## 3 Processing Methods
### Filter-Based Real-Time LEO Satellite Clock Determination
In the right panel of Figure 2, a segment of observation data is input at pre-defined intervals, and the clocks of this arc are estimated, referred to as \"arc-estimation\" in this study. The time required to estimate the parameters differs between the two methods due to the difference in the amount of processing data. When data are input epoch by epoch in the epoch-processing method, the time required to estimate the clocks for a single epoch is usually less than 1 s, with the filter running forward continuously. Due to the longer length of the observation arc in the arc-processing method, the time required to periodically estimate the LEO satellite clocks is longer, which implies a slightly longer prediction time (e.g., 60 s). However, the latter method can hamper bias propagation and accumulation from previous epochs and can handle situations with poor network quality, thereby improving the stability of the LEO satellite clocks [16]. Figure 3 depicts a processing timeline of these two methods for the real-time LEO satellite clock determination. \(T_{0}\) is the initial time of the entire process. In the method where  
Figure 2: Epoch-processing (**left**) and arc-processing (**right**) of real-time LEO satellite clock determination based on the kinematic model using the Kalman filter. LEO clocks are calculated epoch by epoch, the time required to estimate a single epoch, \(T_{\text{epoch}}\), represents the latency of the LEO satellite clock products generated in this scenario. For \"arc-estimation\", \(\Delta T\) denotes the time interval between the launching of two subsequent processing sessions. Point \(A\) marks the beginning of the near-real-time LEO clock arc, \(B\) marks the end of the near-real-time LEO clock arc, and \(C\) represents the time point when the near-real-time clock determination and prediction are completed. \(D\) signifies the end of the prediction arc. As depicted by the blue lines, \(T_{\text{acc}}\) (between \(B\) and \(C\)) for processing one arc is longer than \(T_{\text{epoch}}\) for processing one epoch (typically shorter than 1 s). Consequently, the prediction arc (\(BD\)) needs to be longer to fulfill the needs of real-time applications. Table 2 lists the strategies of filter-based real-time LEO satellite clock determination. The length of observation depends on whether it is \"epoch estimation\" or \"arc estimation\". The choice relates mainly to whether the GNSS observations onboard LEO satellites can be obtained for processing in real time. Additionally, the attitude of GNSS satellites is considered stable, and its impact on the LEO satellite clocks is negligible. Impacts of the Latency and Continuity of GNSS Real-Time Products on the LEO Satellite Clock Determination  
For the LEO satellite constellation, a communication network can be constructed through inter-satellite links to enable real-time downlink of onboard GNSS observation data [4]. Typically, the data downlink delay can be limited to a few seconds or even shorter. However, as shown in Table 1, the latency for receiving real-time GNSS products could be 20-30 s. As a result, when estimating LEO satellite clocks in real-time with the epoch-processing method, as depicted in the left panel of Figure 2, there arises a situation \begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt}} \hline \hline
**Parameters** & **Processing Strategies** \\ \hline Observations & Undifferenced IF code and carrier phase combination (GPS: L1/L2) \\ \hline Length of observation & Arc-estimation: 6 h/Epoch estimation: 30 s \\ \hline Sampling & 30 s \\ \hline Elevation cut-off angle & 3\({}^{\circ}\) \\ \hline GNSS orbits and clocks & CNES real-time products \\ \hline GNSS satellite antenna PCO/PCVs & igs20.atx \\ \hline LEO satellite antenna PCO/PCVs & Operator supplied \\ \hline Phase wind-up & Corrected \\ \hline Estimator & Extended Kalman filter, Kinematic \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The strategies of filter-based real-time LEO satellite clock determination.