## 3 Simulations and Results
### Observation Simulations  
To analyze the spatial and temporal distribution characteristics of ground-based radar observations for continuously ascending Starlink satellites, observation simulations are carried out involving 22 satellites of the V2.0 Mini version (NORAD IDs: 58826-58847) launched on 24 January 2024. Observations are simulated from three different ground station locations selected to provide diverse geometric visibility conditions. The geographic coordinates of the station sites used in this study are shown in Table 1. The measurement data is simulated at 30-s intervals over a 7-day period, starting from 22:32:42 UTC on 7 February 2024. Figure 2: The flowchart of the OD procedure based on an unscented batch filtering method. Theoretical observations (\(\rho\), _Az_, _El_) are obtained by first calculating the satellite's position relative to the radar station in the Earth-Centered, Earth-Fixed (ECEF) coordinate system. This relative position is then transformed into the local East-North-Up (ENU) frame of the ground station, where the x-axis points east, the y-axis points north, and the z-axis aligns with the local zenith. To simulate radar measurements, observational errors are introduced, with standard deviations of 100 m for range \(\rho\) and 100 arcseconds for both azimuth _Az_ and elevation _El_. Observable arcs over the 7-day period are determined by applying the radar's operational constraints: a maximum range of 2000 km (\(\rho\leq 2000\) km) and a minimum elevation angle of \(5^{\circ}\) (_El_\(\geq 5^{\circ}\)). A total of 1005 visible arcs were recorded for the 22 target satellites over a 7-day observation period using Station 1. Figure 3 illustrates the statistical distribution of visible arc durations, measured in minutes. As shown, the majority of the arcs (89%) fall within the 4-8-min range, with the highest frequency observed at 7 min (291 arcs). Figure 4 presents the distribution of observational gaps, defined as the time intervals between consecutive visible arcs. The results show that 84% of these gaps have a duration of approximately 1.5 h (93-100 min), while most of the remaining gaps last around 15 h (806-915 min). Figure 5 displays the distribution of visible arcs for the Starlink satellite with NORAD ID 58836 during the same observation period. The durations of the visible arcs, shown in red, are measured in minutes, whereas the observational gaps, shown in black, are indicated in hours. On average, 6-7 visible arcs are obtained per day, totaling approximately 40 min of daily visibility. Notably, each day's observational gaps invariably include a prolonged interval lasting about 15 h, with shorter gaps interspersed throughout the remaining period. \begin{table}
\begin{tabular}{c c c c} \hline
**Station Number** & **Longitude (deg)** & **Latitude (deg)** & **Altitude (m)** \\ \hline
1 & 75.99 E & 39.47 N & 0 \\
2 & 109.5 E & 18.4 N & 0 \\
3 & 125.31 E & 44.88 N & 0 \\ \hline \end{tabular}
\end{table} 
Table 1: The locations of station sites. Figure 3: Visible arc statistics for the targeted satellites, obtained by Station 1 during the observation period he flowchart of the OD procedure based on an unscented batch filtering method. In addition to Station 1, Station 2 and Station 3 were chosen to simulate observations of the same set of target satellites over the identical 7-day period. A total of 529 visible arcs were obtained from Station 2, and 957 arcs were recorded from Station 3. For Station 2, each satellite had an average of 3-4 access opportunities per day, with a total daily visibility of about 20 min. A distinct observational gap lasting 11-13 h is consistently recorded each day. Owing to the comparable latitude coordinates between the station sites, the statistical characteristics derived from Station 3 demonstrated substantial alignment with those obtained from Station 1. Specifically, Station 3 provided an average of 6-7 visible arcs per satellite per day, with a cumulative daily visibility of approximately 40 min.