The horizontal wavenumbers and modal depth functions are estimated by block sparse Bayesian learning (BSBL) for broadband signals received by a vertical line array in shallow-water waveguides. The dictionary matrix consists of multi-frequency modal depth functions derived from shooting methods given a large set of hypothetical horizontal wavenumbers. The dispersion relation for multi-frequency horizontal wavenumbers is also taken into account to generate the dictionary. In this dictionary, only a few of the entries are used to describe the pressure field. These entries represent the modal depth functions and associated wavenumbers. With the constraint of block sparsity, the BSBL approach is shown to retrieve the horizontal wavenumbers and corresponding modal depth functions with high precision, while a priori knowledge of sea bottom, moving source, and source locations is not needed. The performance is demonstrated by simulations and experimental data.
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