This article examines the problem of identifying the physical parameters of fundamental electrochemistry-based battery models from non-invasive voltage/current cycling tests. The article is particularly motivated by the problem of fitting the Doyle–Fuller–Newman (DFN) battery model to lithium-ion battery cycling data. Previous research in the literature identifies subsets of the DFN model's parameter experimentally. In contrast, this article makes the two unique contributions of: (i) identifying the full set of DFN model parameters from cycling data using a genetic algorithm (GA), and (ii) assessing the accuracy and identifiability of the resulting full parameter set using Fisher information. The specific battery used within this study has lithium iron phosphate cathode chemistry and is intended for high-power applications such as plug-in hybrid electric vehicles (PHEVs). We use seven experimental cycling data sets for model fitting and validation, six of them derived from PHEV drive cycles. This makes the identified parameter values appropriate for PHEV battery simulation and model-based design and control optimization.