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sound travels faster in seawater than in air and it is less quickly attenuated.
The same basic relationship from Eq. 1 that is used to calculate the distance from satellites can be applied to acoustic signals as well. Here, rather than multiplying the time that the GPS signal has traveled by the speed of light, the travel time of the signal is multiplied by the speed of sound in the medium through which it is traveling. The speed of sound in the ocean is roughly 1,500 m/s. This is much slower than the speed of light, and it is also quite variable because the speed of sound in seawater depends on the seawater temperature, salinity, and depth.
Traditional Underwater Positioning and
Local Vehicle Navigation Systems
Underwater vehicles routinely get position and timing from a GPS receiver when they are at the surface, but once they start to descend, this is no longer available. Vehicles navigate underwater using some combination of dead reckoning, vehicle hydrodynamic models, inertial navigation systems (INSs), and local navigation networks (Paull et al., 2014). Positioning in the z direction, the depth in the ocean, is straightforward with a pressure sensor, which can reduce the dimensionality of the prob- lem to horizontal positioning in x and y, or longitude and latitude, respectively.
Dead reckoning estimates the position using a known starting point that is updated with measurements of vehi- cle speed and heading as time progresses. Larger vehicles, such as submarines, may have an onboard INS that inte- grates measurements of acceleration to estimate velocity and thereby position. These measurements are, however, subject to large integration drift errors.
Because of the need for more position accuracy than afforded by the submarine systems discussed above, it comes as no surprise that underwater vehicles also use acoustics for localization. A long-baseline (LBL) acoustic- positioning system is composed of a network of acoustic transponders, often fixed on the seafloor with their posi- tions accurately surveyed. The range measurements from multiple transponders are used to determine position. LBL systems typically operate on scales of 100 meters to several kilometers and have accuracies on the order of a meter. Transponder buoys at the surface can also provide positioning accuracy similar to a seafloor LBL network.
These buoys have constant access to GPS positioning so they do not require a survey.
Short-baseline (SBL) systems operate on a smaller scale, and the SBL transducers are typically fixed to a surface vessel. Ultrashort-baseline (USBL) systems are typically a small transducer array, also often fixed to a surface vehicle, which use phase (arrival angle) information of the acoustic signals to determine the vehicle position.
These types of acoustic localization work in a similar way to GPS localization, with electromagnetic waves; how- ever, they all operate in relatively small regions. Note that these acoustic-positioning methods have been described in the context of underwater vehicles, but they can be used for other purposes as well, including tracking drift- ing instrumentation or even animals underwater.
Long-Range Underwater Acoustics
Propagation in the SOFAR Channel
Attenuation of acoustic signals in the ocean is highly dependent on frequency. The signals commonly used for LBL, SBL, and USBL localization networks typi- cally have frequencies of tens of kilohertz and upward. These signals may travel for a few kilometers, but lower frequency signals on the order of hundreds of hertz or lower are capable of traveling across entire ocean basins underwater. This was demonstrated in 1991 by the Heard Island Feasibility Test, where a signal was transmitted from Heard Island in the Southern Indian Ocean and received at listening stations across the globe, from Ber- muda in the Atlantic Ocean to Monterey, CA, in the Eastern Pacific Ocean (Munk et al., 1994).
Refractive effects of the ocean waveguide are usually taken into account when using the acoustic-positioning methods described above because an acoustic arrival often does not take a direct path from the source to the receiver, and often a number of arrivals resulting from multiple propagation paths are received. The refractive effects of the ocean waveguide become even more impor- tant as ranges increase. Acoustic arrivals can be spread out over several seconds; however, the time arrival struc- ture can be predicted based on the sound speed profile.
The speed of sound in the ocean increases with increasing hydrostatic pressure (depth in the ocean) and with higher temperatures that occur near the surface. This leads to
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