  Direct localization (DLOC) methods, which use the observed data to localize a
source at an unknown position in a one-step procedure, generally outperform
their indirect two-step counterparts (e.g., using time-difference of arrivals).
However, underwater acoustic DLOC methods require prior knowledge of the
environment, and are computationally costly, hence slow. We propose, what is to
the best of our knowledge, the first data-driven DLOC method. Inspired by
classical and contemporary optimal model-based DLOC solutions, and leveraging
the capabilities of convolutional neural networks (CNNs), we devise a holistic
CNN-based solution. Our method includes a specifically-tailored input
structure, architecture, loss function, and a progressive training procedure,
which are of independent interest in the broader context of machine learning.
We demonstrate that our method outperforms attractive alternatives, and
asymptotically matches the performance of an oracle optimal model-based
solution.
