Depth estimation of weak narrowband sources using a hybrid interference-deep learning method

Interference-structure-based passive source localization provides computational efficiency and physical interpretability but suffers performance degradation for weak acoustic targets, where low signal-to-noise ratios (SNRs) obscure the observable interference patterns necessary for reliable depth estimation. Narrowband time-window limitations and environmental mismatches further introduce blind zones and nonlinear distortions between the source depth and the measured interference structure. To mitigate these effects, this study proposes a hybrid depth estimation method that integrates arrival-angle interference features with a deep learning (DL) framework based on a residual network. Sound intensity in the beam domain is employed to exploit multidimensional and nonlinear relationships in the acoustic field, thereby enhancing robustness under weak target and low SNR conditions. Simulation and sea experiment results demonstrate that the proposed method achieves improved depth estimation accuracy compared with conventional interference-based techniques. The findings indicate that the hybrid interference-DL approach effectively extends the applicability of interference-structure-based localization to weak acoustic targets.