Estimating launch and reception angles with a single source and a vertical receiver array

A practical adaptation of double beamforming is introduced for scenarios where only a vertical receiver array (VRA) and an unknown broadband source—such as a passing ship—are available. Unlike the conventional configuration requiring two vertical arrays to directly construct a matrix of Green's functions, this approach forms the matrix by extrapolating a Green's function between the source and the VRA to neighboring ranges using waveguide invariant theory. The required Green's function is first estimated via blind deconvolution. Experimental validation using broadband noise (200–900 Hz) from a ship of opportunity in shallow water confirms the method's effectiveness, with estimated launch and reception angles closely matching model-based eigenray predictions and errors less than 1°.