Information theory and Kalman filtering methods for the determination of polyaromatic hydrocarbons

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Abstract

The Kalman filter is a recursive, digital filtering algorithm which has been used for state and parameter estimation in several areas of chemistry. The filter is based on a two-part model, consisting of a description of the system dynamics, and a description of the measurement process. The algorithm equations allow both linear and nonlinear models to be employed, and offer several advantages over more conventional fitting procedures.

Here, some studies are described which are based on the use of Kalman filtering techniques for the determination of polyaromatic hydrocarbon compounds. Thin-layer chromatographic techniques have been used in conjunction with fluorescence spectroscopic detection to determine these compounds. Several approaches using the Kalman filter have been developed to allow improved analysis characteristics for these compounds. The Kalman filter algorithm has been used to resolve overlapped chromatographic and fluorescence responses. An adaptive Kalman filter algorithm has been combined with a derivative spectroscopic model which allows variable background responses to be subtracted and accurate concentration estimates to be obtained. In addition, the Kalman filter has been used in conjunction with information theory principles in order to determine optimal experimental designs for multidimensional fluorescence measurements. Two related measures of the information yield have been employed to select subsets of an excitation—emission matrix which yield the highest information.

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