## 4 Experimental Validations
### Comparisons of Real-Time Multi-GNSS PPP with and without Quality Control  
To test the performance of the quality control based on additional observations with opposite weight in the multi-GNSS combined PPP, the dual-system, triple-system, and quad-system combined PPP experiments were first carried out at the station BRST. The solution without quality control is also presented as a comparison. On the basis of the GPS system, seven different combined schemes were used, defined as follows: GPS/BDS (GC), GPS/Galileo (GE), GPS/GLONASS (GR), GPS/BDS/Galileo (GCE), GPS/GLONASS/BDS (GRC), GPS/GLONASS/Galileo (GRE), and GPS/GLONASS/BDS/Galileo (GRCE). Figure 7 shows the positioning errors of the seven schemes without and with quality control, respectively. There are more spikes on the positioning error curve without quality control than the solution with quality control due to the unremoved outliers. Although the combination significantly increases the number of observations, the quad-system combination rarely improves the positioning accuracy comparing to the dual-system or triple-system combination because of the influence of outliers on the PPP solutions without quality control. The positioning errors of the robust GC combined PPP, which are denoted by the black curve, achieve obvious improvements. For example, the biggest jump on the positioning curve without quality control is well fixed at epochs around the thirteenth hour. The results of the other combined schemes are also improved remarkably and better positioning accuracy can be achieved. It should be noted that a small positioning error also exists in the GC combined solutions. With the number of observations increasing, it becomes small in the GE and GCE combinations and completely disappears in the GR, GRC, GRE, and GRCE combinations. Table 2 provides the RMS statistic of the positioning error in east, north, and upward components after convergence, and Table 3 shows the convergence time, which is defined as the period from the first epoch to the converged epoch. The positioning is considered to have converged when the positioning errors reach 0.1 m and remain constant for the next 20 epochs. Obviously, the positioning accuracy and the convergence time without quality control are poorer than the solution with quality control for almost all schemes. Although the positioning performance cannot be improved for one single component, in a few cases where the positioning accuracy or the convergence time is already good, the quality control can still improve the results as a whole. Among the schemes with quality control, the positioning accuracy of the GC combined PPP is worst, since the number of the available satellites is the lowest and the BDS geostationary earth orbit (GEO) satellite orbit and clock products have the poorest precision because of the particular orbit design for covering the Asia-Pacific region. Unfortunately, it is also vulnerable to outliers if it lacks quality control. The proposed quality control is the most effective for this case and the best improvement can be achieved. As a result, the positioning RMS  
Figure 7: The positioning error of the multi-GNSS combined PPP without (**left**) and with (**right**) quality control at station BRST. errors are 1.81 cm, 1.82 cm, and 5.64 cm in the east, north, and upward components, respectively, and the convergence time in the horizontal and vertical components is 29.5 min and 40.5 min, respectively. For the triple-system combination scheme, the GCE combined PPP is similar: the corresponding RMS is 1.14 cm, 1.77 cm, and 4.96 cm, and the convergence time is 13.0 min and 31.5 min. Figure 8 describes the number of available satellites for each scheme and the corresponding position dilution of precision (PDOP). It can be seen that the number of available satellites is generally more than 20 for the quad-system combination and almost 30 at some epochs. The quad-system PDOP is the best and the average is 0.65.