**5. Conclusions**

As a key product for real-time PPP-AR, real-time OSB products are currently broadcasted by CNES. Based on the dual-frequency ionospheric-free observation model, the integer feature of ambiguity was recovered by using the OSB products and PPP-AR could be performed. The quality of the OSB products was analyzed, and the performance of the dual-frequency PPP-AR was evaluated. The experimental results showed that:

(1) The mean DA of the GPS and Galileo satellites was above 97% according to the 31-day statistical analysis of the OSB products, whereas that of BDS was less than 60%. The mean MAX and STD of the GPS, Galileo, and BDS satellites were 0.045 and 0.012; 0.081 and 0.028; and 0.292 and 0.085 cycles, respectively. By analyzing the residual distribution of the OSB products, the WL residual percentages within ±0.25 cycles for the GPS, Galileo, BDS-2, and BDS-3 satellites were found to be more than 92%, while the NL residual percentages within ±0.25 cycles for the four systems were 92%, 89%, 79%, and 60%, respectively. Considering the DA, MAX, STD, and ambiguity residuals, we concluded that the reliability of PPP-AR, including the BDS system, may not be guaranteed using the OSB products from CNES, especially for BDS-3. In fact, the experiment described in this paper also confirmed that the advancement of positioning accuracy was constrained after BDS satellites had been incorporated into multi-GNSS PPP-AR.

(2) Due to the accuracy restrictions of real-time products, real-time PPP-AR cannot greatly increase positioning accuracy; however, it can dramatically speed up convergence time. In the kinematic mode, the GPS+Galileo fixed solution reduced the mean convergence time from 19.7 to 9.6 min and increased the convergence ratio within 10 min from 22.2% to 70.2% when compared to the float solution. After convergence, the positioning accuracy of the GPS+Galileo float solution reached about 2, 2, and 4 cm for the E, N, and U components, respectively, while that of the GPS+Galileo fixed solution was further enhanced to 1, 1, and 3 cm for the E, N, and U components, respectively. In the static mode, the overall fixed solution improved the float solution from 1~2 cm to 7~9 mm for the E and N components, and the U component was better than 1.5 cm. The mean convergence times of the GPS-only and GPS+Galileo solutions were 11.4 min and 8.0 min, respectively. The mean ambiguity fixed rates for the kinematic and static modes for the three combinations were more than 97%. In conclusion, the GPS+Galileo solution showed the best performance in the kinematic mode when using the OSB products from CNES, while the GPS-only solution can achieve almost the same performance as the GPS+Galileo solution in the static mode.

(3) A prediction method was proposed to compensate for the short-term missing OSB products, and our experiment showed that the positioning results were more reliable and avoided re-convergence.

**Author Contributions:** Conceptualization, S.D., B.S. and G.H.; methodology, S.D. and B.S.; validation, S.D. and W.X.; formal analysis, S.D. and W.X.; writing—original draft preparation, S.D.; writing review and editing, S.D., B.S., W.X., G.H., Y.G. and P.L.; visualization, S.D., B.S. and W.X.; project administration, G.H.; funding acquisition, G.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (41941019; 42004024), the National Key R&D Program of China (2021YFB2600603; 2021YFC3000503), and the Key R&D Program of Shaanxi Province (2022ZDLSF07-12).

**Data Availability Statement:** The CDDIS website (https://cddis.nasa.gov/archive/gnss, accessed on 2 August 2022) was used to obtain the MGEX data, which include the stations, DCB, and ATX. The precise products obtained from CNES (http://www.ppp-wizard.net/products/REALTIME/, accessed on 2 August 2022) include the satellite orbit, clock offset, and OSB.

**Acknowledgments:** The authors gratefully acknowledge IGS MGEX for providing the GNSS data. We also acknowledge the CNES for providing real-time precise products.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

