# Two-Line Element Outlier and Space Event Detection Method Based on Multi-Strategy Genetic Algorithm
## 3 Results and Discussion  
In this section, we selected targets with real maneuver events as candidate objects. We selected eight typical low-Earth-orbit (LEO) targets as test subjects to validate the proposed method, considering their value in detecting anomalies. Table 1 provides a summary of their key characteristics. While TLE data are accessible for tens of thousands of targets, the selected data were specifically picked to illustrate instances of TLE anomalies. These targets possess high-quality TLE datasets, and their space event histories were obtained. The TLE data were retrieved from the Spacetrack website, while the space event histories were sourced from the International Laser Ranging Service website. NORAD ID 27386 was utilized as an example to illustrate the anomaly and space event detection process, showcasing the efficacy of this method. Initially, all permissible elements in the TLE-derived semi-major axis time series were propagated to each of the subsequent 14 epochs (\(m=14\)) to generate sample data for the prediction error. Subsequently, anomaly detection thresholds were established using the 95 th percentile rule based on the fitting results. Finally, spatial events were identified using the maneuver detection method. To visually showcase the effectiveness of the methods proposed in this paper, we present the results using histogram scatter statistics, as depicted in Figure 3. These results illustrate that the relationship between the semi-major axis and the rate of change of the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**NORAD** & **Mass** & **Launch** & **Period** & **Apogee** & **Perigee** & **Inclination** & **TLE** & **Events** & **TLE** \\
**ID** & **[kg]** & **Date** & **[min]** & **[km]** & **[km]** & **[\({}^{\circ}\)]** & **Quantity** & **Quantity** & **Time Span** \\ \hline
27386 & 8100 & March 2002 & 100 & 791 & 785 & 98.6 & 11,896 & 177 & 2003–2010 \\
36508 & 720 & April 2010 & 99 & 732 & 718 & 92 & 8630 & 179 & 2010–2023 \\
41240 & 553 & January 2016 & 112 & 1343 & 1331 & 66 & 7235 & 47 & 2016–2023 \\
41335 & 1250 & February 2016 & 101 & 806 & 802 & 99 & 10,788 & 73 & 2016–2023 \\
43476 & 600 & May 2018 & 94 & 491 & 470 & 89 & 4139 & 39 & 2018–2023 \\
43477 & 600 & May 2018 & 94 & 491 & 470 & 89 & 4134 & 39 & 2018–2023 \\
37781 & 1500 & August 2011 & 103 & 917 & 902 & 99 & 12,805 & 58 & 2011–2023 \\
39086 & 400 & February 2013 & 101 & 785 & 782 & 99 & 7039 & 63 & 2013–2023 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of selected objects. orbital inclination is not independent, indicating that using a one-dimensional Gaussian mixture model for the analysis may not be appropriate. In this study, a multi-strategy genetic algorithm (MGA) is employed to estimate MGMM. The training process is illustrated in Figure 4. As depicted in Figure 4, the average fitness within the population and the fitness of the optimal individual converge to a consistent result after approximately 20 iterations. This suggests that the MGA utilized for estimating the MGMM parameters can accelerate the convergence speed and identify the global optimal solution in the solution within a certain timeframe. In addition, we compared the statistical properties of our samples and models to ensure that the obtained model effectively captures the intrinsic structure of the samples. Consequently, Figure 5 illustrates a quantile-quantile (Q-Q) plot of the sample model, demonstrating whether the model's distribution aligns with that of the complete training data. The 'X quantiles' are derived from the sample data, while the 'Y quantiles' originate from the generated data of the learned model. The fact that the X and Y quantiles on the Q-Q plot form a straight line indicates that the resulting model conforms to the same distribution as the sample data. This observation validates the effectiveness of our proposed method in learning the distribution structure of multiple variables within the TLE data samples. Figure 4: Iteration process of data.