Analytic Bound on Accuracy of Battery State and Parameter Estimation

Methods for battery state and parameter estimation have been widely investigated, while the achievable accuracy of the estimation remains a critical but somehow overlooked topic. In this paper, the analytic bounds on the accuracy of battery state and parameter estimation accounting for voltage measurement noises are derived based on the Fisher information matrix and Cramer-Rao bound analysis. The state and parameters under discussion include the state of charge, capacity and (ohmic) resistance. The estimation accuracy is influenced by the information contained in the data set used for estimation. It is found that the main contributing factors to the accuracy of SOC estimation are the slope of the OCV curve and number of data points, while the accuracy of capacity estimation is affected by both OCV slope and SOC variation, and that of resistance estimation depends heavily on the current magnitude. The analytic bounds are derived for both standalone estimation, where only one state/parameter is estimated, and combined estimation where they are estimated together. The loss of accuracy in combined estimation compared to standalone estimation is usually expected. However, when the current excitation satisfies certain patterns, such loss can be avoided. The conclusions can be used as guidelines for offline experiment design as well as online evaluation of the accuracy of adaptive state and parameter estimation.