  Key challenges in developing underwater acoustic localization methods are
related to the combined effects of high reverberation in intricate
environments. To address such challenges, recent studies have shown that with a
properly designed architecture, neural networks can lead to unprecedented
localization capabilities and enhanced accuracy. However, the robustness of
such methods to environmental mismatch is typically hard to characterize, and
is usually assessed only empirically. In this work, we consider the recently
proposed data-driven method [19] based on a deep convolutional neural network,
and demonstrate that it can learn to localize in complex and mismatched
environments. To explain this robustness, we provide an upper bound on the
localization mean squared error (MSE) in the ``true" environment, in terms of
the MSE in a ``presumed" environment and an additional penalty term related to
the environmental discrepancy. Our theoretical results are corroborated via
simulation results in a rich, highly reverberant, and mismatch channel.
