An off-grid DOA estimation method for the underwater target via the group sparse way

Abstract

Direction-of-arrival (DOA) estimation is a key research topic in hydroacoustic engineering. In recent years, sparse DOA estimation methods, grounded in compressed sensing theory, have attracted widespread attention. These methods typically discretize the angular domain into a uniform grid, with each grid point representing a potential bearing. By assuming that the source lies on one of the predefined grid points, the DOA estimation problem can be formulated as a sparse recovery problem. However, in practical underwater environments, the probability that a source precisely coincides with a grid point is nearly zero. This off-grid effect introduces a grid mismatch problem, which can lead to non-sparse solutions or large estimation errors. To address this issue, off-grid sparse models have been developed. Most existing approaches introduce a perturbation variable into the sparse model to approximate the displacement between the actual source and its nearest grid point. While effective to some extent, these methods often suffer from significantly increased computational complexity. Moreover, they usually rely on the theoretical assumption that the source displacement is infinitesimally small, which limits their estimation performance in real scenarios. To overcome these limitations, this paper proposes a novel off-grid DOA estimation method based on a group sparse model (GSODE). An enhanced group sparse coding framework, solved efficiently via the fast iterative shrinkage-thresholding algorithm (FISTA), is developed to globally optimize the model. Extensive simulations and experimental validations, including the well-known SwellEx-96 sea trial, demonstrate that the proposed method consistently outperforms conventional DOA estimation approaches as well as the state-of-the-art off-grid root sparse Bayesian learning (OGRSBL).