This is a preprint of a manuscript submitted for publication.

Good state of charge estimation in lithium-sulfur batteries (Li-S) is vital, as the simplest convention methods commonly used in lithium-ion batteries - open-circuit voltage measurement and 'coulomb counting' - are often ineffective for Li-S. Since Li-S is a new battery chemistry, there are few published techniques. Existing techniques based on the extended Kalman filter and the unscented Kalman filter have shown some promise, existing work has explored only one of many possible estimator architectures: a single filter based on a pre-calibrated behavioural reparameterization of an equivalent circuit network whose parameters vary as a function of state of charge and temperature. Such filters have been shown to be reasonably effective in practical cases, but they can converge slowly if initial conditions are unknown, and they can become inaccurate with changes in current density. It is desirable to understand whether other possible estimator architectures offer improved performance. One such alternative architecture is the 'dual extended Kalman filter', which uses voltage and current measurements to estimate into a short-term dynamic circuit parameters then uses the outputs of this in a slower-acting state-of-charge estimator. This paper develops a `behavioural' form of the dual extended Kalman filter, and applies this to a lithium-sulfur battery. The estimator is adapted with a term to model circuit current dependence, and demonstrated using pulse-discharge tests and scaled automotive driving cycles and more for partially discharged batteries. Compared to the published state-of-the-art, the new estimators can be almost 30% for batteries that are initially partially discharged; the new estimators also converge faster. The resulting estimators have the potential to be extended to state-of-health measures, and the 'behavioural' circuit reparameterization is likely to be of use for other battery chemistries beside lithium-sulfur..