An algorithmic approach to adaptive state filtering using recurrent neuralnetworks

On-line estimation of variables that are difficult or expensive to measure using known dynamic models has been a widely studied problem. Applications of this problem include time-series forecasting, process control, parameter and state estimation, and fault diagnosis. In this paper, practical algori thms are presented for adaptive state filtering in nonlinear dynamic system s when the state equations are unknown. The state equations are constructiv ely approximated using neural networks. The algorithms presented are based on the two-step prediction-update approach of the Kalman filter. However, u nlike the Kalman filter and its extensions, the proposed algorithms make mi nimal assumptions regarding the underlying nonlinear dynamics and their noi se statistics. Nonadaptive and adaptive state filtering algorithms are pres ented with both off-line and on-line learning stages. The proposed algorith ms are implemented using feedforward and recurrent neural network and compa risons are presented. Furthermore, extended Kalman filters (EKFs) are devel oped and compared to the filter algorithms proposed. For one of the case st udies, the EKF converges but results in higher state estimation errors that the equivalent neural filters. For another, more complex case study with u nknown system dynamics and noise statistics, the developed EKFs do not conv erge. The off-line trained neural state filters converge quite rapidly and exhibit acceptable performance. On-line training further enhances the estim ation accuracy of the developed adaptive filters, effectively decoupling th e eventual filter accuracy from the accuracy of the process model.