Moving Source Depth Estimation Based on the Toeplitz Matrix Reconstruction

A Toeplitz matrix reconstruction-based method for source depth estimation is proposed. The sound pressure is treated as a superposition of coherent signals arriving from different angles. The synthetic array, created by the relative motion between a hydrophone and the source, is divided into overlapping subarrays. Hermitian Toeplitz matrices are constructed using the cross-correlation coefficient between the receive data of each element and that of the reference element. A high-resolution method is then applied to estimate the grazing angles of horizontal wavenumbers. Estimations of subarrays are integrated through majority voting, which leverages truth-value consistency to reduce noise interference. The estimated wavenumbers are extracted, grouped, and subsequently substituted into the depth ambiguity function to calculate source depth. The final depth estimation is refined through majority voting, further suppressing sidelobe interference. The proposed method does not require precise acoustic environmental information but relies on the nominal sound speed and bottom profile to calculate mode depth functions. Simulations and the Monte Carlo method are used for performance comparison, with the root-mean-square error as the evaluation metric. The effects of synthetic aperture and noise on estimation performance are numerically analyzed. The proposed method is validated using$\text{127}{}$and$\text{112}\,{\text{{Hz}}}$data from the SWellEx-96 experiment, with satisfactory results when the synthetic aperture is greater than or equal to$\text{2}\,{\text{{km}}}$.