Batteries are complex systems involving spatially distributed microscopic mechanisms on different time scales whose adequate interplay is essential to ensure a desired functioning. Describing these phenomena yields nonlinearly coupled partial differential equations whose numerical solution requires considerable effort and computation time, making it an infeasible solution for real-time applications. Anyway, having information about the internal electrochemical states of the battery can pave the way for many different advanced monitoring and control strategies with a big potential for improving efficiency and longevity. For such purposes, in the present paper, a combination of a low-order representation of the essential dynamics associated to the internal electrochemical mechanisms based on Dynamic Mode Decomposition for control (DMDc) is proposed to obtain an improved equivalent circuit model (ECM) representation with continuously updated parameters and combined with an extended Kalman Filter (EKF). The model-order reduction step extensively exploits the model structure, yielding a well structured low-order representation without artificial numerical correlations. The performance of the proposed method is illustrated with numerical simulations based on a well-established reference model, showing its potential usefulness in real-time applications requiring knowledge of the internal electrochemical states besides the state-of-charge.