Abstract: Kalman filter neural network(KFNN) have been widely used in modeling for complex industrial process, because they have abilities to adaptive approximate the nonlinear and dynamic properties of the process. However, the performances of KFNN will diverge because it can’t get accurate statistics of unmeasurable noise by traditional noise estimation methods. A new KFNN with gamma test(GT) is proposed for industrial process modeling with the unmeasurable noise. The moving window idea is introduced to GT algorithm, and the improved GT is used to track the changes of the observable noise covariance in real time because it can get the accurate statistics of the unmeasurable noise only use the input-output data. Then the covariance in the traditional KFNN is replaced by real-time estimation from the improved GT algorithm. In this way, the KFNN is enhanced by the GT algorithm. In order to verify, the proposed KFNN is used to model the industrial process. The efficiency of the new KFNN is verified by complex hydrocyanic acid(HCN) industrial process. Verification show that the performance of the proposed KFNN model superior to those of the traditional KFNN, e.g. the extended Kalman filter artificial neural network(EKFNN) and the unscented Kalman filter artificial neural network(UKFNN). Therefore, the proposed method provides a new solution to get the accurate model of the industrial process with unmeasurable noise.

Key words: Kalman filter;artificial neural network;measurement noise;dynamic industrial process modeling