Sharpness applied to the adaptive beamforming of acoustic data from a towed array of unknown shape

Abstract

When a vessel towing a horizontal line array of underwater acoustic sensors changes course, the array responds by changing its shape so that the sensors no longer lie along a straight line. However, the spatial processing of the acoustic data still proceeds on the assumption that the array is straight with the positions of the sensors being known and invariant. When the array adopts a nonlinear shape so that the actual locations of the sensors no longer coincide with the assumed positions, the performance of the beamformer is observed to deteriorate. This degradation is most marked when an adaptive beamformer is used to optimize the array gain. The adaptive beamformer considered here is a constrained optimum beamformer that is based on the inversion of the observed (signal-plus-noise) cross-spectral matrix of the sensor outputs. The adaptive beamformer responds to any deviation of the sensors from their nominal positions by suppressing the received signals so that the output signal-to-noise ratio of the beamformer, and hence the array gain, decrease in the direction of each signal. One method of overcoming the array shape problem is to monitor the geometrical configuration of the array’s sensors by instrumenting the length of the array with compasses and depth sensors. This paper examines an alternate method whereby data from the acoustic sensors themselves are used to infer the shape of the array. This narrow-band acoustic technique, which relies on at least one acoustic source being present in the far field, evaluates a sharpness function for a variety of possible array shapes. The sharpness is calculated by summing the product of the beam output power squared and the sine of the beamsteer angle over all beamsteer directions from forward endfire to aft endfire. Using simulated data, it is shown that the estimated array shape matches the actual shape when the sharpness attains its maximum value. Also shown is the dramatic reduction in signal suppression when this acoustic technique is applied to the adaptive beamforming of real acoustic data.