## 5 Discussions and Conclusions  
In this paper's work, the multi-GNSS combined PPP model was first built for processing arbitrary combinations as well as the single system positioning. For the quality control of the multi-GNSS combined PPP, a robust method was proposed based on additional observations with opposite weight. The corresponding model and the implementation of quality control were discussed in detail and then the performance was analyzed. Experimental results show that the positioning performance with quality control is better than the solution without quality control benefitting from the control of outliers.  
The positioning accuracy and the convergence time of the multi-GNSS combined PPP with the proposed quality control were evaluated using one week's data from 32 globally distributed stations. The GPS positioning accuracy in the east, north, and upward components is 3.2 cm, 2.7 cm, and 6.7 cm, respectively, and the convergence time is 26.5 min and 23.7 min in the horizontal and vertical components, respectively. The corresponding positioning RMS of the quad-system combined PPP is 1.2 cm, 1.0 cm, and 3.0 cm with an improvement of 62.5%, 63.0%, and 55.2% compared to GPS, and the convergence time is improved by 12.8 min and 12.2 min, respectively.  
For the triple-system combined PPP, the positioning performance of the GRC and GRE PPP is close to that of the quad-system combined PPP and better than that of the GCE combined PPP. For the dual-system combined PPP, the best one is the GR combination, where the positioning accuracy and the convergence time are close to that of the triple-system combination. The convergence time of the GC and GE combinations is about 22 min. The positioning accuracy of the former is 1.9 cm, 1.6 cm, and 4.4 cm in the east, north, and upward components, respectively, and it is 1.8 cm, 1.4 cm, and 4.0 cm for the latter.  
Considering the weak geometry caused by few visible satellites and the complexity of multi-GNSS observation data, it is sometimes difficult to solve all abnormal situations due to the limitation of the single quality control model. The integration of multiple quality control methods might help to improve the stability of the solutions. Therefore, the next step of our work is to study the combination of the statistical testing method, the adaptively equivalent weights method, and this proposed method.  
[PERSON] and [PERSON] designed the processing strategy and the experiments, developed the algorithms and the software, performed the analysis of the experiments, and wrote the paper. [PERSON] helped to analyze the combined positioning results. [PERSON], [PERSON], [PERSON], and [PERSON] helped to improve the manuscript. All authors read and approved the final manuscript.  
This work was supported partly by the scholarship program of China Scholarship Council (CSC), the Program of the National Natural Science Foundation of China (41774025, 41731066), the Special Fund for Basic Scientific Research of Central Colleges (Grant No. 310826165014, 300102268305, Chang'an University), the Special fund for technological innovation guidance of Shaanxi Province (2018 XNCGG05), and the Grand Projects of the Beidou-2 System (GFZX0301040308).  
We thank the MGEX and GFZ for providing the data and products for this study.  
The authors declare no conflict of interest.