Principle and Performance Analysis of the Levenberg–Marquardt Algorithm in WMS Spectral Line Fitting

Abstract

Calibration-free wavelength modulation spectroscopy (WMS) is an efficient technique for trace gas monitoring. It is widely used due to its resistance to light intensity fluctuations, strong suppression of low-frequency noise, fast response time, and excellent environmental adaptability. The calibration-free WMS often employs the Levenberg–Marquardt algorithm for spectral fitting to retrieve gas characteristics. However, to the best of our knowledge, an analysis of the main factors affecting the operational effectiveness of the Levenberg–Marquardt algorithm in calibration-free WMS has merely been reported. In this paper, we have systematically analyzed the Levenberg–Marquardt algorithm’s operating mechanism in WMS-2f/1f. The results show that the number of parameters and the estimation errors of the initial parameters are the main factors limiting the retrieval accuracy of the algorithm, which provides some important guidelines for the subsequent optimization of the spectral fitting scheme.