Robust hybrid Neural–Kalman filter for real-time supercapacitor state-of-charge estimation in electric vehicles

Accurate estimation of supercapacitor state of charge (SOC) is vital for optimal energy management in electric vehicles (EVs), particularly within hybrid energy storage systems (HESS). Challenges arise from nonlinear dynamics, self-discharge, temperature sensitivity, and aging-induced parameter drift. This study introduces KalmanNet, a neural network-enhanced Kalman filter, for supercapacitor SOC estimation. The approach integrates a three-branch equivalent circuit model with a data-driven Kalman gain learner trained solely on voltage and current measurements, without requiring synthetic Kalman gain ground truth. KalmanNet adapts dynamically to system uncertainties while preserving the recursive nature of traditional Kalman filters. Validation using experimental data from commercial supercapacitors under standard EV driving cycles, aging effects, disturbances, and computational load demonstrates its effectiveness. KalmanNet achieves a root mean square error (RMSE) of 0.35%, outperforming the Extended Kalman Filter (2%), Sigma-Point/Unscented Kalman Filters (1.1%), Particle Filters (0.8%), and Recurrent Neural Networks (2.2%). Processor-in-the-loop (PIL) tests confirm real-time feasibility with execution times well below task periods and CPU usage under 0.1%. The results demonstrate KalmanNet’s superior accuracy, robustness, and computational efficiency for real-time EV applications. • First application of KalmanNet for supercapacitor state of charge estimation, combining neural Kalman gain learning with a three-branch equivalent circuit model. • Training framework relies solely on voltage and current measurements, eliminating the need for Kalman gain ground truth. • Extensive validation using experimental data on commercial supercapacitors under electric vehicle driving cycles, aging effects, disturbances, noise, and computational load. • Benchmarking against extended Kalman filter, sigma-point Kalman filter/unscented Kalman filter, particle filter, and recurrent neural networks within a unified model and testing framework to address gaps in existing studies. • Real-time implementation verified via processor-in-the-loop testing on embedded hardware, showing low execution time and CPU usage.