A Detailed Evaluation of the Correlation-Based Method Used for Estimation of the Brillouin Frequency Shift in BOTDA Sensors

This paper thoroughly describes and evaluates the method that was previously presented for estimating the central frequency of noisy Lorentzian curves (spectra) acquired from the measurements with Brillouin optical time domain analysis (BOTDA) sensors. The estimator is based on the cross-correlation technique and addresses the problem of sensitivity to noise and parameter initialization observed in other central frequency estimation methods employed with BOTDA sensors. Most of the current estimation methods rely on optimized rigorous least squares or maximum likelihood estimation (MLE) algorithms, which are sensitive to the parameter initialization and noise as they iteratively attempt to minimize the squared error or maximize the matching probability between the model and noisy curve. Alternatively, the estimation made with the cross-correlation based method is more accurate, noniterative, and insensitive to the parameter initialization. This statement is demonstrated and proved by comparing the correlation-based method with two commonly used iterative curve fitting methods based on the Levenberg-Marquardt algorithm and MLE.