Estimation of ray arrival time delays for large-depth reception in the deep-sea direct-arrival zone using frequency cross-spectral matrix eigen decomposition

Based on the Multiple Signal Classification (MUSIC) algorithm, this paper proposes a method for estimating the multipath arrival time delays of acoustic rays in the deep‑sea direct‑arrival zone using eigen decomposition of the frequency cross‑spectral matrix. Based on ray theory, the expression of the frequency cross-spectrum matrix is derived. Eigen-decomposition is then performed on this matrix, yielding eigenvalues and eigenvectors that can be further partitioned into two mutually orthogonal subspaces. By exploiting the orthogonality between the subspace spanned by the steering vectors and the subspace spanned by the eigenvectors corresponding to the small eigenvalues, a spectral estimation formula with respect to range and time delay is established. The time delay is subsequently estimated by searching over the time delay domain to identify the range-delay pair that exhibits the strongest orthogonality. Theoretical analysis and simulation results demonstrate that the proposed method can accurately estimate the arrival time delays of the direct wave and the first sea-surface reflected wave. The accuracy of the estimation is influenced by the signal bandwidth, frequency step size, and signal-to-noise ratio. The method exhibits high tolerance to mismatches in the sound speed profile and geoacoustic parameters. Processing results from signals received by a hydrophone deployed at a depth of 4430 m during a deep-sea acoustic propagation experiment conducted in the Western Pacific in 2020 show that, although the estimated time delay of the first sea-surface reflected wave could not be obtained, the estimated time delay of the direct wave was successfully extracted and found to be in good agreement with theoretical calculations. Furthermore, the localization strategy for the motion state of the towed sound source, which combines the estimated time delays with a particle filtering algorithm, verifies the engineering applicability of the time‑delay estimation method presented in this paper.