Highly robust vector-synthesis method for multi-frequency distributed acoustic sensing

Rotated-vector-sum (RVS) is widely used in multi-frequency distributed acoustic sensing (DAS), but its synthesis gain collapses in long-haul sensing or with large frequency intervals. To fundamentally elucidate this effect, we develop a theoretical model that separates the coherent and random contributions of the Rayleigh-scattering signal within the RVS framework. Our model reveals that long distances and large frequency intervals raise the amplitude threshold required for the coherent component to provide positive gain, while improper synthesis weights amplify random phase errors. To address these issues, we propose a weight-reconstructed conjugate difference aggregation (WR-CDA) method. This approach minimizes and decouples the threshold from the sensing conditions to guarantee a consistently positive synthesis gain. The reconstructed weights are tied to the phase-error variance, effectively suppressing the influence of the random phase error. Experimental results demonstrate that WR‑CDA reduces the root‑mean‑square noise floor by more than a factor of four and suppresses the spectral noise by an average of 14.8 dB and up to 30.0 dB, relative to conventional RVS. These results demonstrate its potential for weak‑vibration and long‑haul sensing.