## 1 Introduction
In 2016, the authors in [13] introduced a new DF-PPP model, combining the measurements from the GPS, Galileo, and BeiDou systems. The proposed model applies the un-differenced and between-satellite single-difference (BSSD) linear combinations. The latter is able to cancel out some biases related to the receiver, such as the non-zero initial phase bias of the receiver oscillator and receiver clock error. The statistical results showed that the post-processed GNSS PPP technique based on un-differenced observations provided a convergence time improvement of 25% with respect to the GPS-only configuration. In addition, the use of the BSSD technique in post-processing PPP mode improved the precision of the positioning solution by about 25% compared to the GPS-only case. The convergence time of the solution was equal to 10 min when the BSSD model was applied. In [14], the benefits of multi-GNSS for PPP were also investigated. Firstly, a consistency test of precise orbit and clock products supplied by different providers (CNES, Center for Orbit Determination in Europe--CODE-, German Research Centre for Geosciences--GFZ-, etc.) were performed for GPS, GLONASS, Galileo, and BeiDou. Furthermore, to investigate the effectiveness of multi-GNSS data and higher rate precise orbit and clock products, five Asia-Pacific regional stations of the MGEX network were chosen for kinematic PPP tests adopting TriP software developed by Wuhan University [15]and based on IF combination of DF carrier phases and pseudoranges. Furthermore, in this case, the positioning accuracy and fast convergence time benefited from the combined using of multi-GNSS and a higher rate of precise clock corrections. The multi-GNSS PPP approach improved the positioning accuracy by 20% and 80% considering the GPS-GLONASS and BeiDou-only PPP configurations. Using higher rate precise clock products allows for the effect of the errors related to the interpolation to decrease, and the positioning accuracy was enhanced by an average of 30%-50% for the all the configurations excepting for the BeiDou-only PPP. A performance analysis of a multi-GNSS PPP model based on GPS, GLONASS, Galileo, and BeiDou observations, was also shown in [16]. The investigation on PPP accuracy and convergence time was conducted on the basis of data processing results from both kinematic and static modes considering single-and multi-constellation configurations. Data from five stations on sixteen consecutive days were used and all stations were equipped with multi-GNSS receivers. DF observations from GPS L1/L2, GLONASS G1/G2, BeiDou B1/B2, and Galileo E1/E5a signals were adopted to form the IF combined code and carrier-phase measurements model. Multi-GNSS precise satellite orbit and clock products provided by the ESOC (European Space Operations Center, Germany) were adopted for PPP techniques together with different error correction models. The results of static positioning indicated that the BeiDou-only PPP positioning accuracy was lower than the GPS-only case on both horizontal and vertical components. GPS/BeiDou PPP configuration provides a positioning accuracy improvement of 28%, 6%, and 7% in the three coordinates, respectively, with respect to the GPS-only PPP while a slightly worse positioning accuracy is achieved with GPS/GLONASS PPP. The usage of a triple-constellation GPS/BeiDou/GLONASS PPP improved the positioning accuracy by 25%, 20%, and 19% over the GPS/BeiDou and 9%, 8%, and 10% with respect to GPS/GLONASS in the east, north, and up directions. Additionally, the BeiDou-only PPP converged more slowly compared to the GPS-only PPP, but the integration of GPS and BeiDou allowed one to reduce the convergence time by 26%, 13%, and 14% in the three coordinates, respectively, over the GPS-only case. A convergence time improvement of 50%, 29%, and 33% is obtained using GPS/GLONASS PPP when compared to the GPS-only case. Finally, a larger reduction of the convergence time is obtained using triple-constellation in the PPP model.