A state of charge (SoC) a lithium-ion (Li+) battery is estimated at a time instant by first constructing a battery model of the Li+ battery based on a single particle operation. The battery model describes a relationship between the SoC, a charge current, a discharge current, and an output voltage of the Li+ battery. Using a nonlinear optimization, a function expressing a relationship between the SoC and an open circuit voltage of the Li+ battery is determined. The relationship is based on off-line measurements of the charge current, the discharge current, and the open-circuit voltage of the Li+ battery. Then, the SoC and parameters of the battery model are estimated concurrently, wherein the SoC and the parameters are estimated based on the battery model, the function, and on-line measurements of the charge current, the discharge current, and the output voltage.