## 1 Introduction  
The measure of the carrier phase of the signals transmitted by the global satellite navigation systems (GNSS) enables, together with the pseudo range and the Doppler shift measurements, a precise positioning to a centimeter range accuracy (see [1] (Chapter 8) and the references therein) assuming that all error sources can be mitigated and the carrier phase ambiguity is determined. This opened the door for the Real-Time Kinematic (RTK) and the Precise Point Positioning (PPP) techniques for high-precision positioning [2] (Chapter 8). The PPP technique is powerful because it does not require a costly infrastructure of stations such as the RTK one, and hence has been widely used from several decades up to recent applications, either public or commercial [3; 4; 5; 6; 7; 8]. However, a major drawback of PPP is the convergence time. Dual-frequency PPP convergence is long, in the order of tens of minutes, which makes it impracticable for many applications. Until now, some improvements have been made using a third frequency (L1/L2/L5 for GPS, E1/E5a/ E5b for Galileo). It is now widely accepted that PPP techniques can achieve centimeter-level accuracy globally in real time, in particular when they are combined with phase integer ambiguity resolution (AR). To solve for the integer ambiguities, the reference [9] proposed an integer clocks approach and the reference [10] a decoupled clock model. Thanks to these approaches, computing differences between satellites are avoidable for the users, contrary to the original technique from Ge [11]. A prerequisite for integer AR on the user side is the need for a ground stations network for computing precise satellite orbits as well as integer recovery clocks or uncalibrated phase delays in the case of an ionosphere-free dual frequency combination. The adoption of a third and a fourth frequency by recent satellites of the GNSS constellations also requires the knowledge of the interfrequency code biases (IFCB). Recent studies concluded that the goal of centimeter-level accuracy positioning can be achieved after the convergence phase even in real time [12]. In the past few years, the real-time network of stations has evolved constantly. The majority of the GNSS observables collected at each ground station are available through the Intenational GNSS Service (IGS) and the Real-Time Service (RTS) [13]. In particular, the French Centre National d'Etudes Spatiales (CNES) contributes significantly with its own network [14]. Other networks are also available, such as AUSCORS, EUREF, and UNAVCO. It is important to note that the modernization of the stations quickly leads to full GNSS capability, enabling real-time dissemination of the GNSS measurements. Using these real-time measurements, CNES has implemented the method for computing code and phase biases described in [9] and built a real-time demonstrator allowing the dissemination of these code and phase biases as well as orbit and clock corrections [15] called PPP-WIZARD (PPP With Zero-difference Ambiguity Resolution Demonstrator). The biases are broadcast following the Radio Technical Commission for Maritime Services (RTCM) definition, and, in 2020, the IGS decided to define its own State Space Representation (SSR) messages standard, mainly to fill some gaps in the RTCM one, such as the lack of phase-bias messages. This standard is implemented in the CNES demonstrator both on the network side and the user side. Since 2020, the corrections are broadcast in both RTCM and IGS standards. We characterize this bias in terms of noise and time stability and show that it can be casted into the SSR representation proposed by the RTCM or the IGS for phase-bias messages. In July 2018, a collaboration between NRCan (Natural Resources of Canada) and CNES concluded that instantaneous (epoch-by-epoch) convergence is possible thanks to the use of the new E6 Galileo signal [16]. An accuracy of 15 cm is achievable using Galileo alone, and centimeter-level accuracy can be obtained by combining Galileo and GPS measurements.