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This paper presents a novel framework for state-of-charge estimation ofrechargeable batteries in electric vehicles using a two-stage nonlinearestimator called the eXogenous Kalman filter (XKF). The nonlinear estimatorconsists of a cascade of nonlinear observer (NLO) and linearized Kalman filter(LKF). The NLO is used to produce a globally convergent auxiliary stateestimate that is used to generate a linearized model in the time-varying Kalmanfilter algorithm. To demonstrate the proposed approach, we present a model of alithium-ion battery from an equivalent circuit model (ECM). The model haslinear process equations and a nonlinear output voltage equation. The method istested using experimental data of a lithium iron phosphate (LiFePO$_4$) batteryunder dynamic stress test (DST) and federal urban driving schedule (FUDS).Effect on different ambient temperatures is also discussed. Compared with EKFand UKF, our proposed XKF achieve faster convergence rate, which can beattributed to the use of the NLO.

eXogenous Kalman Filter for Lithium-Ion Batteries State-of-Charge Estimation in Electric Vehicles