## 3 Materials and Methods
### Data Processes and Numerical Results  
One of the goals of this case study was to investigate the effect of additional GNSS constellations on the kinematic PPP. In order to assess the accuracy performance of the PPP solutions, the collected data were processed under the following five different solution scenarios based on combining the observations from different satellite constellations with CODE's COM ID precise products:  
**S.1**- GPS-only observations,
**S.2**- GPS and GLONASS observations,
**S.3**- GPS, GLONASS, and BDS observations,
**S.4**- GPS, GLONASS, and Galileo observations, and
**S.5**- GPS, GLONASS, Galileo, and BDS observations. In order to obtain PPP-derived coordinates, the collected kinematic data were processed using GrafNav GNSS Post-Processing Software using the parameters given in Table 3. This software supports the GPS, GLONASS, Galileo, BDS, and QZSS global and regional satellite systems. During the kinematic PPP process, \"Multi-Pass\" processing strategy was chosen. In this approach, the PPP-derived coordinates were calculated three times sequentially as forward, reverse, and forward again using the Extended Kalman Filter (EKF) algorithm [33]. After finalizing the processes along each direction, the converged Kalman Filter error states have been applied to the next processing direction [33]. Figure 4: Multipath and Signal-to-Noise Ratio (SNR) Values of two frequencies for all constellations (for G, R, E, and C from top to down, respectively) in the Kinematic Test Data. In the EKF algorithm, 3D position, receiver clock error, tropospheric delay, and carrier-phase float ambiguities are estimated as EKF states [34]. The deterministic and stochastic models of the PPP processing and the details of the EKF algorithm used to estimate the unknowns are given in [PERSON] and [PERSON] [35], [PERSON] and [PERSON] [36], and [PERSON] [37]. In the PPP module of GrafNav software, the tropospheric delay is corrected using the UNB model developed by the University of New Brunswick [38]. However, the wet part of the tropospheric delay is highly variable and cannot be modeled with sufficient accuracy. Thus, when estimating the receiver position and other unknowns, the tropospheric delay is also predicted [34]. As it was explained before, the PPP technique uses precise products in addition to collected GNSS data to estimate the accurate coordinates. Precise satellite orbit and clock corrections of CODE with COM ID retrieved from the related ftp sites were utilized to estimate the PPP-derived coordinates. Here it is noted that the CODE is one of the IGS Analysis Centers, and broadcasts the precise products for GPS, GLONASS, Galileo, BDS, and QZSS satellite constellations under the IGS MGEX Project. In addition to the assessment of the accuracy performance of multi-constellation GNSS PPP, the effect of different MGEX precise products, produced by different IGS ACs on the PPP results, was also investigated. In this respect, the collected kinematic GNSS data were also processed by applying the following solution scenarios:  
**S.6**- GPS-only observations (with IGS's precise products),
**S.7**- GPS-only observations (with CODE's precise products-COD ID),
**S.8**- GPS+GLONASS+Galileo+BDS observations (with GFZ's precise products), and
**S.9**- GPS+GLONASS+Galileo+BDS observations (with Wuhan University's precise products). The PPP-derived coordinates were also calculated by applying the aforementioned PPP solution approach with GrafNav GNSS Post-Processing Software for Scenarios 6-9. The precise GNSS satellite orbit and clock products were provided from IGS, CODE, GeoForschungsZentrum Potsdam (GFZ), and Wuhan University's Analysis Centers. After the kinematic PPP processing given in Scenarios 1-5, the used satellites in PPP and calculated PDOP values were given in Figure 5, left and right, respectively. Figure 5 shows top-down satellite numbers (left) and PDOPs (right) for G, GR, GRC, GRE, and GRCE combinations, respectively.