## 1 Introduction
The estimable LEO satellite clocks exhibit diverse systematic effects, which contain complicated relativistic effects, temperature-related hardware biases, influences caused by the South Atlantic Anomaly, and some other reasons that are not yet fully clarified [17; 18]. [PERSON] et al. utilized real data from GRACE-FO and Sentinel-3B to identify the factors impacting the stability of LEO satellite clocks and introduced a prediction model that takes into account the systematic effects [18]. A substantial reduction was demonstrated in the prediction errors compared to polynomial fitting, however, with a precision loss of approximately 0.4 to 0.5 ns at a 10 min prediction time. [PERSON] et al. attempted to remove the complicated relativistic effects on LEO satellite clocks for a better clock prediction, leading to a precision loss of about 0.3 to 0.5 ns at a prediction time point of 10 min [19]. [PERSON] et al. proposed to perform the LEO satellite clock prediction with least-squares harmonic estimation and obtained a precision loss of about 0.3 ns within prediction arcs of 15 min [20]. In short, LEO satellite clock prediction over more than 10 min already leads to significant precision loss. This urges the employment of more efficient LEO satellite clock determination methods with ultra-short-term prediction for real-time applications. Processing the LEO satellite clocks in a filter-based manner delivers more efficient but less precise clock solutions. Lots of previous studies have discussed the filter-based LEO satellite Precise Orbit Determination (POD), with the clocks automatically produced as byproducts [11; 21]. The focus, however, was mostly put on the POD accuracy due to the requirements of other applications instead of navigation. Using simulation data, a real-time estimation approach for the LEO satellite clock based on ground tracking stations was proposed for the first time [22]. [PERSON] et al. introduced a method to estimate the LEOsatellite clocks by integrating ground observations from specific regions with onboard observations from LEO satellites. Without using a ground network, the kinematic clock estimation achieved a precision of over 0.3 ns using GNSS products, while incorporating a simulated ground network improved the clock precision to 0.15 ns [23]. In this contribution, using solely the GNSS observations tracked onboard LEO satellite, a real-time clock estimation strategy is introduced containing filter-based near-real-time clock estimation and ultra-short-term clock prediction. The filter-based processing is proposed to be restarted at pre-defined times to hamper bias propagation and accumulation from ancient epochs, allowing also for convergence through processing arcs that are long enough. Using real data from Sentinel-3B, the effects of using different processing arc lengths and time intervals between adjacent processing sessions are discussed, and the total error budget consisting of the near-real-time clock estimation, ultra-short-term clock prediction and the total real-time clock precision achieved under different cases are analyzed. The study begins with an overview of the LEO satellite real-time clock determination method, containing the near-real-time clock determination and the ultra-short-term clock prediction. The near-real-time clock determination is elaborately discussed, particularly emphasizing the selection and utilization of the GNSS real-time products. Afterward, the processing strategy for real-time clock determination is introduced with near-real-time clock precision and efficiency achieved with processing arc lengths discussed. Subsequently, the total error budget of the real-time LEO satellite clock precision is assessed for the near-real-time estimation part, the ultra-short-term prediction part, and then combined. The conclusions and discussions are given at the end.