High-resolution depth estimation for multiple wideband sources in deep sea via sparse Bayesian learning

Source depth estimation via the reliable acoustic path is critical for deep-sea surveillance. In this region, the time delay between direct and surface-reflected waves (D-SR time delay) from a wideband source causes the beamformer power output in its direction to oscillate with frequency, forming an interference structure. The oscillation frequency encodes the D-SR time delay, related to source depth. Conventional methods estimate it using the Fourier transform (FT). However, when multiple sources share similar horizontal ranges, they are angularly unresolvable and fall into the same beam, making the beamformer output a superposition of their interference structures. The FT struggles to resolve closely spaced D-SR time delays from this superposition due to limited resolution, especially under significant power disparities. To address this, this paper estimates the FT coefficients within a sparse Bayesian learning framework. A symmetric generalized-t distribution is developed for the coefficient vector, and variational Bayesian inference is employed for automated estimation. By jointly enforcing structural symmetry and sparsity, the proposed method achieves superior resolution, enabling accurate D-SR time delay separation and subsequent depth estimation. Simulation and experimental results demonstrate a nearly twofold resolution improvement over conventional methods, ensuring robust multi-source depth estimation even under large power disparities.