A battery state estimator which combines an electrochemical solid-state concentration model with an empirical equivalent-circuit model. The battery state estimator uses a reduced-order physics-based electrochemical solid-state concentration model to calculate open circuit voltage of a battery cell, and uses the calculated open circuit voltage in an equivalent-circuit model to evaluate a diffusion voltage drop and other battery cell parameters. The battery state estimator is implemented in an online estimator framework using an extended Kalman filter, with a measured terminal voltage and measured current as inputs. A state of charge of the battery cell can be determined from the calculated open circuit voltage, and the state of charge along with the other parameters from the equivalent-circuit model are used to evaluate battery pack performance and to control battery pack charging and discharging.