Efficiency of constraining the set of feasible solutions in Kalman-filter-based algorithms of spectrophotometric data correction

The problem of improving resolution of spectrometric measurements via numerical processing of the spectrometric data subject to systematic errors of an instrumental type, as well as random errors of a different nature 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 of improving resolution consists in numerically solving this equation on the basis of the acquired data. An algorithm for correction is proposed which is based on the iterative use of the Kalman filter with the incorporation of a positivity constraint. Its applicability to the problem of correction is assessed not only from a purely metrological point of view but also with respect to its suitability for its implementation as a VLSI structure dedicated to measuring systems. For this latter reason a stationary model of the data and a the steady-state version of the Kalman filter is used. The efficiency of this method of correction is demonstrated using both synthetic and real data