Accurate and ultra-fast estimation of Brillouin frequency shift for distributed fiber sensors

[Display omitted] •An accurate and ultra-fast linear least-squares algorithm is used to estimate BFS.•Computation time of proposed algorithm is much less than typical nonlinear fits.•Errors estimated by proposed algorithm and typical nonlinear fits are very similar.•No initial guesses, iterations and convergence criterion are needed.•Proposed algorithm is faster and more accurate than correlation-based algorithm. The original Lorentzian profile-based nonlinear least-squares problem for BFS estimation is converted to a linear least-squares one. Then, Brillouin frequency shift (BFS) can be readily calculated. The typical nonlinear least-squares Lorentzian, Gaussian, pseudo-Voigt and Voigt fits using Levenberg-Marquardt algorithm, the correlation-based algorithm and the proposed Lorentzian model-based linear least-squares fitting algorithm are used to estimate BFS of the measured Brillouin spectra with different values of SNR (signal-to-noise ratio) and frequency step. The results reveal that the proposed algorithm has similar accuracy with the nonlinear fits. However, the computation time of the typical nonlinear fits is 187.56–11481.67 times as long as the proposed algorithm. The proposed algorithm can estimate BFS with less computational burden and higher accuracy than the correlation-based algorithm. If SNR is low, the frequency step should be set to a low value.