Measurement-Based Drift Correction in Spectroscopic Calibration Models

Correct prediction of analyte concentrations from a new spectrum without drift is possible provided the spectrum lies in the row space spanned by the calibration spectra (space-inclusion condition). However, this condition may be violated as on-line spectrometers are compromised by instrumental, process and operational drifts that are not seen during calibration. A space- inclusion condition, which new spectra possibly corrupted with drift should fulfill, is proposed for drift-correction methods. These methods are characterized as either explicit or implicit based on whether or not drift is estimated using on-line reference measurements. A property of the kernel used in explicit methods is proposed based on the space-inclusion condition. The results are illustrated with a simulation study that uses mathematical models for different drift types.