Just as bats use echotomy to locate their surroundings, mathematicians have found that using microphones and speakers on drones can do the same with algebra and geometric principles. Boutin and Gregor Kemper, professors of algorithmal algebra at the Technical University of Munich’s Department of Mathematics, work to reconstruct the shape of a room by using echoes picked up by microphones on drones.
When the microphone hears an echo, the time difference between the time the sound is generated and the time it hears. The time difference indicates the distance at which the sound propagates after bouncing on the wall. The challenge they face is to determine which distance corresponds to which wall, a process called echo ordering. Accurateclassification of echoes ensures that all the walls you hear are really there. In this way, the algorithm does not produce a ghost wall.
This study is directly related to two complementary issues in the project: localization (determining the location of the environment) and mapping (determining the shape of the environment). Research by Boutin and Kemper has shown that rooms can be reconstructed with four non-planar microphones and speakers that emit only one signal. Their work is published in the journal SIAM Applied Algebra and Geometry.
In fact, this echolocation study can be applied in a variety of ways. Such devices can be carried by a person, fixed to a car, or even used underwater. Many engineering applications require a lot of mathematical knowledge, and sometimes you need to use tools in the field of abstract mathematics, the method of exchanging algebra. It is considered to be a very abstract part of mathematics, but it is suitable for very practical engineering problems. This shows how blurred the line between applied mathematics and abstract mathematics is, and engineering is indeed a multidisciplinary discipline.