A battery management system (BMS) ensures performance, safety and longevity of a battery energy storage system in an embedded environment. One important task for a BMS is to estimate the state of charge (SoC) and state of health (SoH) of a battery. The correlation between battery open circuit voltage (OCV) and SoC is an important reference for state estimation. The OCV-SoC correlation changes with respect to battery degradation. To improve the accuracy of state estimation, it is important to have the OCV-SoC correlation updated periodically. This work presents a solution by proposing a novel SoH(SoC) correlation as part of the battery equivalent circuit model (ECM). On-line optimization of SoH(SoC) correlation implicitly optimizes the OCV(SoC) correlation, as well as the capacity of a battery. An associated state and parameter dual estimator is proposed incorporating an Extended Kalman Filter (EKF) as a state observer, Recursive Least Square (RLS) algorithm as an internal resistance identifier, and Parameter Varying Approach as the SoH(SoC) correlation identifier. Battery experiment and simulation results validate that updating the SoH–SoC correlation effectively tracks battery SoH on-line. Furthermore, it implicitly updates OCV(SoC) function, further improving SoC estimation accuracy by 0.5%∼3%.