Depth Estimation Method for Continuous Acoustic Signal Targets in Shallow Water Using a Linear Array

To overcome the limitations of existing methods in processing continuous acoustic signals—particularly issues related to modal aliasing and the constraints of Pekeris waveguide applications—this study proposes a depth estimation approach for continuous acoustic targets using hydrophone linear arrays. A horizontal linear array, designed to meet the resolution requirements of the F–K transform, is deployed to receive continuous acoustic signals. Environmental parameters are incorporated to fit the sound speed profile, and modal time-delay differences are calculated based on normal mode propagation models. Temporal compensation is then applied to each modal component of the received signals across array elements. The corrected signal matrix undergoes a bidirectional F–K transform transformation into the frequency–wavenumber domain, allowing for clear separation of the normal modes of continuous signals. Frequency–wavenumber curves are characterised based on the sound speed profile, and binary mask filters are designed to extract modal energy. Finally, a depth estimation matching function is constructed to facilitate energy search and matching. Simulation results indicate that the proposed method achieves depth estimation errors of less than 5% for 10-s broadband acoustic signals under negative sound speed profiles and real shallow-sea waveguide conditions. The method demonstrates improved stability and applicability in variable sound speed environments, offering greater practical value for real-world shallow-sea scenarios.