Data rectification is the process of removing errors from the measured process data and estimating the true state of the plant. In this study, data rectification is posed in a probabilistic framework and historical plant data is utilized to learn the parameters of the plant model. This approach finds the most likely estimates of the true process states by maximizing the probability of the process states given the measurements. Using Bayes' theorem, this maximization is redefined as the product of the prior probability density function (pdf) of process states and the probability distribution of measurements given the true process states. The technique exploits the existing trade off between these two terms to find the most likely values for the measured process variables. The method of adaptive mixtures is used for both off-line and On-line estimating and updating of the pdf of the measured process variables. It is a recursive nonparametric method that fits a mixture of Gaussian pdf's to the data. The changes in the process operating conditions are reflected by adding new components to the mixture. The maximum likelihood data rectification objective function consists of two pdf's. One represents the likely process states and the other characterizes the likely adjustments to the measured values. The first pdf, given the measured data condition, is estimated by the expectation-maximization (EM) algorithm or adaptive mixtures. The second pdf is modeled by the product of bimodal Gaussian distributions each representing a process sensor. The resultant complex objective function is then maximized by an iterative EM algorithm and the most likely values of the measured process variables are found. The changes in process operation are reflected in the objective function by updating its terms. The pdf of the measured process states is updated using the rectified points and a robust approach has been developed to update the pdf's representing the plant sensors operation. This new approach is implemented for numerical and chemical process examples. The capabilities of the new approach are demonstrated by producing robust estimates for covariance matrices, reliable estimates of mixture probability densities, rejecting the errors in the measurements and yielding reliable rectified values for the measured process variables in these examples. (c) 2004 Elsevier Ltd. All rights reserved.