Near-field source localization: Sparse recovery techniques and grid matching

Near-field source localization is a joint direction-of-arrival (DOA) and range estimation problem. Leveraging the sparsity of the spatial spectrum, and gridding along the DOA and range domain, the near-field source localization problem can be casted as a linear sparse regression problem. However, this would result in a very large dictionary. Using the Fresnel-approximation, the DOA and range naturally decouple in the correlation domain. This allows us to solve two inverse problems of a smaller dimension instead of one higher dimensional problem. Furthermore, the sources need not be exactly on the predefined sampling grid. We use a mismatch model to cope with such off-grid sources and present estimators for grid matching.