In many industrial processes

in addition to the online measurements with delay-free and low inaccuracy

there exist delayed measurements accurately obtained by laboratory analysis. The augmented state Kalman filter is employed to estimate the state by incorporating both the delayed and the delay-free measurements. To overcome the model-plant mismatch of the online soft-sensor model built by the delay-free measurements

the model deviation is employed to update the soft-sensor model. To follow the model drift

the model deviation is treated as a state

and it will be estimated when the offline measurements arrive. In the end the proposed method is used to estimate the tray compositions in the linearized nonlinear binary distillation column model and obtains good results.