An Extended Kalman Filter approach to non-linear multivariate analysis of Laser-Induced Breakdown Spectroscopy spectra

In this paper we present a new approach to multivariate LIBS quantitative analysis, based on the use of an Extended Kalman Filter (EKF). The Kalman filter is widely applied in robotics and automation for predicting the evolution of noisy systems; among the other things, this method can be applied for the fusion of data coming from different sensors. When specialized to the multivariate analysis of LIBS spectra, the Extended Kalman Filter gives accurate predictions of the elemental concentrations even when the corresponding univariate calibration curves are not linear. The method is robust and considerably simpler than other multivariate non-linear approaches, such as the ones based on the use of Artificial Neural Networks and can be easily implemented analytically once the parameters of the calibration curves are determined through a best fitting approach. An example of the application of the method in the presence of strong self-absorption of the analytical lines is presented and discussed.