On October 28th, Prof. Dr. Gregor Kemper (TUM Department of Mathematics) will give a talk entitled “A Drone Can Hear the Shape of a Room”.
Can walls and flat surfaces be recognized using sound waves? Mathematicians have been studying this question from a theoretical standpoint for quite some time. Professor Kemper and his research partner have now proven that nothing more than one drone, four microphones and a loudspeaker is needed to determine the position of walls and other flat surfaces within a room which is furthermore not necessarily assumed to be rectangular. By mounting the four microphones and the loudspeaker on a drone, measurements are being made more practical as the equipment does not have to be installed in the room.
When the loudspeaker sends out a sound impulse, the waves bounce back from the walls. These direct reflections of the impulse are referred to as first order echoes. As every microphone detects a larger number of echoes, the certainty of deciding which echoes are coming from which wall is crucial. The transit time – the time delay between emitting the sound pulse and receiving its echo – can be determined very precisely using the microphones. All transit times from a given wall have a specific relationship with one another. Professor Kemper and his research partner developed a new algorithm that uses this relationship to assign individual echoes to a particular wall. Once the echoes have been assigned to the right walls, the position and the walls are calculated using a geometric approach similar to that used by GPS when determining location data.
In a next step, the researcher’s scenario will become more realistic: they hope to find a mathematical solution for when errors or inaccuracies occur during measurement (TUM press release).
Boutin, M., Kemper, G.: A Drone Can Hear the Shape of a Room, SIAM J. APPL. ALGEBRA GEOMETRY; Vol. 4, No. 1, pp. 123-140. DOI: 10.1137/19M1248534.
As usual, we’ll meet in the TUM-IAS building’s atrium on the 1st floor between 1:00 and 2:00 pm (the talk begins at 1:15 pm). We hope you will join us for a cup of coffee, and please feel free to bring along guests and coworkers!
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