Page 14 - Acoustics Today Summer 2011

Fig. 4. Ferry and Remus tracks.
to source localization and tracking. It has also been success-
fully employed in geoacoustic inversion,24,28,29 tracking of
internal wave fields,30 tracking of frequencies in time-fre-
quency representations,23 and spatial arrival tracking across
26
Applications
Towed array processing
One novel application of MBP in ocean acoustics is its use as a processor for a short towed array. Because a towed array is a moving sensor, it naturally incurs Doppler in the received signal. Here, MBP is a means of exploiting the bear- ing information in the Doppler.
A simple example of this can be seen from the following.
Suppose a narrow-band plane wave signal of radian frequency
Fig. 5. Results for the random walk case.
itive implying up-Doppler. The relation between ω and ω0 is given by the following well known expression:
Here, c is the speed of sound in the water. It is clear then, that if one has knowledge of the source frequency, the bear- ing can be estimated. Passive synthetic aperture bearing esti- mation exploits this idea by casting the problem as joint esti- mation of the source frequency and the bearing angle.
Although the signal in this example is narrowband, the same approach can be used in the broadband case. More information on passive synthetic aperture and its history is available.31,32 (The term “synthetic aperture” refers to the fact that this processor outperforms the conventional processor, and therefore is equivalent to a conventional processor with a significantly longer aperture.) In the following example, the problem is solved by the use of a Kalman Filter.
During an experiment carried out jointly by Boston University and Woods Hole Oceanographic Institution, using the autonomous undersea vehicle REMUS, a short (six-ele- ment) array was towed. During the experiment, a ferry from the mainland of Cape Cod on its way to the island of Nantucket passed through the area. The resulting data pro- vide the basis for this example.33,34
The six-element array, which had an element spacing of 0.75 m, was towed at a speed of 1.5 m/s. The ferry first appeared at an angle very close to broadside (00) to the towed array. The array was moving in a straight line toward the course of the ferry, which was moving at approximately 20 kts, on a straight course from left to right with respect to forward endfire of the array. This configuration is depicted in Fig. 4. The points A and B are the ferry positions for the respective onset and closest point of approach (CPA) of the ferry source used in this work. The distance between these two points is approximately 2 km. Although the radiated sound from the ferry was quite broadband, extending over a band from about 100 to 1000 Hz, there was a particularly strong band of energy occurring between 890 and 920 Hz. This energy band was
Some applications of MBP in ocean acoustics with sequential Bayesian filtering (with Kalman or particle filters) are discussed next.
an array.
ω is arriving at a receiver moving with speed v, where the 0
direction of propagation of the signal is at angle θ with respect to the normal to the direction of motion of the receiver, some- times referred to as broadside. The frequency of the received signal will be Doppler-shifted to frequency ω, and the sign of the product vsinθ determines the sign of the Doppler, i.e., pos-
10 Acoustics Today, July 2011
Fig. 6. Results for the bearing-rate augmented case.