Extracting vibration signal from measured data polluted by thermal noise using a Kalman filtering technique

In practice, a measured vibration signal is often mixed with the inherent thermal noise existing in the measurement system. It is difficult to use traditional frequency-domain filtering techniques as the desired vibration signal and the unwanted thermal noise may have components in the same frequency band. In this research, a dual-sensor vibration measurement system and a Kalman filter based on a linear prediction model are developed to reduce the thermal noise in measured data. This paper presents a mathematical analysis of the linear-prediction-based Kalman filter and examines the effects of the prediction error and measurement error on the filtering performance. The results show that the linear-prediction-based Kalman filter can reduce the prediction error compared to the traditional random-walk model. The effect of unsteady measurement error on filtering performance is also investigated. A simulation example is used for illustration. The simulation result shows that the linear-prediction-based Kalman filter achieves a better anti-drift performance than the conventional low-pass filter, and the delay of the linear-prediction-based Kalman filter is smaller than that of the conventional low-pass filter.