Underwater Robots and Acoustic Navigation
Radio and GPS do not work under water, so an underwater robot must navigate another way. A Doppler velocity log bounces sound off the seabed to measure speed, which can be integrated into position, but the error grows over time. Acoustic beacons at known spots give ranges from the time a sound pulse takes to travel, which pull the estimate back.
Two kinds of navigation
Dead reckoning integrates the measured velocity, so a small bias \(b\) grows into an error of \(b\,t\). Long baseline (LBL) acoustics measures the travel time \(t_i\) of a sound pulse from beacon \(i\), with the speed of sound in water about 1500 m/s:
A filter, here a simple correction toward the position that best fits the ranges, blends the two.
What to notice
With beacons off, the dead-reckoning path slowly drifts away and never comes back. With beacons on, the error stays bounded, small jumps marking each acoustic fix. Sound is slow, so fixes come seconds apart, and the robot must dead-reckon in between. Ocean robots also use inertial sensors, ultra-short baseline systems mounted on a ship, and terrain matching against seafloor maps.