Some novel methods based on recursive optimal estimation. Applications to analytical chemistry

Abstract

Two novel methods based on recursive optimal estimation were approached: fading Kalman filtering (FKF) and networked Kalman filtering (NFK). Fading Kalman filtering was employed to enhance overlapped spectroscopic resolution. Based on the nature of the Kalman filter, that the residual sequence is uncorrelated when the optimal gain is obtained, a new fading optimal adaptive algorithm is proposed and utilized. By on-line adjustment of the fading factor, the convergency and optimality of the Kalman filter were improved using measured outputs or estimated results, even in the presence of model errors and/or the effects of unmeasurable external disturbances. The FKF algorithm developed was applied to overlapped peak resolutions and gave good results. The networked Kalman filtering (NKF) of multiple models was found to have some advantages over the ordinary Kalman filtering and was used to detect concentrations of minor impurities of less than 1% of that of the major analyte.