The passive estimation of harmonic sound source depth is of great significance for underwater target localization and identification. Passive source depth estimation using a single hydrophone with an unknown seabed geoacoustic property is a crucial challenge. To address this issue, a harmonic sound source depth estimation algorithm, seabed independent depth estimation (SIDE) algorithm, is proposed. This algorithm combines the estimated mode depth functions, modal amplitudes, and the sign of each modal to estimate the sound source depth. The performance of the SIDE algorithm is analyzed by simulations. Results show that the SIDE is insensitive to the initial range of the sound source, the source depth, the hydrophone depth, the source velocity, and the type of the seabed. Finally, the effectiveness of the SIDE algorithm is verified by the SWellEX-96 data.

To address the challenge of estimating the depth of a single-frequency (tonal) source using a vertical line array (VLA) without prior knowledge of seabed parameters, a method called OCMS-D (orthogonality-constrained modal search-based depth estimation) is presented. The method exploits the orthogonality of mode depth functions as a physical constraint and leverages the sparsity of propagating normal modes in the received field. A convex optimization model is formulated to jointly estimate modal wavenumbers, depth functions, and complex mode amplitudes. Furthermore, a depth-sign search (DSS) is introduced to compensate for mode phase signs, which effectively suppresses sidelobes in the depth ambiguity function and enables high-accuracy depth estimation. Numerical simulations analyze the influence of signal-to-noise ratio, array parameters and sound speed profile (SSP) uncertainty on the algorithm’s performance. Comparisons with matched-mode processing (MMP) show that OCMS-D exhibits superior robustness to SSP uncertainty and requires a smaller array aperture. Experimental data from the SWellEx-96 campaign demonstrate that the method achieves depth estimation errors of less than 5.4 m for the shallows and less than 10.8 m for the deep spurce. Notably, it requires neither seabed prior information nor source motion, offering a robust array signal processing framework for tonal source localization.