**5. Conclusions**

As one of the typical PPP methods to achieve the centimeter-level positioning by using ultra-rapid satellite clock and orbit products, the satellite clock batch estimation accuracy and its impacts on PPP are analyzed in this contribution.

The source of the satellite clock bias induced by the batch observation model is clarified and divided into the ICB and the TDB. The ICB affects the RMS without affecting the STD, whilst the TDB affects the RMS and the STD of the batch-estimated satellite clock. Furthermore, based on the clarified batch observation model, the observation redundancy suitable for the satellite clock batch estimation is determined by deriving the covariance– variance matrix. The number of stations for GPS satellite clock batch estimation is suggested to be 40 because the accuracy of the batch-estimated satellite clock is saturable. For the application of the batch-estimated satellite clock on PPP, the ICB and TDB are absorbed by the PPP observation model, which impact the convergence time and the positioning accuracy after convergence, respectively.

Based on the experimental results of the satellite clock batch estimation, it can be found that the ICB causes a significant bias for the batch-estimated satellite clock. The TDB is impacted by the assimilation ability of the batch-estimated satellite clock to the satellite orbit error. Furthermore, the simulation experiments of PPP show that the convergence time and the positioning accuracy after convergence are affected by the ICB and TDB of the batch-estimated satellite clock.

**Author Contributions:** Conceptualization, M.L., W.H. and H.L.; methodology, M.L. and H.L.; validation, M.L., R.W. and P.C.; formal analysis, M.L. and H.L.; investigation, M.L. and H.L.; resources, W.H. and H.L.; data curation, M.L. and H.L.; writing—original draft preparation, M.L.; writing—review and editing, M.L.; visualization, M.L. and R.W.; supervision, M.L. and H.L.; project administration, W.H. and H.L.; funding acquisition, W.H. and H.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was jointly funded by the National Key Research and Development Program (No. 2021YFB3901300), the National Natural Science Foundation of China (Nos. 61773132, 61633008, 61803115, 62003108 and 62003109), the 145 High-Tech Ship Innovation Project sponsored by the Chinese Ministry of Industry and Information Technology, the Heilongjiang Province Research Science Fund for Excellent Young Scholars (No. YQ2020F009) and the Fundamental Research Funds for Central Universities (Nos. 3072019CF0401, 3072020CFT0403).

**Data Availability Statement:** The data supporting this research can be found at the hyperlinks as: https://cddis.nasa.gov, accessed on 1 March 2022.

**Acknowledgments:** The authors would like to appreciate the analysis center of WHU, GFZ and IGS for providing the data.

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