Deep neural networks (DNNs) are advantageous for representing complex nonlinear relationships. This paper applies DNNs to source localization in a shallow water environment. Two methods are proposed to estimate the range and depth of a broadband source through different neural network architectures. The first adopts the classical two-stage scheme, in which feature extraction and DNN analysis are independent steps. The eigenvectors associated with the modal signal space are extracted as the input feature. Then, the time delay neural network is exploited to model the long term feature representation and constructs the regression model. The second concerns a convolutional neural network-feed-forward neural network (CNN-FNN) architecture, which trains the network directly by taking the raw multi-channel waveforms as input. The CNNs are expected to perform spatial filtering for multi-channel signals, in an operation analogous to time domain filters. The outputs of CNNs are summed as the input to FNN. Several experiments are conducted on the simulated and experimental data to evaluate the performance of the proposed methods. The results demonstrate that DNNs are effective for source localization in complex and varied water environments, especially when there is little precise environmental information.

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Horizontal samples of a point source in a shallow water waveguide are processed by the Prony method. First, when the source position is known, a high resolution estimation of the normal mode parameter Km (the horizontal component of mode wavenumber) can be obtained. Owing to the weak damping process, βm, the modal attenuation coefficient, can be obtained by using a modified Prony method. In this article, an ‘‘interval average and iterative’’ approach is proposed. Numerical examples illustrate that a 10−4 resolution of Km (150-Hz frequency) is provided by a 500-m data length, roughly an order of magnitude smaller than the data length required by the linear spectrum analysis technique. Second, when the source position is unknown but the waveguide characters (Km, βm) are known, the same procedure can be used for source position estimation. Some numerical examples in typical shallow water are presented.

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