Andrzej Barwicz

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. >

The use of deconvolution and iterative optimization for spectrogram interpretation

The problem of spectrogram interpretation is considered under the assumption that the parameters of spectral peaks-their positions and magnitudes-contain the information essential for spectrometric analysis. The subsequent use of Tikhonov deconvolution and iterative correction of the estimates of those parameters is proposed. Deconvolution is used for transforming the processed spectrogram in such a way as to facilitate finding initial estimates of its parameters. The advantages of the proposed approach, i.e., gains in accuracy of estimating the parameters of peaks, are demonstrated using both synthetic and real-world spectrophotometric data.

Combined use of Tikhonov deconvolution and curve fitting for spectrogram interpretation

Abstract The problem of numerical correction of spectrograms is addressed. A new method of correction is developed which consists of sequential use of the Tikhonov deconvolution algorithm, for estimating the positions of spectral peaks, and a curve-fitting algorithm, for estimating their magnitudes. The metrological and numerical properties of the proposed method for spectrogram interpretation are assessed by means of spectrometry-based criteria, using synthetic and real-world spectrograms. Conclusions are drawn concerning computational complexity and accuracy of the proposed method and its metrological applicability.

Spline-based variational method with constraints for spectrophotometric data correction

The raw results of spectrophotometric measurements are subject to systematic errors of an instrumental type which may be reduced 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 spectrometric data consists in numerically solving this equation on the basis of the raw results of measurements. An algorithm of correction is proposed which is based on the approximation of the solution with a spline function whose parameters are determined using a variational method with the positivity constraint imposed on the set of feasible solutions. The efficiency of the incorporation of this constraint into the algorithm of correction is demonstrated using synthetic data. The possibility of improving resolution of spectrometric data is shown on a set of real spectrophotometric measurements. >

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.

Neural-network-based method of calibration and measurand reconstruction for a high-pressure measuring system

The problem of applying the neural networks for static calibration of measuring systems and for measurand reconstruction is addressed. A multilayered neural network based method for the static calibration of this system is proposed. The functioning of the calibrated measuring system is based on three fiber-optic transducers whose static characteristics are nonmonotonic and significantly influenced by temperature. The applicability of the proposed calibration method is demonstrated in the case under consideration using synthetic and real data. The neural network is designed and implemented in a general purpose microcontroller. In comparison with the spline-based method of calibration, for the same reference data, the proposed method allows obtention of a better quality of calibration and, most important, when calibrated, the multilayered neural network does not require the measurement of temperature for pressure reconstruction.

Numerical correction of spectrometric data using a rational filter

Raw spectrometric data are subject to systematic errors of an instrumental type that may be reduced provided a mathematical model of the spectrometer used, or its pseudoinverse, i.e. an operator of reconstruction, is identified. The idea to identify this operator directly during calibration of the spectrometer is developed in this paper. The applicability of an operator of reconstruction having the form of a rational filter is studied when it is used for correction of the instrumental errors introduced by an absorption spectrometer. An algorithm for identification of this operator is proposed and studied using spectrometric‐type synthetic data and real‐world spectrometric data. The proposed operator is compared with some existing algorithms of spectrometric data correction, using accuracy‐related criteria, both non‐specific and specific to spectrometry. Copyright

A cubic FIR-type filter for numerical correction of spectrometric data

The raw results of spectrometric analysis are subject to systematic errors of an instrumental type that may be reduced provided a mathematical model of the instrumental imperfections or its pseudoinverse, i.e., an operator of reconstruction, is identified. The idea to identify the operator of reconstruction, having the form of a cubic FIR-type filter, directly during calibration is developed in this paper. A corresponding algorithm is proposed and studied using spectrometric-type synthetic and real-world spectrophotometric data. The results are compared with those obtained by means of the algorithms, often used for spectrometric data correction.

Kalman-filter-based algorithms of spectrophotometric data correction III. Use of splines for approximation of spectra

An alternative method to that presented in the first paper of the series for improving the resolution of spectrophotometric measurements via processing of spectrometric data is proposed. It is based on the approximation of the solution with a spline function the parameters of which are determined by means of a recursive Kalman-filter-based algorithm. It is assumed in the paper that the model of the spectrophotometric data has the form of an integral, convolution-type equation of the first kind. It is shown, using synthetic and real-world spectrophotometric data, that the proposed method allows for significant reduction of computational requirements as well as an improvement in the quality of correction.

An application-specific processor dedicated to Kalman-filter-based correction of spectrometric data

An application-specific processor dedicated to Kalman-filter-based measurand reconstruction in spectrometric applications is proposed. It is intended to act as co-processor of a host processor, performing relatively sophisticated processing of measurement data subject to systematic errors of an instrumental type and to random errors of various natures. It is basically designed for improving the resolution of spectrometric measurements commonly used in environmental laboratories, but it may be useful in other applications where similar processing of measurement data is required. Examples of applications of the processor in environmental measurements, its metrological advantages and limitations, as well as perspectives of its development, are presented. >