The Kalman filter in analytical chemistry

During the past ten years, the means by which more information can be extracted from experimental data have become an important area of research in analytical chemistry. Digital filters have been demonstrated to have a number of applications to analytical problems. These techniques typically involve a least-squares fit of experimental data to some model of the process being filtered. One method for filtering experimental data is based on the Kalman filter, a recursive, linear digital filter first developed for use in navigation, but now used in many fields. This paper discusses the implementation of Kalman filters in analytical chemistry. The principles of state-space digital filtering are reviewed, and the development of state/space models is discussed. Discussion is focused on the discrete Kalman algorithms. Two examples are provided to demonstrate the operation of the discrete Kalman filtering algorithm. Similarities between Kalman filtering and weighted least-squares methods are considered, and the specific advantages and disadvantages of linear and nonlinear Kalman filtering approaches are evaluated. To illustrate the range of problems which benefit from use of the filter, a comprehensive literature survey of the application of Kalman filtering to chemical problems is provided.