## 2 Methodology  
The basic SGP4 model used in this study was obtained from MathWorks [39]. This specific SGP4 prediction model is a modified version of the works of [PERSON] and [PERSON], who used the latest Brouwer's equations for the gravitational and density function for the atmospheric model calculations [40]. A small variation in any equation or constant makes a huge difference in estimating the semimajor axis or the inclination. Many studies have been conducted on testing the accuracy of the TLE data sets [33; 41; 42]. One such study that fits a variety of objects in various orbits was analyzed by [PERSON] and [PERSON] using the latest SGP4 model [43]. They conducted extensive research on 1120 objects and came to a conclusion that the SGP4 model has an error in the magnitude of 100 meters in the altitude while the average inaccuracies in the semi-synchronous and geosynchronous orbits are 0.7 and 1.9 km, respectively, and the errors in the elliptical orbit do not exceed 10 km. Hence, the accuracy of this modified matlab model must also be tested. A sample test case that was given in the original Spacetrack Report No. 3 was compared with the proposed modified MATLAB algorithm developed in this study [44]. The accuracy comparison between the two cases is given in Table 1 (in the units of min and km). T\({}_{since}\) is the propagated time from the reference TLE set fed in; \(X\), \(Y\), and \(Z\) are the position vectors; \(X\)_DOT_, \(Y\)_DOT_, and \(Z\)_DOT_ are the velocity vectors. This table reveals differences in the predicted values in the order of \(10^{-7}\) and \(10^{-8}\) in the position vectors (in kilometers) and the velocity vectors (in kilometers per minute), respectively. These small errors could be due to the change in various constants in the past, improvement of the prediction model, or changes in data quality. Nevertheless, the magnitude of these errors does not affect the prediction performance of the algorithm developed in this study. This result suggests that the magnitude differences of \(10^{-7}\) and \(10^{-8}\) in the position and the velocity vectors, respectively, may not create a considerable difference in the predicted semimajor axis or the inclination. The MATLAB version of the SPG4 model was downloaded from MathWorks, and it was modified to suit the scope of this study [39]. Each TLE must be propagated separately for each data point or day in the SGP4 model. Hence, MATLAB must be restarted each time a TLE is fed in to the SGP4 model. To reduce the processing time, the model was modified in such a way that an array of days/propagation periods can be fed into the model once to estimate the orbital parameters of the required satellite for a prolonged period. In the two case studies of TOPEX and Envisat, a period of 3 years was propagated at once. The SGP4 model was also modified in such a way that orbital parameters, such as inclination, semimajor axis, right ascension of the ascending node (RAAN), argument of perigee, orbital energy, and eccentricity, are obtained instead of the position and state vectors. A function is created to convert the Cartesian position and velocity parameters of any satellite in orbit into classical orbital elements. This changed model of SGP4 was merged with another algorithm, which directly obtains the value of the orbital parameters, such as inclination, semimajor axis, RAAN, argument of perigee, orbital energy, and eccentricity, directly from the TLE sets that were fed into the modified SGP4 model for the same period. Therefore, in the end, the whole algorithm package will compare the values of the orbital parameters estimated using this changed algorithm with the corresponding values of the orbital parameters observed from the TLEs and provide the maneuvers as a function of time, which forms a peak that represents the sudden change found in the difference between the observed and propagated orbital parameters. This change is identified with the two parameters; the threshold and the window length.