A New Method for State of Charge Estimation of Lithium-Ion Batteries Using Square Root Cubature Kalman Filter

Abstract

State of charge (SOC) is a key parameter for lithium-ion battery management systems. The square root cubature Kalman filter (SRCKF) algorithm has been developed to estimate the SOC of batteries. SRCKF calculates 2n points that have the same weights according to cubature transform to approximate the mean of state variables. After these points are propagated by nonlinear functions, the mean and the variance of the capture can achieve third-order precision of the real values of the nonlinear functions. SRCKF directly propagates and updates the square root of the state covariance matrix in the form of Cholesky decomposition, guarantees the nonnegative quality of the covariance matrix, and avoids the divergence of the filter. Simulink models and the test bench of extended Kalman filter (EKF), Unscented Kalman filter (UKF), cubature Kalman filter (CKF) and SRCKF are built. Three experiments have been carried out to evaluate the performances of the proposed methods. The results of the comparison of accuracy, robustness, and convergence rate with EKF, UKF, CKF and SRCKF are presented. Compared with the traditional EKF, UKF and CKF algorithms, the SRCKF algorithm is found to yield better SOC estimation accuracy, higher robustness and better convergence rate.

Hyperbolic‐singular‐value‐decomposition‐based square‐root accurate continuous‐discrete extended‐unscented Kalman filters for estimating continuous‐time stochastic models with discrete measurements

“…We emphasize that all these fixed‐stepsize state estimators expose explicitly their quantities of the predefined numerical integration subdivision steps utilized in the experiments of Section 5.2 in their abbreviations. We pay a particular attention to the above‐listed ode45‐based EKF methods and CKF ones of various sorts because of their practical value in estimating lithium‐ion battery state of charge in electrical engineering . Note that the non‐square‐root continuous‐discrete and discrete‐discrete UKF‐type state estimators have been also examined but always failed because the covariance matrices computed by those filters lose their positive definiteness in our target tracking scenario with the increasingly ill‐conditioned measurement equation .…”

“…We pay a particular attention to the above-listed ode45-based EKF methods and CKF ones of various sorts because of their practical value in estimating lithium-ion battery state of charge in electrical engineering. 42,43 Note that the non-square-root continuous-discrete and discrete-discrete UKF-type state estimators 12,13,40,41 have been also examined but always failed because the covariance matrices computed by those filters lose their positive definiteness in our target tracking scenario with the increasingly ill-conditioned measurement equation (58).…”

State‐of‐charge estimation of power lithium‐ion batteries based on an embedded micro control unit using a square root cubature Kalman filter at various ambient temperatures

“…The state dimension determines the volume point and weight of the SRCKF and can be stored and calculated in advance. Therefore, the design and implementation of the SRCKF is simpler and can be performed smoothly by the on‐board embedded MCU …”

Online State of Charge and State of Health Estimation for a Lithium-Ion Battery Based on a Data–Model Fusion Method

“…Amongst others, the ECMs have a better trade-off between accuracy and complexity and thus are favorable candidates for application in micro-controller units. Generally, ECMs are used to simulate the dynamics of an LIB, while the states of interest are estimated in real time with various observers, such as the Luenberger observer [20], the extended Kalman filter (EKF) [21][22][23], the square root cubature Kalman filter [24], the unscented Kalman filter (UKF) [25], the sliding mode observer (SMO) [26], the particle filter (PF) [27], and the nonlinear observer [28]. For these methods, the ECMs are calibrated offline and the model parameters are assumed to be fixed during operation.…”