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Source depth estimation is an important yet very difficult task for passive sonars, especially for horizontal linear arrays (HLAs). This paper proposes an efficient two-step depth estimation scheme using narrowband and broadband constructive and deconstructive striation patterns due to interference between the direct (D) and sea surface reflected (SR) arrivals at an HLA on the bottom of deep water. First, the horizontal source-array ranges are derived from triangulation results of solid angle estimates by subarray beamforming. The applicable areas of the method in deep water are investigated through Mento Carlo simulations, assuming different subarray partitioning ways of a given HLA aperture. Second, cost functions are built to match the measured beam intensity striations with modeled ones. To mitigate the spatial smoothing effect of the beam intensity striations during beamforming, a criterion of the largest subarray aperture is established, and a computationally efficient way is presented to model the replicas by the D-SR time delay templates at a single element of the array calculated by ray theory. The performance degradation due to limited source range spans, the distortion of the beam intensity striations, and range estimation errors has been analyzed. Two experimental datasets verify the effectiveness of the proposed method.
Wu et al. (2023) studied this question.