The effects of array shape perturbation on beamforming and passive ranging

The problem of beam formation from a towed line array whose shape has been distorted is considered. Emphasis is placed on the beam broadening and range estimation effects of array shape perturbations and how the resulting losses can be regained if the actual element positions are known. Specific illustrations are provided for various levels of shape distortion. For example, a 15-m bow in a 232.5-m-long array broadens the beamwidth by a factor of 3 at 50 Hz. As another example, a 6-m bow in an 800-m-long array leads to a 20-pereent range underestimation at 10 km for a 100-500-Hz broadband source.