# Anomaly Detection and Identification in Satellite Telemetry Data Based on Pseudo-Period
## 1 Introduction  
The massive amounts of telemetry data transmitted by an in-orbit satellite are the sole observational basis of the satellite's operation. Through the analysis of telemetry data, ground telemetry, track, and command (TT&C) stations can determine the satellite's operational state and detect possible anomalies in a timely fashion, assisting the normal operation of the in-orbit satellite. Currently, the fixed threshold method is the main method for anomaly detection in telemetry data in engineering [1,2]. With the simple mechanism and rapid detection speed, this method can be used to detect anomalies beyond the threshold in a timely manner. However, due to the influence of complex noise in the actual telemetry data, the fixed threshold method is prone to producing false alarms in the detection. In addition, the method cannot detect anomalies within the threshold. The current detection and identification studies are based on the relevant features extraction of telemetry data using data mining methods. Historical telemetry data have been used for modeling, with the measured data compared with the predicted data of the proposed model in order to achieve the anomaly detection and identificationof the measured data [3; 4; 5]. The performance of this method is directly related to the modeling accuracy. When the data type changes, the data model must be updated. Based on the threshold method, [PERSON] [6] used the semi-major axis change method (SACM) to extract the mean and standard deviation of telemetry data in different periods as the migration variables for anomaly detection and identification. However, this method showed limited accuracy for anomaly identification. To diagnose the satellite faults, [PERSON] [7] used empirical mode decomposition to extract the telemetry data features from the time-frequency domain. However, the characteristic frequencies of each component in the data must be determined first, which is difficult in practical application. [PERSON] [8] used a fuzzy interval-set and tried to detect the potential value of the time series, where the algorithm regarded each subsequence as an interval-set depending on its value space and the subsequence boundary. The experimental results indicated that the algorithm had better discriminative performance than the piecewise aggregate approximation method. However, when the interval approximation was used for anomaly identification, the accuracy of this method was unsatisfactory. Neural networks have been employed to detect and identify anomaly data [9; 10; 11]. While these methods are more accurate, their precision mainly depends on the amount of training data. Thus, the performance of these methods becomes significantly worse when insufficient training samples are used. [PERSON] [12] used the stochastic subspace identification (SSI) method to extract the fault feature vectors of the vibration signal of a wind turbine bearing, and then input the fault feature vectors into the multi-kernel support vector machine (MSVM) for fault pattern identification. The experimental results showed that this algorithm could successfully identify fault types of bearing. However, this method is similar to the neural network method in that a sufficiently large training data set is required to achieve high accuracy, and the number of the parameters that must be set is also large, decreasing the speed of the identification. With the increasing complexity of satellites, the amount of telemetry data is also expanding. Due to their limited feasibility in use for the diagnosis of anomalous satellite telemetry data, the methods described above cannot meet engineering requirements. A fault diagnosis method based on the phase-plane trajectory chart was proposed in [13; 14; 15]. By comparing the difference in the phase-plane trajectory between the measured data and the sample data, rapid detection of anomaly data was achieved, and the related features of the phase-plane trajectory were further extracted to identify the anomaly data.