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Estimation of the acoustic wave numbers presents great interests in shallow environments. They provide relevant material to infer the sediment parameters. Using a horizontal array,the wavenumbers are obtained with usual spectral estimation methods in the spatial dimension. The computation of the wavenumber spectra at several frequencies leads to a frequency wave number (f−k) diagram,which is appropriate for the characterization of dispersive propagations. In this paper,a Compressed Sensing (CS) method is proposed to improve the separation of the wavenumbers. The CS approach is particularly relevant since only few modes are propagating. However,at higher frequencies the number of propagating mode increases and the wavenumber separation becomes more difficult,especially when using short arrays. This paper introduces a wideband particle filtering (PF) algorithm for the wavenumber tracking. It takes advantage of the dispersion relation which is true in every waveguides. The consecutive use of CS and PF allows computing the f-k representation for array measurements that does not respect the usual requirements of array length. An application on the 32 sensor SHARK array of the SW06 campaign illustrates the whole methodology.

In underwater acoustics, shallow-water environments act as modal dispersive waveguides when considering low-frequency sources, and propagation can be described by modal theory. In this context, propagated signals are composed of few modal components, each of them propagating according to its own wavenumber. Frequency-wavenumber $(f-k)$ representations are classical methods allowing modal separation. However, they require large horizontal line sensor arrays aligned with the source. In this paper, to reduce the number of sensors, a sparse model is proposed and combined with prior knowledge on the wavenumber physics. The method resorts to a state-of-the-art Bayesian algorithm exploiting a Bernoulli–Gaussian model. The latter, well suited to the sparse representations, makes possible a natural integration of prior information through a wise choice of the Bernoulli parameters. The performance of the method is quantified on simulated data and finally assessed through a successful application on real data.