# Anomaly Detection and Identification in Satellite Telemetry Data Based on Pseudo-Period
## 5 Simulation Results
The following results were obtained [0.971 0.949 0.986 0.837 0.789 0.779 0.774], and the threshold value of the similarity judgment was set to 0.940. It was found that pseudo-periods 1, 2, and 3 had high similarity with normal data, and the eigenvector distribution in each pseudo-periodic data interval was close to that of the normal data. Therefore, the data of pseudo-periods 1, 2, and 3 could be regarded as normal data. On the other hand, low similarities were obtained between pseudo-periods, 4, 5, 6, and 7, and normal data. Compared with the normal number and the eigenvector distribution in each pseudo-periodic data interval, there were differences in the A1, A2, B1, and B2 regions. Therefore, pseudo-periods 4, 5, 6, 7 were regarded as anomaly data. To further determine the possible fault types, pseudo-periods 4, 5, 6, and 7 were analyzed. In comparison with the three typical anomaly data templates of the measured data, the same statistical interval was used for statistical analysis, as shown in Table 5.  
The similarity values between the 4, 5, 6, and 7 data and the typical anomaly data are shown in Table 6. The obtained results showed that the anomaly data evolved from Type 2 to Type 1. To verify the applicability of the proposed method, five groups of data with 1000 different period lengths were used to test the accuracy of the pseudo-period partition and anomaly identification, respectively. These data were generated in the same system of the measured data, as described above. Table 7 shows the results obtained by the anomaly identification using the first pseudo-period data of each group. As shown in Table 7, the symbolization method based on the data shape could accurately extract the pseudo-period of the satellite telemetry data. The statistical results of each pseudo-period obtained by the phase-plane trajectory statistics method could identify different abnormal states of the telemetry data. Therefore, the proposed method could achieve the anomaly detection and identification of satellite telemetry data. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Pseudo-Period** & **Cosine Similarity** & \multicolumn{2}{c}{**Abnormal Data Templates**} & **Identification** \\ \cline{2-5}  & **1** & **2** & **3** & **Result** \\ \hline
4 & 0.940 & 0.994 & 0.724 & Type 2 fault \\
5 & 0.960 & 0.996 & 0.698 & Type 2 fault \\
6 & 0.984 & 0.965 & 0.787 & Type 1 fault \\
7 & 0.986 & 0.975 & 0.841 & Type 1 fault \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The similarity between the 4, 5, 6, and 7 datasets and typical anomaly data. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Abnormal Data Templates** & **A1** & **A2** & **B1** & **B2** & **C1** & **C2** \\ \hline
1 & 0.097 & 0.051 & 0.162 & 0.151 & 0.348 & 0.288 \\
2 & 0.062 & 0.074 & 0.070 & 0.078 & 0.364 & 0.349 \\
3 & 0.232 & 0.150 & 0.188 & 0.098 & 0.153 & 0.176 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Eigenvector of the trajectory plane for typical anomaly data. To compare the accuracy and speed of the anomaly identification between the method in this paper and the MSVM method, 600 groups of the telemetry data of the momentum wheel speed of the same satellite were used for testing. Each group had a length of 1000. The dataset contained four types of anomalies. For the MSVM method, 200 and 500 groups of data were used as the training samples, and 100 groups of data were used as the test samples. The comparison results are shown in Tables 8 and 9. According to Tables 8 and 9, when a smaller number of groups was used as the training sample, the proposed method had higher accuracy and approximate speed than the MSVM. When the number of the training sample was increased, while the accuracy of MSVM was improved and was close to that of the proposed method, the identification time of MSVM was also increased and was clearly greater than that of the proposed method.