Nonlinear Polynomial Graph Filter for Anomalous IoT Sensor Detection and Localization

Detecting the existence of anomaly and localizing the faulty sensors in the Internet-of-Things (IoT) systems are extremely critical, since the incorrect data could lead to catastrophic consequences in many vertical industry applications. The difficulties of such problems come from deriving an explicit error function for each sensor in IoT, and the data continuity in the temporal domain would also be seriously challenged. To overcome these difficulties, the irregular spatial information of the IoT sensors is utilized by constructing an adjacency matrix using the distances among different sensors, and the nonlinear polynomial graph filter (NPGF) is employed to characterize the relationships among the collected sensor data. The NPGF provides a more accurate model for reconstructing the sensor data by taking the data nonlinear relationships into account. The error functions at each sensor for newly detection data are theoretically derived, and it is demonstrated that the error at the anomalous sensor performs differently from that of the normal sensors if the adjacency matrix is designed appropriately. The proposed NPGF-based algorithm is illustrated and validated with a real-world data set for temperature monitoring. The simulation results demonstrate the superior performance of our scheme in both anomaly detection and faulty sensor localization when compared with existing algorithms, such as the graph frequency algorithm and oversampling PCA (OS-PCA) method, especially for the case of small sensor data deviations.