Direct position determination of multi-tone acoustic signals using off-grid sparse Bayesian learning in the underwater environment.

High-precision target localization is crucial for underwater surveillance, while existing direct position determination algorithms suffer from limited positioning accuracy due to the use of a fixed grid and the pseudo-target interference at beam intersections. This paper proposes an off-grid sparse Bayesian learning-based direct position determination (DPD-offGSBL) algorithm tailored for commonly used multi-tone acoustic signals, capable of handling coherent, incoherent, and mixed signals. Specifically, a unified frequency-domain data model is established, accommodating both coherent and incoherent signals. Then, an off-grid sparse signal representation for multiple frequencies is formulated and we explore the joint sparsity among arrays to enhance the suppression of pseudo-targets. Furthermore, we derive the Cramér-Rao bound (CRB) for multi-tone signal localization as a theoretical benchmark. Numerical simulations demonstrate that DPD-offGSBL outperforms the counterparts in positioning accuracy and multi-target resolution, and approaches the CRB under various scenarios. Results of SWellEx-96 Experiment Event S5 confirm the practical applicability of DPD-offGSBL for single underwater acoustic source localization.