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