# Theoretical bounds on the accuracy of state and parameter estimation for batteries

**2017 American Control Conference, ACC 2017, Seattle, United States, 24-26 May 2017**(0743-1619). p. 4035-4041. (2017)

[Konferensbidrag, refereegranskat]

Today it is standard to use equivalent circuit models to describe the dynamic behavior of Li-ion vehicle batteries. The parameters and states change with operating point and are therefore continuously estimated using bayesian observers, though without knowing to what degree the performance can be improved. Posterior Cramér-Rao Lower Bounds (CRLBs) can be used to theoretically quantify the optimal accuracy of bayesian estimators. In this paper we apply this to a second-order nonlinear equivalent-circuit model of a lithium-ion battery. It is shown, by numerical calculations, how the posterior Cramér-Rao Lower Bounds depend on the amplitude and frequency of the current, and on the slope of the Open Circuit Voltage (OCV) curve. Furthermore, it is investigated how much the accuracy is reduced in combined estimation of the states and the resistance compared to when the resistance is perfectly known. More importantly, it is also shown that the Mean Square Errors (MSE) of an Extended Kalman Filter (EKF) are close to the posterior CRLBs, which means that, under the investigated circumstances, it is not possible to significantly reduce the MSEs by replacing the EKF by any other observer.

**Nyckelord: **Circuit simulation, Circuit theory, Electric batteries, Equivalent circuits, Extended Kalman filters, Kalman filters, Lithium-ion batteries, Mean square error, Open circuit voltage, Secondary batteries, Bayesian estimators, Dynamic behaviors, Equivalent circuit model, Nonlinear equivalent circuit, Numerical calculation, Optimal accuracy, State and parameter estimations, Theoretical bounds, Parameter estimation

Denna post skapades 2017-08-30.

CPL Pubid: 251502