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Arrival Times:
The cross power spectrum has a peak at the time difference between each pair
of hydrophone signals. These spectra are based on the convolution of the Fourier
transforms of the input data series.
To understand the time series plot below, take a look at channels 0 and 6. The call comes earlier in time in channel 6 than in channel 0. The small peaked spectrum in the second row at the right shows the cross power spectrum between channels 0 and 6. The peak here shows that the signal in channel 6 comes 378 samples earlier than the signal in channel 0. This corresponds to a difference in travel distance of about -59 m given the speed of sound in water meaning that channel 6 is 59 m closer to the source of the sound than is channel 0.
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Source Location:
The 8 hydrophones yield 28 distinct pairs and hence 28 time differences for
a single sound source. Each of these time differences constrains the sound
source to be located on a hyperboloid centered on the line (in 3 dimensions)
between the corresponding pair of hydrophones. The best estimate sound source
position is the location closest to the intersections of these 28 surfaces.
Here a chirp was emitted from an underwater speaker at a known location. The circle attached to the line is the computer's reconstructed postion of this sound source. The other circle is the approximate location of the sound source as determined from GPS coordinates. The calculated location of this chirp is within +/-5 m of the measured location (GPS coordinates). North is to the top of the figure. The shoreline is shown in black and the hydrophone locations are shown by the small circles.
