Performance Analysis of Extended Kalman Filter Combined with Neural Network for Nonlinear State Estimation

Abstract

Accurate state estimation for high-order nonlinear dynamic systems remains a challenging problem, particularly when system models are incomplete or subject to strong nonlinearities. In systems involving higher-order derivatives such as angular acceleration and jerk, conventional Extended Kalman Filters (EKF) often suffer from degraded accuracy due to model uncertainties and limitations of first-order linearization. The objective of this study is to develop and evaluate a unified state estimation framework that enhances EKF performance for high-order nonlinear systems by integrating a Neural Network (NN) directly into the prediction step. In the proposed approach, the NN is trained online to approximate the unknown high-order nonlinear dynamics and its output is embedded into the EKF state prediction model. To further improve linearization accuracy under strong nonlinearities, complete first- and second-order Jacobians are incorporated into the EKF formulation. The effectiveness of the proposed EKF–NN framework is verified through comprehensive simulations conducted on a fourth-order nonlinear system. The results demonstrate fast convergence, high estimation accuracy, and statistical consistency for all system states. In particular, the high-order state β, which is typically difficult to estimate reliably, is reconstructed with bounded error and without divergence. The main contribution of this work lies in the direct integration of online neural network learning with higher-order EKF linearization, resulting in a robust and accurate state estimation method suitable for strongly nonlinear dynamic systems.