Source depth estimation using a small-aperture horizontal moving array

For the source depth estimation in shallow water, considering the normal mode theory which indicates the information of the depth that the depth information of the source and receiving hydrophones is contained in the modal energy distribution, an approach using a small-aperture horizontal moving array has been proposed. The normal mode model for the signals received by a horizontal moving array in the shallow water dynamic sound filed has been established and the real small aperture of array is expanded into a virtual large aperture using synthetic aperture algorithm. The sparse asymptotic minimum variance criterion was used to estimate the modal energy distribution. The negative index of Camberra distance was used to calculate the mode matched degree, which indicates the probability distribution of the source depth. Both simulations and experiments showed, based on the sound field structure of the normal mode theory wave model, the lower the source frequency, the smaller the synthetic aperture distance required to achieve estimate the source depth estimation. When the sound source is at a certain angle from the end-fire direction of the array, the effect on the required synthetic aperture is the same as that when the relative velocity changes. In a typical shallow-sea stratified waveguide, when the signal-to-noise ratio is 10 dB, the depth of the 200 Hz and 350 Hz sound sources is accurately estimated, and the synthetic aperture is required to be greater 12 times and 16 times the depth of the waveguide, respectively. © 2021 Acta Acustica.