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This paper describes the application of an extended Kalman filter (EKF) combined with a per-unit (p.u.) system to the identification of suitable battery model parameters for the high-accuracy state-of-charge (SOC) estimation and state-of-health (SOH) prediction of a Li-Ion degraded battery. Variances in electrochemical characteristics among Li-Ion batteries caused by aging differences result in erroneous SOC estimation and SOH prediction when using the existing EKF algorithm. To apply the battery model parameters varied by the aging effect, based on the p.u. system, the absolute values of the parameters in the equivalent circuit model in addition to the discharging/charging voltage and current are converted into dimensionless values relative to a set of base value. The converted values are applied to dynamic and measurement models in the EKF algorithm. In particular, based on two methods such as direct current internal resistance measurement and the statistical analysis of voltage pattern, each diffusion resistance (RDiff) can be measured and used for offline and online SOC estimations, respectively. All SOC estimates are within ±5% of the values estimated by ampere-hour counting. Moreover, it is shown that RDiff is more sensitive than other model parameters under identical experimental conditions and, hence, implementable for SOH prediction.