Closed-form estimation of normal modes from a partially sampled water column

The output of a vertical linear array is used to infer about the parameters of the normal mode model that describes acoustic propagation in a shallow water. Existing subspace algorithms perform singular vector decomposition of the array data matrix to estimate the sampled model functions. Estimates are exact only if the sensing array is totally covering the water column. We design a new subspace algorithm free from this very restrictive requirement. We use two short hydrophone arrays and activate a monochromatic source at different depths. Estimates of both the modal functions and the wave numbers are obtained in a fully automatic and search-free manner. The algorithm can be qualified as truly high resolution in the sense that, while using short sensing arrays, estimation error becomes arbitrarily low if observation noise is arbitrarily low. This method compares advantageously to existing subspace techniques, as well as transform-domain techniques that require impulsive sources, among other constraints. With two (eigen and singular) vector decompositions, the proposed technique has the complexity of a regular subspace algorithm.