Outlier-Robust Extended Kalman Filter for State-of-Charge Estimation of Lithium-Ion Batteries

Abstract

This study presents two outlier-robust extended Kalman filtering (OREKF) methods for battery-state estimation. The first method is the auto-tuning (AT)-OREKF method, and the second is the expectation-maximization (EM)-OREKF method. The AT-OREKF is an optimization-based adaptive EKF in which the parameters defining the prior and noise distributions are automatically learned using gradient-based methods. The EM-OREKF is a robust EKF that uses probabilistic inference, for which the expectation-maximization algorithm is applied to determine the hyperparameters of latent variables corresponding to outliers. An outlier is a data point or value that differs considerably from all or most of the other data in a dataset. AT-OREKF does not detect outliers, but adaptively tunes the parameters of optimization-based state estimation, known as moving horizon estimation, which implies that the resulting estimation can be vulnerable to dominant outliers. By contrast, EM-OREKF detects bad data in real-time using a variational EM algorithm to estimate the distribution of binary random variables, indicating outliers. To demonstrate the robustness of the proposed AT-OREKF and EM-OREKF methods, the Urban Dynamometer Driving Schedule was applied to the lithium-ion battery simulations in electric vehicle driving. The simulation results show 25.76% and 93.85% reductions in estimation errors upon applying the AT-OREKF and EM-OREKF, respectively, when compared with an ordinary EKF. The EM-OREKF shows better robustness to dominant outliers; however, the AT-OREKF can be used as an alternative because it is reliable in the presence of low outliers and requires less computation.

Keywords

• Estimation of the battery state
• robust estimation and outliers
• Kalman filtering
• expectation maximization
• adaptive estimation