Numerical Formulae for TOA-based Microphone and Source Localization
Numerical Formulae for TOA-based Microphone and Source Localization
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基于 TOA 的麦克风和源定位的数值公式
DOI：
10.1109/iwaenc.2014.6954002
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Trung-Kien Le and Nobutaka Ono
中科院分区：
文献类型：
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作者：
Yoshikazu Murase;Hironobu Chiba;Nobutaka Ono;Shigeki Miyabe;Takeshi Yamada and Shoji Makino;Qu Zhang,Hideki Kakeya;Trung-Kien Le and Nobutaka Ono
本文给出了基于到达时间（TOA）的麦克风和声源定位问题的数值公式，该公式根据每个麦克风和每个声源之间的距离分别确定麦克风和声源的位置。这是一个纯粹的数学几何问题。具体地说，我们证明了当麦克风的数量或源的数量至少是九个，麦克风的位置和源的位置的公式给出了简单的距离矩阵。如果我们知道关于任意两个麦克风或两个源之间的距离的额外信息，则在至少八个麦克风或源的情况下给出类似的陈述。这些公式的准确性已被一万个独立的实验所证实，这些实验中的点的坐标具有独立的均匀分布。
This paper presents numerical formulae for the Time-of-Arrival (TOA)-based microphone and source localization problem, which determines the positions of microphones and sources based on distances between each microphone and each source respectively. This is a purely geometrical problem in mathematics. Concretely, we show when the number of microphones or the number of sources is at least nine, the formulae of the microphone positions and source positions are given simply from the distance-matrix. A similar statement is given in the cases of at least eight microphones or sources if we know an extra information about the distance between any two microphones or two sources. The accuracy of these formulae are proven shortly by ten thousand independent experiments of which coordinates of points have an independent Uniform distribution.