Error Analysis for Parameter Estimation of Li-ion Battery subject to System Uncertainties

Lithium-ion battery parameter estimation is a dynamic research field in which creative and novel algorithms are being developed to tune high-fidelity models for advanced control of energy systems. Amidst these efforts, little focus has been placed on the fundamental mechanisms associated with estimation accuracy, giving rise to the question, why is an estimate accurate or inaccurate? In response, we derive a generalized multivariate estimation error equation for the least-squares objective, which reveals that the error can be represented as the product of system uncertainties (i.e., in model, measurement, and parameter) and uncertainty-propagating sensitivity structures. We then relate the error equation to conventional error analysis criteria, such as parameter sensitivity, the Fisher information matrix, and the Cramér-Rao bound, to assess the benefits and limitations of each. Broadly, these criteria share the principal deficiency of neglecting estimation bias and system uncertainties, which are inevitable in practice. The error equation is validated through a series of experimental uni- and bivariate estimations of lithium-ion battery electrochemical parameters. These results are also analyzed using the error equation to study the composition of errors under various data sets. Finally, the bivariate analysis indicates that adding an additional target parameter to the estimation without increasing the amount of data intrinsically reduces the error robustness to the influence of system uncertainties.