## 3 Data and Strategies  
### Data Collection  
In this study, the ISL observations and publicly available SLR observation of the BDS-3 were collected. To validate the effectiveness and stability of the method proposed, we selected and processed one month's data, within the day of year (DOY) from 036 to 064 in 2021. The details are shown in Table 1.  
For the ISL observations, there are four types of links for BDS-3 satellites: MEO-MEO, MEO-IGSO, IGSO-IGSO, and MEO-GEO. Specifically, for MEO satellites, due to the symmetrical nature of their walker constellation, the chain building relationship of each satellite within the constellation is the same. Each MEO satellite can continuously build a chain with four MEO satellites in the same orbit, four MEO satellites in different orbits, and intermittently build a chain with twelve MEO satellites in different orbits. Figure 2 is a schematic diagram of MEO satellite chain building.  
For the SLR observations, throughout the experiment period, there were nine SLR ground stations in total capable of tracking BDS-3 satellites. The distribution of these nine SLR stations is shown in Figure 3.  
Furthermore, the SLR observations cannot be maintained continously at all times. As a result, the actual SLR stations involved in data processing vary from day to day, and the number of the SLR observations also differs accordingly. In order to better support the subsequent analysis, we present the tracking profile of BDS-3 satellites by each SLR station, taking three days as an example, as illustrated in Figure 4. In each subgraph, the horizontal axis indicates the identifier of the available SLR stations, whereas the vertical axis signifies the number of actual SLR observations within a specific DOY.  
\begin{table}
\begin{tabular}{c c} \hline
**Item** & **Description** \\ \hline Data length & 30 days (DOY 036-064, 2021) \\ Stations & 9 valid SLR stations \\ Satellites & 3 ICSO satellites and 24 MEO satellites of BDS-3 \\ Observations & ISL and SLR observations \\ \hline \end{tabular}
\end{table}
Table 1: Explanation of the collected data.  
Figure 3: Distribution of available SLR stations during the experimental period.  
Figure 2: Diagram of the chain building for MEO satellites.  
To be clear, Table 2 presents the detailed statistical results of the number of effective SLR stations per satellite and the total number of effective observations per station.  
It can be seen from Figure 4 and Table 2 that, on one hand, there is a limited quantity of SLR observations overall, and on the other hand, there is significant variation in the number of satellites tracked by different stations at different times, both from station to station and from one observation period to another. For instance, during DOY 052, there are six SLR stations available for tracking the BDS-3 satellites, with a total of 41 observations. Yet, there are merely three valid stations tracking BDS-3 satellites during DOY 53, with the total SLR observations reduced to nearly half, at 21. In addition, some stations did not track any satellites during a period, meaning there are no effective observations, such as stations 7237, 7249, and 7819 on DOY 051. This is likely to affect the accuracy of the determinated orbit. What is more, it should also be noted that the sparse SLR data may limit the scalability and robustness of the ISL and SLR combined approach. Therefore, a thorough understanding  
\begin{table}
\begin{tabular}{c c c c} \hline
**Satellite** & **DOY 051** & **DOY 052** & **DOY 053** \\ \hline C20 & 0 & 6 & 10 \\ C21 & 4 & 17 & 7 \\ C29 & 2 & 7 & 10 \\ C30 & 15 & 11 & 7 \\ Total & 21 & 41 & 34 \\ \hline \end{tabular}
\end{table}
Table 2: Status of valid SLR data.  
Figure 4: Tracking of the BDS-3 satellite by SLR stations (DOY 051-053).  
of the errors and their characteristics that may exist in SLR observations and adoption of reasonable models for processing are key factors affecting this method. The specific processing strategies are described in detail in the next section.