February Fourier Talks 2008

A Method of Incorporating Finite Source Extent Into the Sonar Beamforming Process

Conventional beamforming methods are generally formulated in terms of far-field point sources, with emitted signals following a unidirectional path to a sensor array. This is not a valid assumption for sources with appreciable apparent spatial extent, such as close aboard targets in the near-field of a sonar array. In an effort to improve target localization and tracking, a model has been developed for incorporating the uncertainty associated with spatial target extent into the beamforming of signals received at an array of sensors. Assuming that the amplitudes of small volume elements of a distributed source are statistically independent, it is shown that the beam response may be expressed as a convolution of the beampattern of a point source and a "directivity factor" for the actual extended source. Equivalently, this may be thought of as an average of the beampattern weighted by a probability density function (PDF) representing the spatial distribution of the source about its center of mass angular coordinates. It is then straightforward to obtain the beam response using Fourier analysis. Results are derived theoretically for the general three dimensional array case, and then specialized to two and one dimensional arrays. Because signals may be beamformed in azimuth, as well as elevation, a PDF that best allows modeling of directional response properties is optimal. One such choice for volumetric and planar arrays is the Von Mises-Fisher distribution, a function of the angular deviations of the source elements from the center of mass and a parameter which incorporates the uncertainty associated with target distance, size and aspect angle. Multiparameter PDFs, such as the Fisher-Bingham distribution, will also be considered. Results will be presented for volumetric, planar and linear sonar arrays.