## 5 Analysis of Results
### Static Application Validation  
The positioning errors of the four real-time precise point positioning solutions are computed in the east, north, and height directions. The proposed PPP models are compared with the station's coordinates computed from the geodetic-grade post-processed GPS PPP model. Figure 5 illustrates the three-hour positioning errors of GPS, GLONASS, Galileo, and BeiDou PPP solutions, respectively, on DOY 225 as an example. As previously mentioned in Table 1, only GFZ, IGS, and WHU analysis centers offer BeiDou orbit and clock corrections. For the GPS PPP model, it is obvious that the obtained positioning accuracy through the five products is within the decimeter level with superiority of BKG, CNE, and WHU products; furthermore, CNE and WHU products accelerate the convergence time compared with the other products, and there are some clear gaps in the obtained solutions from the IGS products. This is due to interruption in the real-time data streams. It is also found that the GLONASS PPP solution's accuracy is within the sub-meter level in the north and height components, but not in the east component. This is attributed to the GLONASS orbit and clock products' accuracy attainable from the five centers and the GLONASS satellite configuration; on the other hand, by using the five products, real-time Galileo PPP solutions achieve decimeter position accuracy in three directions. Moreover, acceleration in the Galileo PPP's convergence time is achieved in the three components. An exception is the height component obtained from GFZ and WHU products. For the BeiDou RT-PPP solutions, the positioning errors are within the decimeter level for GFZ products; however, the positioning errors are increased to the meter level and sub-meter level for the IGS and WHU products, respectively. This is because the ZED-F9P module collects only BeiDou-2 satellite signals, which are noisier than the BeiDou-3 satellite signals; in addition, the GFZ BeiDou orbit and clock products' accuracies are better than those of their counterparts from IGS and WHU analysis centers. For additional assessment of the PPP processing models' accuracy, the root mean square error (RMSE) for the positioning errors over the three examined days are calculated and given in Figure 6. Obviously, the RMSEs for the GPS PPP processing model by utilizing the five products types are within the centimeter-to-decimeter level in both the east and north directions, while it is within a few decimeters in the up direction; in contrast, the positioning error of the GLONASS PPP is increased to the meter level in the east component on the first two days and the few-decimeter level on the third day. For the north and up components, the positioning errors are within the few-decimeter level. An exception is the meter-scale error in the up-component on DOY 225, which is derived from WHU orbit and clock products. This may be due to GLONASS satellite configuration and the accuracy of WHU products. The real-time Galileo PPP's accuracy ranges are 0.080-0.452, 0.039-0.531, and 0.122-0.756 m in the east, north, and up directions, respectively. On DOY 227, the results obtained through WHU products are an exception, particularly in the east and up positions; additionally, the up positioning accuracy is estimated from the GFZ products. This might be attributed to the accuracy of the products on this day; on contrary, the BeiDou PPP's accuracy ranges from the sub-meter to the meter level with observed improvements for GFZ products on DOY 225; moreover, it is obvious that the WHU products are better than the other products on the three examined days. Figure 5: _Cont._  
Figure 5: Positioning errors of real-time GPS, GLONASS, Galileo, and BeiDou PPP using various products on DOY 225. Figure 6: RMSE values for the static PPP solutions on the three examined days. To further examine the real-time PPP solutions' accuracy, the RMSE values for the 3D position errors are calculated at 30, 60, 120, and 180 min intervals (Figure 7).