Kalman filter quantitative resolution of shifted ESCA spectra after optimal alignment by simulated annealing

Summary The quantitative separation of overlapped responses accomplished by the Kalman filter algorithm is deteriorated by the errors in the model due to shifts of the component peaks. This is particularly true for spectral resolution in Electron Spectroscopy for Chemical Analysis (ESCA). A computational approach for the quantitative resolution of overlapping ESCA spectra when there is loss of collinearity between the pure component peaks and the mixture peak, has been developed. The procedure makes itera tive use of the Kalman filter for resolving the mixture spectrum with the component spectra aligned according to some values of the position parameters, and of the simulated annealing algorithm to find the optimal alignment. The performance of simulated annealing in pursuing this task, has been compared with those of simplex and steepest descent, by analyzing a set of overlapped synthetic spectra and some ESCA spectra of powder mixtures of lead compounds.