An approach to array element localization using a far-field source
Craig S. MacInnes, David Paul Knobles · The Journal of the Acoustical Society of America · 2001
An approach is introduced for the towed array element localization problem. The method uses a dominant acoustic far-field source to obtain the true array shape. Constraints are introduced that significantly reduce the dimensionality of the problem. The array shape is expanded in terms of Chebyshev type II polynomials. The array elements are constrained to be in sequential order, and the arc length between elements is conserved as the array transforms from a straight to a curved configuration. A simulated annealing (SA) algorithm is used to find the expansion coefficients that minimize the inverse of the magnitude of the plane-wave beamformer response evaluated at the bearing to the source. The minimum of the cost function is obtained when the array elements are in their correct positions. Simulated studies are made for several array shapes. In all cases examined the expansion method with SA is able to find an accurate solution, independent of the initial array configuration. The analysis suggests that the use of broadband as opposed to single-frequency cost functions has the effect of reducing the number of local minima in the cost function that have values near the global minimum. [Research supported by the U.S. Navy.]