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This paper describes a novel adaptive battery model based on a remapped variant of the well-known Randles' lead-acid model. Remapping of the model is shown to allow improved modeling capabilities and accurate estimates of dynamic circuit parameters when used with subspace parameter-estimation techniques. The performance of the proposed methodology is demonstrated by application to batteries for an all-electric personal rapid transit vehicle from the urban light transport (ULTRA) program, which is designated for use at Heathrow Airport, U.K. The advantages of the proposed model over the Randles' circuit are demonstrated by comparisons with alternative observer/estimator techniques, such as the basic Utkin observer and the Kalman estimator. These techniques correctly identify and converge on voltages associated with the battery state-of-charge (SoC), despite erroneous initial conditions, thereby overcoming problems attributed to SoC drift (incurred by Coulomb-counting methods due to overcharging or ambient temperature fluctuations). Observation of these voltages, as well as online monitoring of the degradation of the estimated dynamic model parameters, allows battery aging (state-of-health) to also be assessed and, thereby, cell failure to be predicted. Due to the adaptive nature of the proposed algorithms, the techniques are suitable for applications over a wide range of operating environments, including large ambient temperature variations. Moreover, alternative battery topologies may also be accommodated by the automatic adjustment of the underlying state-space models used in both the parameter-estimation and observer/estimator stages.