# Anomaly Detection and Identification in Satellite Telemetry Data Based on Pseudo-Period
## 2 Pseudo-Periodic Extraction of Satellite Telemetry Data
### Symbolization Method of Satellite Telemetry Data  
Since satellite telemetry data usually have a high sampling frequency, pseudo-periodic analysis of the raw telemetry data incurs a heavy computational cost. To improve the efficiency of pseudo-periodic extraction, the raw telemetry data should be compressed. Symbolic processing is a compression method based on the data shape features. This method has a high compression rate and fast compression speed and can reduce the noise and outliers' interference in the data. Symbolic aggregate approximation (SAX) [21] is a data symbolization processing method based on piecewise aggregate approximation (PAA). The principle of SAX is as follows: the data are divided into segments of equal lengths, and then the mean value of each segment data is converted into the corresponding discrete characters. Regardless of the specific characteristics of the data, SAX exhibits strong robustness and a high compression rate. However, SAX uses equal length symbolization partition, and therefore, its shortcomings are similar to those of the fixed segmentation method. Furthermore, the use of mean approximation data can lead to the loss of the local shape information of the data, making SAX vulnerable to the interference of trend noise. The data in Figure 1 are symbolized by SAX. The symbol set is chosen as {**a, b, c, d**}. By referring to the period of the data, the fixed segment length of data is set to be 50. The number of segments is inversely proportional to the compression; namely, the data compression ratio is 20:1, and the data symbolization sequence is {**dbdbdbcbcbbbcabca**}. The data in Figure 1 show a trend change after 500 s. The data symbolization sequence is divided into Sequence 1 {**dbdbdbcbcb**} and Sequence 2 {**bbcbcbca**} at 500 s. A comparison of the two sequences shows that the character sequence of Sequence 1 is more obvious, while there are only local, regular changes in Sequence 2. This result occurs because SAX retains the trend-type noise of the raw data, which interferes with the pseudo-periodic extraction of the data. In light of the above limitations, this paper proposed a symbolization method based on the tilt angle in terms of the data temporal shape. The method had three main components: data filtering, shape salient points extraction, and data symbolization. Since the raw telemetry data are quite noisy, which affects the accuracy of data shape extraction, first, the raw data should be filtered. First-order digital attenuated memory filter is a kind of a time-domain filter. Compared with the classical frequency filter, this approach could rapidly filter  
Figure 1: Measured data of the solar panel current of a satellite. noise with different frequencies and has a better robustness with respect to different types of data. The first-order digital attenuated memory filter is described as follows:  
\[\widetilde{x}_{i+1}=\widetilde{x}_{i}+G[x_{i+1}-\widetilde{x}_{i}] \tag{4}\]  
where \(x_{i}\) is the raw data, \(\widetilde{x}_{i}\) is the filtered data, and \(\widetilde{x}_{1}=x_{1}\), \(G\) is the memory length of the filter, and \(G\in[0,1]\). The value of \(G\) is inversely proportional to the memory time. If \(G\) is too large, the ideal filtering result cannot be obtained. If the value is too small, a phase delay of the filtering result will occur. The confirmation of \(G\) value always depends on the experience. Therefore, \(G\) was set to be \(G\geq 0.8\) in this paper. A first-order digital attenuated memory filter was used to filter the data in Figure 1, and the filtering results are shown in Figure 2.  
The salient points of the data include the starting and ending points, turning points, and local extremum points. The essence of salient point extraction is to achieve data compression. [PERSON] (2018) proposed the method of extraction of the important points based on the data shape. [PERSON] (2018) improved the method of extracting the important points and proposed an extraction method based on the key points (KP) with an improved compression rate.