*Article* **Satellite Clock Batch Estimation Accuracy Analysis and Its Impacts on PPP**

**Menghao Li, Weiquan Huang \*, Hui Li, Renlong Wang and Peng Cui**

College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China **\*** Correspondence: huangweiquan@hrbeu.edu.cn; Tel.: +86-153-0366-9953

**Abstract:** The ultra-rapid satellite clock product based on the satellite clock batch estimation is commonly used for high-precision and reliable precise point positioning (PPP) services. In order to clarify the effect of different ranging errors on the satellite clock batch estimation accuracy, the source of the satellite clock bias induced by the batch observation model is classified into the initial clock bias (ICB) and time-dependent bias (TDB). In addition to the effect of the ICB and TDB, the analytic relationship between the observation redundancy and the satellite clock batch estimation accuracy are derived and verified. The suitable number of stations is suggested to be 40 for the satellite clock batch estimation to achieve the counterbalance between the efficiency and saturable accuracy. For the PPP based on the batch-estimated satellite clock, the impacts of the ICB and TDB on PPP are clarified. The satellite clock batch estimation and PPP experiments are carried out to investigate the impacts of the ICB and TDB on the satellite clock batch estimation accuracy and the PPP performance. 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. The convergence time and the positioning accuracy after the convergence of PPP are primarily affected by the ICB and TDB, respectively.

**Keywords:** satellite clock batch estimation; ICB; TDB; saturable accuracy; PPP

**Citation:** Li, M.; Huang, W.; Li, H.; Wang, R.; Cui, P. Satellite Clock Batch Estimation Accuracy Analysis and Its Impacts on PPP. *Remote Sens.* **2022**, *14*, 3932. https://doi.org/10.3390/ rs14163932

Academic Editors: Shengfeng Gu, Xiaopeng Gong, Yidong Lou and Chuang Shi

Received: 27 June 2022 Accepted: 11 August 2022 Published: 13 August 2022

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