Kalman-filter-based algorithms of spectrometric data correction-Part I: an iterative algorithm of deconvolution

This series of two papers aims to present the different solutions of the problem of improving the resolution of spectrometric measurements via numerical processing of spectrometric data subject both to systematic instrumental errors and to random measurement errors. It is assumed that the model of the spectrometric data has the form of a convolution-type equation of the first kind. The method for improving the resolution consists in numerically solving this equation using the acquired data. In this first paper of the series, an algorithm of correction is proposed which is based on the iterative use of the Kalman filter incorporating a non-negativity constraint. Its applicability to the problem of correction is assessed not only from a purely metrological point of view (accuracy, resolution) but also with respect to its suitability for implementation as a VLSI processor dedicated to measuring systems. For this latter reason a time-invariant model of the data and a steady-state version of the Kalman filter is used. The efficiency of this approach to correction is demonstrated using both synthetic and real-world data.