When a thin flexible line array of hydrophones is towed through the sea, the straightness of the array can be affected by transverse motions of the tow vessel, by ocean swells and currents, and by motion-induced hydrodynamic forces acting on the array. Traditionally, the spatial processing of the data from the hydrophones proceeds on the assumption that the array is always straight. The spatial processor considered here is a constrained optimal (adaptive) beamformer based on inversion of the observed (signal-plus-noise) cross-spectral matrix of the hydrophone outputs. When the actual positions of the hydrophones deviate from their assumed positions, the adaptive beamformer responds by suppressing the received signals, resulting in a decrease in the output signal-to-noise ratio of the beamformer. Two methods of overcoming the signal suppression problem are compared and results are presented both for simulated data and for real data collected from an experimental towed array as the tow vessel changed course. Both methods infer the spatial distribution of the hydrophones along the array and require at least one acoustic source to be present in the far field. One method is an optimization technique where a cost function, known as sharpness, is calculated by integrating the product of the beam output power squared and the sine of the beamsteer angle over all beamsteer angles from forward endfire to aft endfire. When the estimated positions of the hydrophones coincide with the actual positions, the sharpness is a maximum. The other method uses the eigenvector corresponding to the largest eigenvalue of the cross-spectral matrix to extract the phase of the signal at each of the hydrophones and then, after assigning a direction to the source of the signal, uses the relative phase information to estimate the positions of the hydrophones along the array. Both techniques use only data from the hydrophones themselves to estimate the shape of the array and do not require data from additional nonacoustic sensors such as compasses and depth sensors.
