## 4 Experimental Validations
### Influence of Cycle Slips on PPP Estimation  
The positioning performance of the PPP estimation will be decreased by the unmodeled error due to the failure in detecting cycle slips. To analyze the influence of cycle slips on PPP estimation and validate the proposed quality control based on additional observations with opposite weight, the cycle detection algorithm uses the relatively loose threshold condition where the cycle slip will be defined if the epoch-difference geometry-free phase combination is more than three times larger than the difference between wavelengths on two frequencies, or the epoch-difference MW combination is larger than four cycles. By applying these experienced thresholds, the precision of PPP estimation is investigated in terms of the unit weight STD and the maximum weighted residual at each epoch. The weighted residuals are used to process the phase and pseudorange residuals uniformly. Figure 3 shows the unit weight STD with and without quality control, and Figure 4 shows the corresponding maximum weighted residuals. Figure 3: The unit weight STD of the single GPS PPP solution with and without quality control at station BRST. Figure 2: Distribution of stations used for evaluating the performance of multi-GNSS combined real-time kinematic PPP. It can be seen from Figures 3 and 4 that there are several large anomalies on the unit weight STD curve and the maximum weighted residual curve of the single GPS PPP solution without quality control. For example, the maximum weighted residual occurs on the G07 phase data between the epochs 1142 and 1151 (11:31:00 and 11:35:00, coordinated universal time (UTC)) and reaches about 0.26 m, which is 0.84 m in terms of the original residual. The corresponding unit weight STD is about 0.18 m at this epoch. Similarly, the phase weighted residuals of the G05 satellite are also abnormal, with the variation from 0.11 m to 0.07 m at epochs 2180 to 2297 (20:09:30 to 21:08:00, UTC time) and the unit weight STD is from 0.06 m to 0.04 m. The corresponding original residual is from 0.32 m to 0.28 m. At the last few epochs after 21:46:00, the weighted residual of the G29 satellite is also abnormal. There are also some other small anomalies for the solution without quality control. The anomalies might be caused by the ignorance of cycle slips, where one is about 0.24 m and 0.19 m for L1 and L2, respectively. The magnitude is enlarged by the ionospheric-free combination and other observations' residuals might be influenced through their common parameters. In order to analyze these anomalies, the times of the difference between wavelengths on two frequencies for the epoch-difference geometry-free observations and the elevation angle are presented in Figure 5.  
Figure 4: The maximum weighted residual of the single GPS PPP solution with and without quality control at station BRST. Figure 5: \(Cont.\)  
Figure 5 shows that the epoch difference of the geometry-free phase combination is abnormal at epochs around 11:31:00, 20:09:30, and 21:50:30 for G07, G05, and G29 satellites, respectively. It indicates that cycle slips are easy to occur at the period when the elevation angle is low and they are difficult to be detected by the data preprocessing procedure. The larger residual and worse PPP estimation performance will be caused by these unmodeled cycle slips. The geometry-free phase variation of the G07 satellite is largest and reflects the largest cycle slip, which results in the greatest impact on the positioning error curve. Figure 6 shows the positioning error of the single GPS PPP solution with quality control and without quality control. Without quality control, the positioning error fluctuates more widely and the convergence time is longer than that of the solution with quality control. The additional observations with opposite weight are used to remove the influence of the undetected cycle slips if the unit weight STD or the maximum residual does not satisfy the threshold condition.