Derivative preprocessing and optimal corrections for baseline drift in multivariate calibration

The characteristics of baseline drift are discussed from the perspective of error covariance. From this standpoint, the operation of derivative filters as preprocessing tools for multivariate calibration is explored. It is shown that convolution of derivative filter coefficients with the error covariance matrices for the data tend to reduce the contributions of correlated error, thereby reducing the presence of drift noise. This theory is corroborated by examination of experimental error covariance matrices before and after derivative preprocessing. It is proposed that maximum likelihood principal components analysis (MLPCA) is an optimal method for countering the deleterious effects of drift noise when the characteristics of that noise are known, since MLPCA uses error covariance information to perform a maximum likelihood projection of the data. In simulation and experimental studies, the performance of MLPCR and derivative-preprocessed PCR are compared to that of PCR with multivariate calibration data showing significant levels of drift. MLPCR is found to perform as well as or better than derivative PCR (with the best-suited derivative filter characteristics), provided that reasonable estimates of the drift noise characteristics are available. Recommendations are given for the use of MLPCR with poor estimates of the error covariance information.