Incipient sensor fault detection for time-varying stochastic systems under Kalman filtering framework

This article is concerned with incipient sensor fault detection for time-varying stochastic systems under the Kalman filtering framework. Generally, incipient sensor faults are hard to detect since it is submerged by noise. By means of the stochastic theory, the accurate relationship among the sensor fault magnitude, the acceptable false alarm rate (FAR) and missed detection rate (MDR) is given. Then, an incipient sensor fault detection algorithm is proposed by using the weighted moving average method. The weight matrix and window length of the weighted moving average method are properly chosen to ensure the detectability of incipient sensor faults in a probabilistic sense, which means the FAR and MDR are in the acceptable range. Finally, a simulation example is provided to demonstrate the usefulness of the derived results.