Optimization of the moving averaging–moving differential algorithm for Φ-OTDR

The moving averaging-moving differential (MA-MD) algorithm is widely adopted for event recognition and positioning in phase-sensitive optical time-domain reflectometry (Φ-OTDR) vibration sensing. In this paper, two theorems about the two critical parameters of this algorithm, the MA window width and the MD interval, are found, proved, and verified. According to them we can not only obtain an optimal signal-to-noise ratio and avoid missing the vibration signal but also greatly improve the signal-searching efficiency. Work in this paper is of essential importance for understanding the characteristics of the MA-MD algorithm and will remarkably benefit its practical applications.