*Article* **High-Rate One-Hourly Updated Ultra-Rapid Multi-GNSS Satellite Clock Offsets Estimation and Its Application in Real-Time Precise Point Positioning**

**Guoqiang Jiao 1,2 and Shuli Song 1,\***


**Abstract:** The requirement of timeliness is increasing while obtaining precise tempo-spatial information with the development of global navigation satellite systems (GNSSs). Due to the poor network environment and communication conditions in some regions or application scenarios, it is difficult for users to receive real-time (RT) precise products. The hourly updated ultra-rapid products with low latency and high accuracy are of great interest in GNSS real-time and near-real-time fields. However, it is difficult to achieve the high-rate one-hourly updated precise clock estimation (PCE); since many ambiguity parameters need to be estimated, the computation is time-consuming. At present, the highest time resolution of ultra-rapid clock offsets is 15 min. The low samplings affect the prediction accuracy of clock offsets and the precise point positioning (PPP) performances. To meet these requirements, we proposed an efficient method and design a new framework for high-rate one-hourly updated ultra-rapid PCE. We modified the epoch-difference (ED) PCE model in the parameter estimation. According to the characteristics of the modified ED PCE model, the Open Multi-Processing (OpenMP) and Intel Math Kernel Library (MKL) technologies are used to construct a parallel system to realize the parallelism among satellites, epochs, and stations. The comprehensive assessment in the precision of clock offsets and PPP performances is conducted. The result demonstrates that the one-hourly updated multi-GNSS clock offsets with 30 s sampling can be obtained within 20 min. The estimated clock offsets accuracy increases with the improvement of the time resolution. The STD and RMS are improved by (0.97 to 9.09% and 0.12 to 5.56%) in the observation session, (2.82 to 23.08% and 0.95 to 9.09%) in the first hour of the prediction session, and (0.11 to 3.85% and 0.12 to 4.19%) in the second hour of the prediction session compared with low-rate products, respectively. The high-rate one-hourly updated ultra-rapid clock offsets significantly improves the RT-PPP performances. The positioning accuracy can be improved by 1.52~25.74%, and the convergence time can be improved by 21.96~65.75%. The RT-PPP performances are basically the same as GeoForschungsZentrum Potsdam (GFZ) rapid products and slightly better than the Center National d'Etudes Spatiales (CNES) RT products (CLK93). The one-hourly updated ultra-rapid products with low latency, high accuracy, and not limited by network conditions can be well applied to real-time or near real-time applications and research.

**Keywords:** high-rate; one-hourly updated ultra-rapid clock offsets; precise clock estimation (PCE); epoch-difference (ED); parallel processing; precise point positioning (PPP)
