Robust multivariate calibration algorithm based on least median of squares and sequential number theory optimization method

With the help of constraints on the concentrations to be estimated in direct multivariate calibration, an algorithm for least median of squares (LMS) was developed. The sequential number theory optimization (SNTO) method developed in statistics was used for robust multivariate calibration in order to reach the global optimization. The computational complexity of LMS is dramatically reduced by means of the constraints on the concentrations to be estimated and the SNTO method. The algorithm was applied to a simulated data set and to two sets of real data from two-and/or three-component analytical systems. Comparisons with the least squares technique show that the proposed method is efficient in terms of computational complexity and is robust to a large number of outliers in the data.