无人机可以听到房间的形状

IF 1.6 2区 数学 Q2 MATHEMATICS, APPLIED
M. Boutin, G. Kemper
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引用次数: 5

摘要

我们展示了人们可以通过放置在具有一般位置和方向的无人机上的四个非平面麦克风接收到的一阶回声来重建具有平面墙壁的房间的形状。信号源位于房间和无人机上的两种情况都要考虑。如果麦克风的位置是随机选择的,那么概率为1,任何墙壁的位置都是正确重建的,只要它被四个麦克风听到。我们的算法使用一个简单的回波排序准则来恢复回波的壁分配。我们证明,如果安装麦克风的无人机的位置和方向在所有无人机位置和方向的6维空间中不位于某一维(最多5维)上,那么通过我们的回波分选准则得到的壁面分配一定是正确的,因此通过我们的算法得到的重建是正确的。我们的证明使用了计算交换代数的方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Drone Can Hear the Shape of a Room
We show that one can reconstruct the shape of a room with planar walls from the first-order echoes received by four non-planar microphones placed on a drone with generic position and orientation. Both the cases where the source is located in the room and on the drone are considered. If the microphone positions are picked at random, then with probability one, the location of any wall is correctly reconstructed as long as it is heard by four microphones. Our algorithm uses a simple echo sorting criterion to recover the wall assignments for the echoes. We prove that, if the position and orientation of the drone on which the microphones are mounted do not lie on a certain set of dimension at most 5 in the 6-dimensional space of all drone positions and orientations, then the wall assignment obtained through our echo sorting criterion must be the right one and thus the reconstruction obtained through our algorithm is correct. Our proof uses methods from computational commutative algebra.
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
19
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