Fusing line spectrum enhancement, physics-informed features, and data-driven models: Underwater weak acoustic source ranging using deep learning

Accurate ranging of underwater weak acoustic sources remains a critical challenge in complex marine environments due to severe acoustic energy attenuation, multipath interference, and strong ambient background noise. This work proposes an integrated framework combining line spectrum enhancement, conventional beamforming-based feature extraction, and data-driven learning for weak acoustic source ranging. Test datasets were collected from a 2025 sea trial, using a 24-element array with Global Positioning System-synchronized ground truth. After quality screening, 2584 valid samples were obtained from nine stations. For training, bellhop-based simulation was used, which involves seven key parameters, including the sound speed profile and sound source depth, with a maximum ranging distance of 13 km and 30 000 training samples generated. Comparative experiments against multipath matching of arrival angles, machine learning methods, a convolutional neural network (CNN), and Transformer achieves the best performance across all metrics [mean absolute error (MAE) = 477.09 m, root mean square error (RMSE) = 809.93 m, mean absolute percentage error (MAPE) = 8.90%]. Compared with CNN (MAE = 527.73 m, RMSE = 907.65 m, MAPE = 9.68%), the Transformer reduces RMSE, MAE, and MAPE by approximately 9.60%, 10.77%, and 8.06%, respectively. Experimental results and arrival angle perturbation tests verify the effectiveness of the presented framework in weak acoustic source ranging.