Target echo interference characteristic in the deep water: Modeling and application in depth estimation

For an active detection system in deep water, multipath propagation and target scattering induce complex coupling effects, challenging conventional methods reliant on multipath delay matching. To address the problem, this study has investigated the characteristics of the target echo interference observed on the two-dimensional (frequency and target range) intensity plane, focusing on depth estimation applications in the reliable acoustic path environment. We first establish a ray-based echo interference model integrated with highlight scattering, decomposing the intensity plane into propagation interference (related to target depth), scattering interference (linked to target size), and cross-term components. Second, an f-warping transformation is proposed to resample the intensity plane. By straightening the originally curved propagation interference, it ensures that the inverse Fourier transform of the warped intensity plane exhibits a constant time delay. Finally, a hybrid framework combines time-delay matching with multi-frame stability assessment, utilizing adaptive weighting to suppress scattering interference while preserving propagation-related features. Simulations and experimental data have been used to validate the depth estimation method, and the errors for multiple sets of experimental data are all under 8% of the real target depth.