## 4 Key Technology
### Health Monitoring  
On the basis of simulation data and telemetry data and with the help of visualization tools, health monitoring shall not only comprehensively and fully display the operational status information of constellation to the O&M personnel but also perform a real-time evaluation of the constellation status to prevent failure. For the polymorphic constellation states, the traditional monitoring method needs to define the basis for determining the health state of constellation. By refining or quantifying the health status of equipment, it is necessary to provide evaluation criteria for subsequent health status assessment. The health state division is classified in qualitative and quanti  
Figure 7: Flow chart of data fusion. tative ways. In engineering applications, it is mostly classified quantitatively, that is, by determining the state boundaries of key status parameters, and the thresholds of each performance parameter need to be determined with sufficient expertise and the support of equipment test data. The abnormal condition detection is to determine the health status threshold in quantitative state division, and \(M\) parameters are judged every \(N\) seconds. When a status parameter exceeds the health threshold by more than or equal to \(X\) times, an abnormal condition occurs. Generally, such a fault detection method refers to a parameter that exceeds a certain interval for several times continuously or a combination of \"and\" \"or\" for multiple judgment conditions. In more complicated cases, after one condition is satisfied, other conditions shall be transferred to the other conditions for further judgment. Obviously, the traditional limit checking approach has unavoidable shortages. Firstly, there are a large number of abnormalities or symptoms that cannot be detected only by threshold checking. Secondly, the threshold value is highly dependent on domain knowledge, which is time-consuming and labor-intensive, and an unreasonable threshold value will result in either no anomalies being detected or a large number of false alarms, making the detection system insensitive to real anomalies. In order to address the limitations of the traditional methods mentioned above, various machine-learning-based fault detection methods, such as nonlinear regression, core element analysis and support vector machines, have been proposed. In particular, the one-class support vector machine (OCSVM) combined with the one-class classification (OCC) algorithm based on the support vector machine (SVM) has shown great potential in fault detection [22]. The basic principle of OCSVM is shown in Figure 8. The model uses the normal operation data of the constellation as training samples and maps it to the high-dimensional feature space through the kernel function. The operation data can be from historical data or credible simulation data [23]. Assuming the coordinate origin as the only abnormal sample point, an optimal hyper-plane exists to separate the training sample from the coordinate origin and maximizes their interval. The optimization objective can be expressed by Equation (12):  
\[ \begin{split}&\min_{\omega,\xi,\rho}\frac{1}{2}\|\omega\|^{2}+ \frac{1}{cn}\sum_{i=1}^{n}\xi_{i}-\rho\\ &\text{\emph{subject}}\ \ \text{to}\ :\omega\cdot\phi(z_{i})\geq \rho-\xi_{i},\xi_{i}\geq 0\end{split}  \tag{12}\]  
where \(v\) is a user-defined parameter used to control the upper limit of the outliers number in the training set. Its value range is (0, 1). \(\xi\) are the slack variables. \(z_{i}\) is the element in the given data set. \(n\) is the size of the data set. \(\phi(z_{i})\) stands for the mapping function corresponding to the kernel function. \(\omega\) represents the vector perpendicular to the decision boundary. \(\rho\) denotes the bias term. Figure 8: Principle diagram of OCSVM. A RBF Gaussian kernel function is adopted, and its form is given as:  
\[K(z_{i},z_{j})=exp(-\frac{\|z-z_{j}\|^{2}}{2\sigma^{2}}) \tag{13}\]  
where \(\sigma\) is the width parameter of the RBF Gaussian kernel.