Covariance-Weighted Spectral Delay Fusion With a One-Dimensional Affine Model for High-Precision Distributed Optical-Fiber Sensing

Periodic disturbances can produce ambiguous delay estimates, limiting reliable high-precision localization in distributed optical-fiber sensing. We develop spectral delay fusion for a sensing system using a dual-wavelength bidirectional Mach-Zehnder interferometer, with four phase traces recovered by heterodyne detection and digital demodulation. With calibrated propagation parameters and timing offsets fixed, the six pairwise delay predictions form a one-dimensional affine line segment parameterized by the position of a single dominant disturbance, with sensitivities determined by propagation direction and chromatic dispersion. A generalized least-squares estimator combines unwrapped delays from robust cross-spectral phase slopes with wrapped delays from polarity-invariant phase alignment to jointly estimate position and integer ambiguities under the proposed model, using an effective joint covariance to account for shared-channel and cross-representation dependence. Experiments use a 131.335-km sensing fiber at 1530 and 1550 nm, with periodic phase perturbations applied at five nominal positions from 25 to 125 km. Across the reported groups of 20 records, the proposed method yields sample standard deviations of 1.007-1.685 m at a drive voltage of 500 mV and 0.449-1.324 m at 1 V. The ratio of the smallest single-pair sample standard deviation to that of the proposed method ranges from 2.57 to 19.56 at 500 mV and from 2.12 to 2900 at 1 V. The upper ratio reflects unstable single-pair phase-slope delay estimates for periodic disturbances in the 1-V, nominal 50-km group, where the proposed covariance-weighted fusion maintains meter-scale localization repeatability.