Modal shading coefficients for high-resolution source depth localization

Abstract

In this article the minimum variance principle is applied to the modal shading coefficients to improve source depth localization. It is shown that for a long, well-populated vertical array, the source depth localization function based on the minimum variance principle is approximately the same as the depth function based on normal mode theory. For a limited aperture vertical array, the modes are spatially undersampled. In this case, the modal shading coefficients based on the minimum variance principle are shown to significantly improve the depth resolution assuming sufficient signal-to-noise ratio. But, as the signal-to-noise ratio decreases, the depth resolution for the minimum variance case approaches the (conventional) modal beamformer result.