An algorithmic approach to adaptive state filtering using recurrent neural networks

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 algorithms are presented for adaptive state filtering in nonlinear dynamic systems when the state equations are unknown. The state equations are constructively approximated using neural networks. The algorithms presented are based on the two-step prediction-update approach of the Kalman filter. However, unlike the Kalman filter and its extensions, the proposed algorithms make minimal assumptions regarding the underlying nonlinear dynamics and their noise statistics. Nonadaptive and adaptive state filtering algorithms are presented with both off-line and on-line learning stages. The proposed algorithms are implemented using feedforward and recurrent neural network and comparisons are presented. Furthermore, extended Kalman filters (EKFs) are developed and compared to the filter algorithms proposed. For one of the case studies, the EKF converges but results in higher state estimation errors that the equivalent neural filters. For another, more complex case study with unknown system dynamics and noise statistics, the developed EKFs do not converge. The off-line trained neural state filters converge quite rapidly and exhibit acceptable performance. On-line training further enhances the estimation accuracy of the developed adaptive filters, effectively decoupling the eventual filter accuracy from the accuracy of the process model.