TL;DR:
GPS radio signals do not travel far through water, so underwater robots use sound (sonar and acoustic positioning) and motion sensing (inertial navigation).
Dead reckoning adds up movement from a known start, so its error grows with time until a fix corrects it.
Sonar depth is
d = c × t / 2, with sound speedcabout 1,480 m/s in fresh water.
A small submersible sinks below the surface of a lake and its GPS receiver goes blind. Radio waves are absorbed quickly by water, so the satellites might as well not exist. The robot still has to know where it is, how deep it is, and what is below it. The tools it uses are sound, motion sensors and careful bookkeeping.
Sonar: measuring with sound
Sound travels much better than radio in water. Sonar sends a pulse of sound and listens for the echo. The distance is d = c × t / 2, where c is the speed of sound, t is the time until the echo returns, and the 2 accounts for the round trip. In fresh water at about 20 °C, c is roughly 1,480 m/s, and it changes with temperature, salinity and pressure.
Because c varies, serious surveys measure it with a sensor and correct the depths. A speed guess that is too high by 20 m/s makes a 20 m depth read about 20 × 1500 / 1480 ≈ 20.3 m.
Inertial navigation and dead reckoning
Dead reckoning means starting from a known position and adding up each movement: speed and heading, times time. An inertial measurement unit (IMU) senses acceleration and rotation. Many underwater vehicles also use a Doppler velocity log, which bounces sound off the bottom to measure speed over the ground, and a compass or gyro for heading.
The trouble is that errors add up. Suppose the speed estimate has a steady error of 0.01 m/s. After 10 minutes, or 600 s, the position is off by 0.01 × 600 = 6 m. After an hour it is 36 m off. The error never shrinks by itself.
Acoustic positioning
To correct drift, vehicles use sound beacons. In long-baseline systems, several transponders sit at known spots on the bottom, and the vehicle measures its travel time to each. One-way range is c × t. A time of 0.40 s gives 1480 × 0.40 = 592 m. With ranges from three or more beacons the position can be solved by trilateration, the same geometry GPS uses.
Ultra-short-baseline systems use one transducer array on a ship that measures both the range and the direction to the vehicle. Either way, each fix resets the drifting estimate, and the vehicle continues with dead reckoning until the next one. If the vehicle can surface, a GPS fix there does the same job.
Worked example: a submersible mapping a lake bottom
A small vehicle runs a survey in a lake of roughly constant depth. It has a downward echo sounder, a Doppler velocity log, a heading sensor, and starts at a surface GPS fix.
At one point the echo returns after 27 ms. Depth below the vehicle:
d = 1480 × 0.027 / 2 ≈ 20.0 m.The sounder's beam is a cone. Say its full width is 30°, so the half-angle is 15°. The strip of bottom it sees at 20 m depth is
2 × 20 × tan 15° = 2 × 20 × 0.268 ≈ 10.7 mwide.To cover the lake with no gaps, the vehicle runs parallel lines closer together than that width. Spacing them 8 m apart gives overlap of
10.7 − 8 = 2.7 mbetween neighbours, which also helps stitch the data.Each depth reading is stored with the vehicle's estimated position at that moment, so the map is only as good as the navigation.
At 0.01 m/s of speed bias, drift is 0.6 m per minute (
0.01 × 60). If a long line takes 5 minutes (300 s), the error is0.01 × 300 = 3 mby the end, comparable to the gap between lines. Corrections from a surface fix or acoustic beacon between lines keep neighbouring lines from sliding out of alignment.
In deeper water the strip gets wider, which is why a shallow area needs closer lines. The same sums apply to the sea floor, with the speed of sound adjusted.
Building and testing underwater robots: Water and electricity are a poor combination. Seal electronics in a watertight housing, pressure-test it empty before adding parts, and fit a leak sensor. Keep lithium batteries in a vented, protected compartment and never charge them unattended. Test first in a shallow, calm place on a tether, and keep hands and hair away from spinning thrusters. Do not swim near a running vehicle.
Where it goes wrong
Wrong sound speed. Temperature layers bend and speed up or slow down the sound, giving wrong ranges.
Multipath. Echoes bounce off the surface, walls or the bottom and arrive late, which looks like a longer range.
Noise. Thrusters and other equipment are loud underwater and can drown out weak echoes.
Drift. Heading errors rotate the whole track, which grows with distance.
Beacon placement. If beacon positions are surveyed badly, every fix is wrong in the same way.
Currents. A current pushes the vehicle off its heading line without the heading sensor noticing.
How real robots use it
Underwater vehicles blend all of these in a filter that weighs each source by its uncertainty, in the way described in how self-driving cars combine their sensors. They surface for GPS when the mission allows, and some vehicles use feature matching on sonar images to recognise places they passed before, an idea called SLAM. The challenge of working far from direct control also appears in how Mars rovers drive with a signal delay.
Try it yourself
In a swimming pool or a bath, with an adult nearby, tap two stones together underwater and listen with a hydrophone or a waterproof microphone. Or work on paper: pick a sound speed, choose three beacon positions on graph paper, and draw a circle around each with radius c × t. The place where the three circles meet is the vehicle.
Frequently asked questions
Why not use radio underwater?
Water absorbs radio waves quickly, especially at the high frequencies GPS uses. Sound carries much farther.
Is sound faster in seawater?
Usually slightly, because of the salt and pressure. Sound speed in seawater is around 1,500 m/s, and it changes with temperature.
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