Inverse Optimal Filtering Method for the Instrumental Spreading Correction in Size Exclusion Chromatography

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Abstract
The Kalman filter based techniques are adapted to solve the most general form of Tung's integral formula, i. e. when a non-uniform, non-symmetric calibration model is employed to correct chromatograms obtained in size exclusion chromatography from instrumental broadening errors. Through this method, the inverse smoothing of a chromatogram contaminated with measurement noise of known statistics is optimally performed by minimizing the estimation error variance. The method is numerically very “robust”, improves the signal to noise ratio, provides good validation checks, and does not involve any previous parameter estimation procedure.