Enhanced Deep-Learning-Aided Kalman Filter Based on KalmanNet for Robust Nonlinear State Estimation

Accurately estimating the real-time state of dynamic systems from noisy measurements is a fundamental task in signal processing. State-space models (SSM) are commonly utilized to model system dynamics and account for uncertainty in both system state evolution and measurement data. Kalman filter (KF) and its variants are widely recognized for their low computational complexity and ability to address state evolution and measurement update. In practice, accurately modeling the system dynamics and obtaining model parameters are difficult, especially for nonlinear systems. These tasks often require predefined motion and measurement models that rely on coarse approximations and extensive manual tuning. In this paper, we propose DL-KF, a robust Deep Learning aided Kalman Filter designed to perform KF in nonlinear dynamic environments where the process model is unavailable and the system noise is also unknown. However, a linear measurement model is assumed. DL-KF utilizes a Long Short-Term Memory (LSTM) network to capture nonlinear process dynamics and generate state priors from historical measurements. Additionally, a Gated Recurrent Unit (GRU) is utilized to independently learn innovation covariance, addressing measurement noise uncertainty, followed by the computation of the Kalman gain within the Kalman filter framework. By integrating an SSM framework with deep learning modules, the proposed method strikes the balance between the flexibility of data-driven approach and the interpretability of classical Kalman based approaches. Empirical results demonstrate that DL-KF significantly outperforms traditional model-based filters, including the KF, EKF, and UKF. Furthermore, it surpasses state-of-the-art hybrid methods such as KalmanNet, Split-KalmanNet, and AKNet, particularly in challenging scenarios involving high nonlinearity (e.g., the Lorenz attractor) and maneuver-induced model mismatches. The algorithm’s efficacy and robustness are further validated through extensive experiments on real-world tunnel radar and NCLT datasets.