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

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 Pk 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 Pk 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.