Incorporation of a positivity constraint into a Kalman-filter-based algorithm for correction of spectrometric data

Improving the resolution of spectrometric analyses by numerical processing of spectrometric data subject to systematic errors of an instrumental type, as well as to random errors, is addressed. It is assumed that the model of the spectrometric data has the form of an integral, convolution-type equation of the first kind. The method for improving the resolution consists of numerically solving this equation on the basis of the acquired data. A new algorithm for dealing with this problem is proposed; it is based on the Kalman filter constrained in such a way that the negative values of the solution are suppressed. The efficiency of this constrained algorithm is demonstrated using both synthetic and real-world data