A fast closed-form approximate iterative fitting algorithm based on laser absorption spectrum

Abstract

This paper presents a novel approach—an efficient closed-form approximation iterative fitting algorithm based on laser absorption spectra. Through this closed-form approximation iterative fitting, key parameters such as peak value, spectral line width, and normalized signal area serve as indicators for iteration completion, improving the speed without compromising accuracy. Furthermore, it employs the spectral signal of n cycles as a window for further processing, minimizing external interference. The results show that the proposed method averages 9.75 iterations, while the Levenberg–Marquardt fitting method averages 60.17 iterations. The average iteration time for the proposed method is 588.83 ms, a substantial 81.7% reduction compared to the 3210.5 ms required by the Levenberg–Marquardt fitting. These results decisively demonstrate the efficacy of the proposed method in reducing iteration time and enhancing measurement precision.