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Real-time electrochemical state information of lithium-ion batteries attributes to a high-fidelity estimation of state-of-charge (SOC) and state-of-health (SOH) in advanced battery management systems. However, the consumption of recyclable lithium ions, loss of the active materials, and the interior resistance increase resulted from the irreversible side reactions cause severe battery performance decay. To maintain accurate battery state estimation over time, a scheme using the reduced-order electrochemical model and the dual nonlinear filters is presented in this article for the reliable co-estimations of cell SOC and SOH. Specifically, the full-order pseudo-two-dimensional model is first simplified with Padé approximation while ensuring precision and observability. Next, the feasibility and performance of SOC estimator are revealed by accessing unmeasurable physical variables, such as the surface and bulk solid-phase concentration. To well reflect battery degradation, three key aging factors including the loss of lithium ions, loss of active materials, and resistance increment, are simultaneously identified, leading to an appreciable precision improvement of SOC estimation online particular for aged cells. Finally, extensive verification experiments are carried out over the cell's lifespan. The results demonstrate the performance of the proposed SOC/SOH co-estimation scheme. [ABSTRACT FROM AUTHOR]