Enhancements to multidimensional methods in analytical chemistry

This work presents new methods for extracting information from multivariate data sets based on the Kalman filter, a digital filter for recursive estimation of parameters associated with a linear model. Parallel Kalman filter networks are used to take advantage of the diagnostic properties of the Kalman filter, namely its ability to detect the extent and nature of modeling errors in real-time.;The potential of the network is demonstrated for reaction-rate methods of analysis, using data from the molybdenum blue method for the determination of phosphate. These Kalman filter models, implemented in quasi-continuous form, describe first-order reactions with a range of rate constants. The best model for a given set of data is selected by examining the innovation sequences. This algorithm successfully corrects for errors arising from variations in the pseudo-first-order rate constant yielding improved concentration estimates.;The ability of Kalman filter networks to perform recursive principal components analysis (PCA) is also demonstrated. Application to absorbance matrices such as those in chromatography with multisensor detection are considered. This network contains discrete models for describing one- and two-component bilinear responses. The model deviations can be used to elucidate the rank of the data set such that peak purity detection can be performed in real-time using an algorithm called evolving principal components innovations analysis (EPCIA). The fundamental and experimental limitations of this approach are examined for unresolved mixtures in liquid chromatography with UV-visible detection. The results can indicate the presence of minor impurities. Furthermore, the innovation sequences estimate the elution profiles of the individual components. These profiles were further refined with the iterative target transform.