Electrochemical properties of the battery are described in partial differential equations that are impossible to compute online. These internal states are spatially distributed and thus difficult to measure in the battery operation. A space-time separation method is applied to model the electrochemical properties of the battery with the help of the extended Kalman filter. The model is efficiently optimized by using LASSO adaptation method and can be updated through data-based learning. The analytical model derived is able to offer a fast estimation of internal states of the battery, and thus has potential to become a prediction model for battery management system.