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wavelengths per unit distance in the direction of propaga- tion.) A conventional delay-and-sum beamformer, where the weights are set to unity, is optimal in the sense that the output signal-to-noise ratio is a maximum for an incoherent noise field. However, when the noise field includes coher- ent sources (such as interference), then an adaptive beam- former that is able to maximize the output signal-to-noise ratio by applying a set of weights that are complex numbers is implemented. This has the effect of steering a null in the direction of any unwanted interference (a jammer).
Figure 1 shows a comparison of the frequency-wave num- ber spectrum for an actual underwater acoustic field sensed by an array using the conventional weight vector (left) and an adaptive weight vector (right). The adaptive beamformer suppresses the side lobes and resolves the various contribu- tions to the acoustic pressure field, which are shown as surfac- es (ridges) associated with towed array self-noise (structural waves that propagate along the array in both axial directions, i.e., aft and forward); tow-vessel radiated noise observed at, and near, the forward end-fire direction (i.e., the direction of the longitudinal axis of the array) for the respective direct propagation path and the indirect (surface-reflected) mul- tipath; and three surface ship contacts. The adaptive beam- former better delineates the various signal and noise sources that compose this underwater sound field (Ferguson, 1998).
Towed-Array Shape Estimation
When deep, submarines rely exclusively on their passive so- nar systems to sense the underwater sound field for radiated noise from ships underway and antisubmarine active sonar transmissions. The long-range search sonar on a submarine consists of a thin flexible neutrally buoyant streamer fitted with a line array of hydrophones, which is towed behind the submarine. Towed arrays overcome two problems that limit the performance of hull-mounted arrays: the noise of the submarine picked up by the sensors mounted on the hull and the size of the acoustic aperture being constrained by the limited length of the submarine.
Unfortunately, submarines cannot travel in a straight line forever to keep the towed array straight, so the submarine is “deaf ” when it undertakes a maneuver to solve the left-right ambiguity problem or to estimate the range of a contact by triangulation. Once the array is no longer straight but bowed, sonar contact is lost (Figure 2).
Rather than instrumenting the length of the array with head- ing sensors (compasses) to solve this problem, the idea was
Figure 1. Left: estimated frequency-wave number power spectrum for a line array of hydrophones using the conventional frequency-do- main beamforming method. The maximum frequency corresponds to twice the design frequency of the array. Right: similar to the left hand side but for an adaptive beamformer. From Ferguson (1998).
Figure 2. Left: a towed array is straight before the submarine maneu- ver, but it is bowed during the maneuver. Right: variation with bear- ing and time of the output of the beamformer before, during, and after the change of heading of the submarine. The total observation period is 20 minutes, and the data are real. When the array is straight, the contact appears on one bearing before the maneuver and on another bearing after the maneuver when the submarine is on its new head- ing and the array becomes straight again. Estimating the array shape (or the coordinates of the sensor positions in two dimensions) during the heading changes enables contact to be maintained throughout the submarine maneuver. From Ferguson (1993a).
to reprocess the hydrophone data so that the shape of the array could be estimated at each instant during a submarine maneuver when the submarine changes course so that it can head in another direction (Ferguson, 1990). The estimated shape had to be right because a nonconventional (or adap- tive) beamformer was used to process the at-sea data. Uncer- tain knowledge of the sensor positions results in the signal being suppressed and the contact being lost. The outcome is that submariners maintain their situational awareness at all times, even during turns.
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