelane biases along with ionosphere-free code and phase clocks. Transformations were applied to each product to obtain uncombined OSBs, all of which are detailed in the paper.
“Integer clocks” for PPP-AR must be used conjointly with their corresponding biases to recover the integer property of ambiguities at the user end. This characteristic also implies that the satellite clock combination process currently used within the IGS must be modified to combine both satellite clocks and biases simultaneously. When doing so, it becomes possible to use the integer properties of the clocks to precisely align satellite clock estimates from ACs. This means that one can estimate an ambiguity-like parameter for each AC-satellite pair in the combination process and fix these parameters to integers. As an example, the following figure shows that the standard deviation of all ambiguity residuals over a day is about 0.013 narrowlane cycles, which indicates that ionosphere-free phase clocks can be precisely aligned to better than 1.3 mm (~ 4 ps).
Figure 1: Ambiguity residuals from the ionosphere-free phase clock solution (Banville et al 2020) [typo: ERM should be EMR]
The combined clock/bias products were then used to compute PPP solutions for 209 globally distributed stations over a one-week period using the NRCan PPP software. The figure below shows the accuracy of 24-hour static solutions (after a daily 7-parameter transformation) for all products. The top panel shows the float solutions and the bottom panel the PPP-AR solutions. The benefit of AR is quite obvious for the east component, with an improvement of about 60%. The combined products (labeled IAR) performed as good, if not better, than products from individual ACs. This confirms the interoperability of the products and their applicability in the positioning domain.
Figure 2: RMS error of static PPP (float) and PPP-AR solutions (Banville et al. 2020)
This blog post is a short summary of the key results presented in the Banville et al. (2020) paper. For more details, please refer to the paper. This work is a fist step towards generating combined PPP-AR products for the IGS.
Banville S, Geng J, Loyer S, Schaer S, Springer S, Strasser S (2020) On the interoperability of IGS products for precise point positioning with ambiguity resolution. J Geod 94. doi:10.1007/s00190-019-01335-w