The use of Kalman filtering and correlation techniques in analytical calibration procedures

Abstract

Different chemometric methods to improve calibrations are described. A Kalman filter is applied for processing and predicting slowly varying parameters of a linear calibration graph. The results are used for the evaluation of unknown samples, and for deciding whether to calibrate again or to analyze the next unknown sample. Another approach of the calibration problem, particularly in chromatography, is the use of correlation techniques. The noise reduction property of correlation chromatography is used to extend the calibration graph to very low concentrations. Furthermore, an experimental technique to determine a calibration curve and the unknown sample simultaneously under exactly the same conditions is described.

Simultaneous Determination of Amlodipine, Hydrochlorothiazide, and Valsartan in Pharmaceutical Products by a Combination of Full Spectrum Measurement and Kalman Filter Algorithm

“…Assumption of initial guesses, which means either (i) C and P values are subjectively selected based on personal experience and the properties of the samples, (ii) some preliminary experiments are conducted to define the initial C and P values [1,5], or (iii) Beer-Lambert's law is applied at some selected wavelengths to calculate the initial C value (for individual substances in the mixture) by solving linear equation systems, while the variance P is calculated based on a specific guideline for statistical errors in analytical chemistry (i.e., applying Horwitz equation to calculate relative standard deviation (RSD), accordingly the standard deviation and variance at that concentration are defined) [5,7,10,12].…”

“…is assumption was applied in some previous studies [5,7], in which a series of .txt preliminary experiments were conducted with different initial guesses (C est(0) and P est(0) ) to identify the suitable initial concentration and variance for the Kalman filter. Moreover, there were studies suggested automatically carrying out the preliminary experiments (employing self-written computer programs); however, the calculation speed was generally slow, which required some repeated calculations to select proper C est(0) and P est(0) values [1,5].…”

“…is method in combination with spectrophotometry was applied to analyze mixtures of metal ions and components in multicomponent pharmaceutical dosages [3,4]. In the previous works [5][6][7][8], equations for calculating employing Kalman filter algorithm were given. However, the method for selection of initial values including initial concentrations and initial variances for the Kalman filter still has not been dealt with.…”

Long-term reproducibility detection method for quantitative LIBS using Kalman filtering

“…Wang et al 10 used the PLSR method to model the relative deviation of the laser pulse intensity distribution and the fluctuation of the spectral intensity to achieve the correction of the spectral intensity and improve the long-term reproducibility of the LIBS measurements. Smit et al 11 proposed that the Kalman filtering method can be used to process and predict the slowly varying parameters of a linear calibration curve; the experimental results of high-performance liquid chromatography (HPLC) were used for quantitative analysis of the unknown samples and to decide whether to calibrate again or analyse the next unknown sample. Sun et al 12 used Kalman filtering with a corrected model to estimate element concentrations and smooth quantitative results.…”