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

The results of spectrophotometric measurements are subject to systematic errors of instrumental type which may be partially corrected provided a mathematical model of the instrumental imperfections is identified. It is assumed that this model has the form of an integral, convolution-type equation of the first kind. The correction of the results of the measurements subject to random measurement errors consists in the numerical solution of this equation on the basis of these results. A new method for solving the problem of correction is proposed; it is based on application of the Kalman filter modified in such a way that the negative values of the solution are prohibited. The efficiency of this regularization method is demonstrated. It is studied using both synthetic and real data