Hybrid vehicle state estimation using closed-form liquid neural networks and nonlinear Kalman filtering

Accurate estimation of vehicle dynamic states is crucial for vehicle stability control and autonomous driving systems. However, critical states such as sideslip angle are difficult to measure directly using onboard sensors, especially under complex driving conditions and significant sensor noise. To address these issues, this paper proposes a hybrid vehicle state estimation framework, which integrates closed-form continuous-time (CfC) networks with an enhanced unscented Kalman filter (UKF). In the proposed framework, a CfC-based network is designed to process sequential IMU and GPS measurements and provide preliminary state predictions along with corresponding uncertainty estimates. These predictions of the network are then incorporated into a model-based UKF as pseudo-measurements, and the corresponding uncertainty is utilized to construct the measurement covariance. Furthermore, a data-driven sigma points sampling strategy is developed by exploiting the intrinsic multi-step predictive feature of CfC-models, enabling more accurate approximations of the local observation distribution. The proposed framework is first validated on both KITTI dataset and generated dataset using Carsim. Moreover, real-world experiments are conducted based on a test platform. Experimental results demonstrate that the proposed hybrid framework can simultaneously deal with unknown noise and achieve superior accuracy and robustness compared with learning-based and model-based baselines. We release the source code at https://github.com/HITXCI/w-state.