Rapid parameter estimation with incomplete chemical calibration models

Abstract

The use of calibration models to predict analyte concentrations in samples showing responses from poorly calibrated components, or samples showing drift in the instrumental response function, is seldom successful. These incomplete calibration models cannot account for variations not encountered in the calibration step. Simple modifications are possible which remedy this difficulty for classical least squares (CLS) regression. By using sequential regression for the prediction step, extensions are possible which lessen errors due to overfitting, and permit prediction of well-modelled components in the presence of unmodelled components. Implementation of the sequential regression is conveniently done through use of the Kalman filter. Use of filter models for dynamics and measurement also permits correction of drift of various types. The use of CLS calibration with Kalman filter prediction is presented and tested with simulated spectroscopic data. Comparisons are made to other calibration and prediction methods.