Classical least squares formulation

In this chapter different aspects of data processing and reconciliation in a dynamic environment were briefly discussed. Application of the least square formulation in a recursive way was shown to lead to the classical Kalman filter formulation. A simpler situation, assuming quasi-steady-state behavior of the process, allows application of these ideas to practical problems, without the need of a complete dynamic model of the process. 

As in the classical steady-state data reconciliation formulation, the optimal estimates are those that are as close as possible (in the least squares sense) to the measurements, such that the model equations are satisfied exactly. 

Fluorimetry was considered in the 1950s as the natural detector for pharmaceuticals, due to its improved selectivity and sensitivity compared with UV-Vis absorption. Recent FIA applications include the determination of diazepam, nitrazepam, and oxazepam in pharmaceutical formulations using acidic hydrolysis and fluorimetric detection. Oxidation with Ce(IV) and measurement of the fluorescence from the released Ce(III), which can be considered as a classical strategy, is an appropriate technique for mixtures of amoxycillin and clavulanic acid where kinetic data are used in combination with partial least-squares multivariate calibration. 

LS-SVMlab, http //www.esat.kuleuven.ac.be/sista/lssvmlab/. LS-SVMlab, by Suykens, is a MATLAB implementation of least-squares support vector machines (LS-SVMs), a reformulation of the standard SVM that leads to solving linear KKT systems. LS-SVM primal-dual formulations have been formulated for kernel PCA, kernel CCA, and kernel PLS, thereby extending the class of primal-dual kernel machines. Links between kernel versions of classic pattern recognition algorithms such as kernel Fisher discriminant analysis and extensions to unsupervised learning, recurrent networks, and control are available. 

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