Objective Phase-sensitive optical time-domain reflectometers (Φ-OTDR) face challenges in vibration detection accuracy and localisation due to inherently low signal-to-noise ratio (SNR) stemming from Rayleigh scattering randomness, laser coherence decay, and complex environmental disturbances. This paper aims to address interference from spatially independent noise and non-stationary structural noise within the envelope signal, enhancing vibration peak prominence and improving localisation accuracy while maintaining the system's spatial resolution.

Methods This paper proposes an Adaptive Moving Variance (AMV) denoising algorithm that operates directly on the IQ-demodulated envelope signal. The core of this algorithm lies in introducing gradient-driven local adaptive windows for variance estimation, replacing traditional fixed-window differencing or complex modal decomposition. The specific workflow comprises: first applying a moving baseline average to smooth the envelope; Subsequently, a gradient matrix is computed between adjacent smoothed trajectories to capture local correlations and abrupt features; Thereafter, gradient-constrained linear scaling of the baseline window determines the adaptive window width at each position; The local mean and variance within this adaptive window are then calculated; Finally, the variance standard deviation is computed along the trajectory direction, forming a one-dimensional positioning curve whose peak indicates the vibration source location (Fig.3).

Results and Discussions The effectiveness of this algorithm was validated through simulations and experiments using the publicly available Φ-OTDR dataset. Under simulated complex non-stationary noise conditions, AMV processing elevated the envelope signal-to-noise ratio from 9.3 dB to 20.3 dB, achieving a vibration localisation error of 2.52 metres (Fig.5). In experimental testing covering nine operating conditions (involving PZT vibrations at 1-3 V voltage and 50-200 Hz frequency), the AMV algorithm attained a peak signal-to-noise ratio of 51.0 dB (Tab.1). Under 1V/200Hz conditions, its signal-to-noise ratio surpassed suboptimal algorithms (CEEMDAN and EEMD) by 42% (Fig.11); in high-vibration environments (3 V), the performance advantage exceeded 20 dB (Tab.1). These results validate AMV's selective enhancement mechanism: amplifying coherent statistical effects by expanding the sampling scale during vibration segments, while maintaining compact sampling windows during steady-state segments to prevent signal dilution.

Conclusions The proposed Adaptive Mobile Variance (AMV) algorithm significantly enhances peak prominence and localisation accuracy in Φ-OTDR systems without compromising spatial resolution. By leveraging statistical consistency between adjacent trajectories and employing gradient-driven adaptive windows for variance estimation, this algorithm effectively suppresses spatially independent and non-stationary structural noise. Simulation and experimental results confirm that, compared to existing algorithms, this algorithm demonstrates superior performance in enhancing signal-to-noise ratio and achieving precise vibration localisation.