A simple algorithm for the implementation of second-order-polynomial based peak-tracking methods

Abstract

Abstract A simple algorithm is proposed in this paper for the implementation of second-order-polynomial-based peak-tracking methods used in FBG sensors. By assuming that wavelengths samples are evenly distributed in the acquired reflective spectrum, which is always desired for most interrogation systems, we decomposed the Moore-Penrose of the coefficient matrix into the multiplication of an upper triangular matrix and a symmetric matrix, and consequently derived an equation nearly as simple as that of the centroid method for the determination of peak wavelength. The algorithm does not involve matrix multiplication and inverse matrix solution, so it can be easily fulfilled with solely fixed-point operations and consumes only one tenth of the calculation time needed by conventional method. Besides, the symmetric feature of the factorization makes it possible to facilitate the calculation with an existing FIR core. By using a piecewise linear fitting to the wavelength samples, the algorithm is also applicable in cases where wavelength sampling interval is not constant. An interrogation system was built up based on FPGA and a commercial spectrometer with a wavelength nonlinearity of 3 nm. It was able to interrogate over 50 FBG sensors at the same time at a measurement frequency of 17 kHz by using the proposed algorithm.