Near-field source localization using sparse recovery techniques

Near-field source localization is an important aspect in many diverse areas such as acoustics, seismology, to list a few. The planar wave assumption frequently used in far-field source localization is no longer valid when the sources are in the near field. Near-field sources can be localized by solving a joint direction-of-arrival and range estimation problem. The original near-field source localization problem is a multi-dimensional non-linear optimization problem which is computationally intractable. In this paper, we use a grid-based model and by further leveraging the sparsity, we can solve the aforementioned problem efficiently using any of the off-the-shelf l₁-norm optimization solvers. When multiple snapshots are available, we can also exploit the cross-correlations among the symmetric sensors of the array and further reduce the complexity by solving two sparse reconstruction problems of lower dimensions instead of a single sparse reconstruction problem of a higher dimension.