  Underwater acoustic localization has traditionally been challenging due to
the presence of unknown environmental structure and dynamic conditions. The
problem is richer still when such structure includes occlusion, which causes
the loss of line-of-sight (LOS) between the acoustic source and the receivers,
on which many of the existing localization algorithms rely. We develop a
semi-blind passive localization method capable of accurately estimating the
source's position even in the possible absence of LOS between the source and
all receivers. Based on typically-available prior knowledge of the water
surface and bottom, we derive a closed-form expression for the optimal
estimator under a multi-ray propagation model, which is suitable for
shallow-water environments and high-frequency signals. By exploiting a
computationally efficient form of this estimator, our methodology makes
comparatively high-resolution localization feasible. We also derive the
Cram\'er-Rao bound for this model, which can be used to guide the placement of
collections of receivers so as to optimize localization accuracy. The method
improves a balance of accuracy and robustness to environmental model mismatch,
relative to existing localization methods that are useful in similar settings.
The method is validated with simulations and water tank experiments.
