## 2 Methodology
Window length is the time span between each of the maneuvers, whereas detection limits are set on the basis of the peaks that represent the sudden change found in the difference between the observed and propagated orbital parameters. Most active satellites frequently perform only in-plane and out-of-plane maneuvers to change their semimajor axis and inclination, respectively. In-plane maneuvers are responsible for the changes that are brought about in the orbit's shape and size by altering the semimajor axis; eventually, the orbital energy is also changed in this process. This type of maneuver evinces a sudden change in the mean motion, thereby changing orbital energy. By contrast, out-of-plane maneuvers are responsible for the changes that are brought about by the orientation of the plane by evincing an abrupt change in the inclination. In this study, an algorithm was set to detect sudden changes in the orbital parameters by calculating the difference between the adjacent segments of the orbital parameters propagated by \begin{table}
\begin{tabular}{c c c c} \hline
**Time Since** & **X** & **Y** & **Z** \\ \hline
0 & 5.14 \(\times\) 10\({}^{-6}\) & 8.3 \(\times\) 10\({}^{-7}\) & 3.5 \(\times\) 10\({}^{-6}\) \\ \hline
360.0000000 & 2.23 \(\times\) 10\({}^{-6}\) & 5.84 \(\times\) 10\({}^{-6}\) & 7.05 \(\times\) 10\({}^{-6}\) \\ \hline
720.0000000 & 1.56 \(\times\) 10\({}^{-6}\) & 3.47 \(\times\) 10\({}^{-6}\) & 1.88 \(\times\) 10\({}^{-6}\) \\ \hline
1080.00000000 & 4.67 \(\times\) 10\({}^{-6}\) & 5.1 \(\times\) 10\({}^{-6}\) & 3.6 \(\times\) 10\({}^{-7}\) \\ \hline
1440.00000000 & 1.37 \(\times\) 10\({}^{-6}\) & 5.89 \(\times\) 10\({}^{-6}\) & 1.06 \(\times\) 10\({}^{-6}\) \\ \hline
**Time Since** & **XDOT** & **YDOT** & **ZDOT** \\ \hline
0 & 5 \(\times\) 10\({}^{-8}\) & 1.5 \(\times\) 10\({}^{-7}\) & 6 \(\times\) 10\({}^{-8}\) \\ \hline
360.0000000 & 8.6 \(\times\) 10\({}^{-7}\) & 3 \(\times\) 10\({}^{-8}\) & 3.4 \(\times\) 10\({}^{-7}\) \\ \hline
720.0000000 & 1.4 \(\times\) 10\({}^{-7}\) & 5.2 \(\times\) 10\({}^{-7}\) & 3.5 \(\times\) 10\({}^{-7}\) \\ \hline
1080.00000000 & 1.8 \(\times\) 10\({}^{-8}\) & 5.4 \(\times\) 10\({}^{-7}\) & 1.1 \(\times\) 10\({}^{-7}\) \\ \hline
1440.0000000 & 4 \(\times\) 10\({}^{-7}\) & 3 \(\times\) 10\({}^{-7}\) & 6.7 \(\times\) 10\({}^{-7}\) \\ \hline \end{tabular}
\end{table} 
Table 1: The accuracy comparison between the two cases. Difference in the values of the sample case provided in Spacetrack Report No. 3 and the results of the Matlab model. The output is given at 360-min intervals in km and minutes. SGP4 and the observed orbital parameters obtained from the TLEs. First, the required TLE data were downloaded from either the CelesTrak or the Space Track websites as text files [45; 46]. Then, the text files were fed into the algorithm to recover the history of the satellite's orbital parameters. Five observed orbital parameters, comprising semimajor axis, inclination, RAAN, eccentricity, and orbital energy, were extracted. In parallel, the TLE data were also fed into the SGP4 propagator to propagate the estimated orbital parameters, with the first TLE as the starting reference point; then, the parameters were propagated using SGP4 to the time the next TLE was available. The process was repeated until the last available TLE. Similarly, the five corresponding orbital parameters, comprising semimajor axis, inclination, RAAN, eccentricity, and orbital energy, were propagated. Once the two processes were completed, the observed and propagated orbital parameters were compared, and the differences between their respective values were found. Figure 1 illustrates the approach used to detect a satellite's maneuvers. Once the differences between the corresponding propagated and observed orbital parameters were found, potential maneuvers were marked when the difference between the adjacent values exceeded a user-specified detection limit.