Extended Kalman Filter (EKF)and Neural Network Based EKF : Comparison of simulation performance in state estimation for some nonlinear dynamical systems

Bayesian filtering techniques play a crucial role in state estimation for dynamical systems, particularly in the presence of uncertainty and noise. The Extended Kalman Filter (EKF) is a widely used method for nonlinear state estimation, but its performance can be limited by model inaccuracies and assumptions. In this study, we explored the integration of neural network methods into the EKF framework, aiming to enhance adaptability and estimation accuracy. We compared the performance of the standard EKF and the Neural Extended Kalman Filter (Neural EKF) on two nonlinear systems: the Duffing oscillator and the Van der Pol–Duffing oscillator. Using artificially generated stochastic data, we conducted an error analysis based on Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) metrics. All computations and simulations were performed using Python. Our results show that while the Neural EKF can approximate nonlinear dynamics with reasonable accuracy, the standard EKF consistently outperforms it when the true system model is available. These findings highlight both the strengths and limitations of hybrid approaches that combine traditional filtering methods with machine learning techniques for state estimation tasks