Optimal calibration of Kalman filters for state of charge estimation of lithium-ion cells

State Of Charge (SOC) estimation of lithium-ion cells is one of the core functionalities of any Battery Management System (BMS), the majority of which employ model-based algorithms such as the Unscented Kalman Filter (UKF). Equivalent-Circuit Models (ECMs) are commonly used in KF schemes due to their reasonable SOC estimation accuracy at a moderate computational cost. Kalman filters also require tuning the process and measurement noise covariances, which greatly affect the state of charge estimation performance and can lead to filter divergence if tuned incorrectly. To account for this, the noise covariances are typically calibrated through trial-and-error and updated automatically from data using an adaptive law that compensates for a poor tuning, giving rise to the Adaptive Unscented Kalman Filter (AUKF). This paper aims to overtake the trial-and-error methodology and avoid the adaptive law entirely via a novel UKF design strategy that tackles two objectives: (i) SOC estimation accuracy, addressed by an optimal data-driven calibration procedure that maximizes the performance regardless of the KF initialization and working conditions, and (ii) computational efficiency, achieved by an ad hoc, BMS-oriented, model reduction strategy for ECMs. The performance of the proposed UKF design strategy is extensively validated on real lithium-ion cell data, comparing it to the state-of-the-art AUKF paradigm. Results show that the optimally-tuned UKF based on the reduced-order model can be more accurate than the AUKF calibrated via trial-and-error and equipped with the full-order model while also being computationally lighter, insensitive to initial conditions, and robust to model mismatch.