Traditionally, soft sensors are developed based on measurement data only, but here we consider an adaptive soft sensor that uses data generated from a fitted, first principles model of the distillation columns. The contribution of the paper is a procedure for moving window soft sensor design that incorporates a priori knowledge, which is especially suitable when the training sample is small and contains measurement errors. In addition, we propose a continuous adaptation of all model parameters based on new data, instead of the usual procedure of only updating the bias. The accuracy of the predicted product quality is investigated by calculating the coefficient of determination and root mean squared error for the test sample. Several approaches were considered, and we found that a constrained optimization approach was superior. The constraints on the model parameters of soft sensors are derived from a fitted, rigorous distillation unit model. The improved estimator quality resulted in the successful industrial application of advanced process control systems. (C) 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.