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This article examines the problem of Lithium-Sulfur (Li-S) battery state estimation. Such estimation is important for the online management of this energy-dense chemistry. The literature uses equivalent circuit models (ECMs) for Li-S state estimation. This article's main goal is to perform estimation using a physics-based model instead. This approach is attractive because it furnishes online estimates of the masses of individual species in a given Li-S cell. The estimation is performed using an experimentally-validated, computationally tractable zero-dimensional model. Reformulation converts this model from differential algebraic equations (DAEs) to ordinary differential equations (ODEs), simplifying the estimation problem. The article's first contribution is to show that this model has poor observability, especially in the low plateau region, where the low sensitivity of cell voltage to precipitated sulfur mass complicates the estimation of this mass. The second contribution is to exploit mass conservation to derive a reduced-order model with attractive observability properties in both high and low plateau regions. The final contribution is to use an unscented Kalman filter (UKF) for estimating internal Li-S battery states, while taking constraints on species masses into account. Consistent with the article's observability analysis, the UKF achieves better low-plateau estimation accuracy when the reduced-order model is used.