KAN-based Deep Learning EKF for Nonlinear Systems

This paper is concerned with the problem of state estimation of nonlinear systems with model mismatch. The extended Kalman filter (EKF) is regarded as an effective tool to solve filtering problems because of its low complexity and reliability. Nevertheless, it is extremely difficult for EKF to acquire desired performance due to high-nonlinearity and model mismatch. To improve the tracking accuracy of EKF, we propose a KAN-based deep learning EKF which combines KalmanNet with Kolmogorov-Arnold Networks (KANs). Additionally, aiming at further getting more stable performance in long-term tracking with model mismatch, we propose a hybrid architecture combining KAN-KalmanNet with EKF (KKNEKF). Numerical simulations demonstrate the validity and superiority of the proposed KKNEKF than EKF and KalmanNet, which shows better performance and higher accuracy.