Beamforming spatially spread signals with the Kent distribution

Beamforming of near-field sonar signals from sources with appreciable spatial extent is more difficult to perform than the case of far-field point sources. Earlier, a model was developed in which the beam response of an extended source is formulated as a convolution of the beampattern of a point source and a probability density function representing the spatial distribution of the real source about its center of mass angular coordinates. Because beamforming is performed in both azimuth and elevation, a form that best allows modeling of directional response properties should be chosen. The choice in the present analysis is the Kent distribution, a function of the angular deviations of the source elements from the center of mass and five parameters which incorporate apparent target spread, ellipticity and orientation. These, in turn, reflect the uncertainty associated with target distance, size and aspect angle. Results are presented for three-dimensional arrays.