Kalman filter for updating the coefficients of regression models. A case study from an activated sludge waste-water treatment plant

A Kalman filter was developed to overcome the problems caused by process drifting. Different types of models were used to predict response variables of an activated sludge waste-water treatment plant. These models were constructed using MLR, PCR, and PLS. The MLR-type regression coefficients were calculated for both the PCR and PLS models. After that, the Kalman filter was used to estimate these coefficients, recursively. Both the PCR and PLS `inner relationʹ coefficient vectors were also estimated in this way and the results were then compared. The effect of the number of variables was also briefly studied. The testing was carried out using sequential process data. The prediction ability was measured by a Q2-value as a function of a lag in the updating of the coefficients.