Kalman filtering approaches for solving problems in analytical chemistry

Abstract

SUMMARYThe application of the Kalman filter to the solution of a variety of problems in analytical chemistry is reviewed. Five examples are selected from the literature to illustrate the use of Kalman filtering techniques for obtaining least-squares estimates for several parameters of analytical importance. These examples include multicomponent curve resolution and concentration estimation, correction for variable background responses, calibration with drift compensation, and estimation of kinetic parameters for first-order reactions and for heterogeneous charge-transfer reactions. An adaptive Kalman filtering technique is required for the solution of the background correction problem, and the extended Kalman filter algorithm is required for the solution of the nonlinear kinetic problems. For each case, the results that were obtained are summarized, and some advantages of Kalman filtering over traditional least-squares approaches are discussed. KEY WORDS Kalman filter Calibration Curve resolution Parameter estimationThere are many instances in chemistry when parameters must be determined from analytical data. Chemical species concentrations, kinetic parameters and calibration parameters are examples of some of the most important parameters which can be obtained from spectroscopic, chromatographic or electrochemical measurements. Parameter estimation methods used for chemical problems are usually based on least-squares techniques. One method which has been employed recently for solving these sorts of problems is the Kalman filter. The Kalman filter is a recursive, digital filtering algorithm which allows the estimation of states and parameters from noisy measurements. This approach is convenient for determining some of the important chemical parameters described above, and it offers a flexible approach in these cases. An extensive review of Kalman filter applications in analytical chemistry has been published recently; it includes a discussion of the algorithm and a comprehensive survey of recent applications. 'Here, the focus is a more detailed discussion of some specific examples from the literature which demonstrate the flexibility of the Kalman filter for the solution of specific chemical problems. Five examples have been chosen which illustrate the essential features of the Kalman filter. These examples include multicomponent curve resolution and concentration kinetic parameter estimation, 5 s 6 calibration with drift correction, '-lo compensation for variable background responses, and estimation of electrochemical kinetic parameters in conjunction with digital filtering techniques.

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