## 4 Test Results
### Real-Time LEO Satellite Clocks  
As shown in Figure 5, the interval \([D,D+\Delta T]\) represents the actual time window when the predicted LEO satellite clocks need to be used by users in real time. In other words, the real-time clocks of interest to users are those within the prediction period [\(T_{process}\), \(T_{process}+\Delta T\)]. This implies that the prediction time \(T_{pre}\) needs to be at least longer than \(T_{process}+\Delta T\). As mentioned before, \(T_{obs}\) in Figure 5 is set to 6 h, and \(T_{process}\) amounts to about 18-20 s. For possible delays in the GNSS real-time products and transmission of the LEO onboard GNSS observations, \(T_{process}\) is set to 30 s in this study. In this sub-section, \(\Delta T\) is tested for 60, 120, 180, 240 and 300 s, and \(T_{pre}\) is consequently set to 90, 150, 210, 270, and 330 s.  
Using the connected near-real-time clocks determined based on different \(\Delta T\) in Section 4.1, and according to the corresponding \(T_{pre}\), predictions are performed based on Equation (9) to obtain the real-time Sentinel-3B satellite clocks. The fitting time is tested from 90 to 1800 s with a step of 30 s. The most suitable one, as shown in Table 4, is the one delivering the smallest STD in prediction errors. The clocks determined based on the batch least-squares reduced-dynamic model with the final CODE products are taken as the reference.  
The daily precision of the predicted and then connected real-time clocks within [\(T_{process}\), \(T_{process}+\Delta T\)] is listed in Table 4. The precision of the near-real-time clocks is about 0.2 to 0.3 ns. As the \(T_{pre}\) increases from 90 to 330 s, the precision loss due to prediction is from about 0.06 to 0.17 ns, with the total error budget of the real-time clocks amounting to 0.2 to 0.35 ns. As \(T_{pre}\) increases, the precision of real-time clocks gradually decreases due to the slightly increasing prediction errors. As shown in Figure 9, the STD of the near-real time clocks decreases slightly with the increasing \(\Delta T\) (blue bars), while the precision loss due to prediction increases substantially when increasing the \(\Delta T\) (red bars). Therefore, it can be inferred that the total error budget of real-time LEO satellite clocks (yellow bars) based on near-real-time determination and ultra-short-term prediction mainly comes from the prediction, and a small \(\Delta T\) is preferred if possible.  
In summary, there are several key factors affecting the final error budget of the real-time LEO satellite clocks:  
1. The processing time \(T_{process}\) is mainly dependent on the processing arc length \(T_{obs}\). For the very similar \(T_{process}\), it is preferable to have a longer \(T_{obs}\) to enhance the short-term stability of the near-real-time clocks. The time interval between subsequent processing sessions (\(\Delta T\)) is independent of the precision of the near-real-time clocks but directly determines the prediction time \(T_{pre}\) and the usable prediction window [\(T_{process}\), \(T_{process}+\Delta T\)] for real-time applications. The latter is directly related to the predicted clock precision, i.e., the precision of real-time LEO satellite clocks.  
Figure 8: MDEVs of the connected near-real-time Sentinel-3B clocks at the last \(\Delta T\) period over each processing arc.  
The precision of the connected near-real-time LEO satellite clocks of the last \(\Delta T\) period within the 6 h processing arcs is similar to the kinematic daily solutions. The major differences in the real-time clocks for different \(\Delta T\) come from the clock prediction, more concretely, from the different prediction times. Further research is needed to improve the ultra-short-term prediction of LEO satellite clocks, i.e., within 5 min.  
When setting \(\Delta T\) to 60 s, a real-time clock precision around or lower than 0.3 ns can be achieved.