Traditionally, soft sensors are developed based on measurement data only, but here we consider a moving window (MW) soft sensor (SS) that uses data generated from a calibrated, rigorous model of the distillation columns of an FFC unit at Gazpromneft-Omsk Refinery. The contribution of the paper is that a procedure is developed for MW SS 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 (R2) and root mean squared error (RMSE) 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 SSs are derived from a calibrated, rigorous distillation unit model. The improved estimator quality resulted in the successful industrial application of advanced process control (APC) systems.