Toshio Shibazaki

Real-time quantitative analysis of unresolved liquid chromatographic peaks with the use of the kalman filter

Abstract It is shown that unresolved peaks in high-performance liquid chromatography can be deconvoluted and quantitated precisely by the Kalman filter. Naphtha

Resolution of overlapped chromatograms by means of the kalman filter : Dimensional reduction of error covariance matrices and state estimate vectors

Abstract If many samples are successively injected into a high-performance liquid chromatograph at short intervals, then overlapped chromatograms will be obtained. A simplified version of the Kalman-filter algorithm is described for rapid resolution of several such overlapped peaks on small laboratory computers; the dimensionalities of the error covariance matrix P k and state estimate vector X k are reduced to far less than the total number of the peaks. Computer simulation shows that at least twenty partially overlapped Gaussian peaks, used as a model of the successive injections can be successfully resolved, with the 4 × 4 matrix P k and 4-vector X k . This version is independent of the number of injections and is effective for the resolution of a finite number of peaks in that injection mode. The algorithm of small dimensions is applicable to a wide variety of peak resolution procedures.

Resolution of overlapped chromatograms by the use of a Kalman filter : III. Effects of overlapping and outstripping of a solvent peak on the analysis

Abstract The effects of a solvent peak on Kalman filter analysis of overlapped chromatograms which result from successive injections of a series of samples at short, regular intervals in high-performance liquid chromatography are demonstrated. Twenty peaks in the overlapped chromatograms derived from five successive injections of samples with a solvent peak and three components (phenetole, pyrene and perylene) were resolved and quantitated by a reduced Kalman filter of four dimensions. The 4-min injections gave satisfactory calibration lines for the three components: 1.009 > A (slope) > 0.993; correlation coefficient > 0.99993. This method is concluded to be useful for rapid, precise determination of a series of samples. It will lead to novel designs of experimental procedures in various areas of analytical chemistry.

Resolution of overlapped chromatograms by means of the kalmam filter : Data Processing of Liquid Chromatographic Signals without Solvent Peaks

Abstract If several samples are injected successively at short intervals into a liquid chromatograph, overlapped chromatograms of the samples will result. This paper describes an application of this successive-injection method to determination of samples without solvent peaks. Twenty peaks in the overlapped chromatograms resulting from five successive injections of samples with four components (phenetole, biphenyl, pyrene and perylene) were resolved and quantified by a reduced four-dimensional Kalman filter. The period of the single chromatogram of the four components is ca. 14 min, and the period of the five overlapped chromatograms ca. 26 min, for injection intervals of 3 min. The calibration lines for the four components are all straight and satisfactory; the slope, A, of every line was 1.005>A>0.9996 with correlation coefficients better than 0.999992. This successive-injection method with the reduced Kalman filter is time-saving for trivial routine work.