State filtering with identified error dynamics and dynamic networks

In this paper a practical algorithm is presented for adaptive state filtering when the underlying nonlinear state equations are partially known. The unknown dynamics are constructively approximated using neural networks. The proposed algorithm accounts for the unmodeled nonlinear dynamics and makes no assumptions regarding the system noise statistics. The proposed filter is implemented using static and dynamic, feedforward and recurrent neural networks. A case study is considered and comparison with extended Kalman filters (EKFs) performed. The developed EKF does not converge. The off-line trained neural state filters converge quite rapidly and exhibit acceptable performance. Online training further enhances the filter performance, decoupling the eventual filter accuracy from the accuracy of the available system model