# Orbit Determination of Korean GEO Satellite Using Single SLR Sensor
## 2 SLR Data Generation
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Latitude & 35.5901665597\({}^{\circ}\) \\ Longitude & 127.920064752\({}^{\circ}\) \\ Height & 934.063 m \\ Repetition rate & 60 Hz nominal for SLR \\  & 10 Hz for DLT \\ One sigma error for range measurements & 4 mm \\ \hline \end{tabular}
\end{table} 
Table 2: Geochang station information. SLR—satellite laser ranging; DLT—debris laser tracking. Figure 5: Ground trajectory of Compass-G1 (red cross) and SLR stations (blue dots). Table 3 provides the number of observations of Compass-G1 by sorting the number of observations of each SLR stations into descending order. The type of SLR observations used in this study was normal point data. The number of passes indicates the number of attempts to track Compass-G1. Among those observations, Changchun station made the most SLR observations during the period, whereas Beijing station only obtained 10 SLR observations in the same period. The total observations in this period were 813 for Changchun, and the average number of measurements per one-day arc of about 2.227 was obtained by dividing by 365 days. Figure 6 shows the number of observations in one week-length arc with respect to the day of the year at the epoch. The arc that performed the most frequent observations of Compass-G1 in the whole period was from 21 October to 27 October at Changchun station. The number of observations was 62 in this period. For more detailed analysis, the distribution of the number of observations in one arc is calculated as in Figure 7 and Table 4. The amount of observation data for each arc existing in 2017 is counted, and the results are divided into five observation intervals to calculate the distribution. The ratio of the interval of zero to four observations is the highest. Although many arcs are concentrated in the area where the number of observations is 25 or less, several arcs have more than 40 observations in an arc. In the arc of 62 observations, the observations were concentrated on the front part of the arc. There were 18, 10, 10, and 24 observations of Compass-G1 in Changchun station for 21, 22, 23, and 24 October, respectively. Therefore, it can be concluded from the analyses that more than 60 SLR \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Station Name** & **Station Number** & **No. Passes** & **No. Observations** \\ \hline Changchun & 7237 & 270 & 813 \\ Yarragadee & 7090 & 106 & 288 \\ Shanghai & 7821 & 66 & 277 \\ Mount Stromlo & 7825 & 20 & 43 \\ Komsomolsk & 1868 & 9 & 26 \\ Beijing & 7249 & 3 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: SLR tracking statistics of Compass-G1 in 2017. Figure 6: The number of Compass-G1 measurements in 2017.  
observations for GK-2B will be available in one SLR station if the observation procedure is operated with no restricted conditions. Based on statistical analyses of Compass-G1, Table 5 shows two observation scenarios. Scenario 1 set the generation of appropriate SLR observations for GK-2B to nine per one day, which results in 63 observations per week-length arc. The observation time is 2 h, spanning from midnight to 02:00, considering that GEO satellites can be only observed at night, and observation gap is 15 min. Scenario 2 extends the observation time into 3 h with the same observation gap, resulting in 13 observations per day and 98 observations per arc. The observation time for Scenario 2 spans from midnight to 03:00. Figure 8 represents simulated SLR observations for these two scenarios, in which the root-mean-square (RMS) of measurement noise is 4.316 mm. Unobservable periods are 22 h and 21 h for Scenario 1 and Scenario 2, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**\# of Observations** & **Ratio (\%)** & **\# of Observations** & **Ratio (\%)** \\ \hline
0–4 & 22.84 & 35–39 & 1.95 \\
5–9 & 13.37 & 40–44 & 3.06 \\
10–14 & 20.33 & 45–49 & 2.51 \\
15–19 & 12.26 & 50–54 & 1.39 \\
20–24 & 11.42 & 55–59 & 0.28 \\
25–29 & 5.85 & 60–64 & 1.11 \\
30–34 & 3.62 & 65–69 & 0 \\ \hline \hline \end{tabular}
\end{table}