TDOA多边定位以定位声源 [英] TDOA multilateration to locate a sound source

问题描述

我想在 2D 空间中找到声源的坐标.没有诸如光之类的参考物可以附加到此声音，但是，已知这种声音在两对AB和AC麦克风之间的到达时间差(TDOA)，以及声音的速度和麦克风的精确位置也是已知的相对于彼此.但是，传输的绝对时间是未知的，因此c = d/T是不可能的.

I would like to locate the coordinates, in 2D space, of a source of sound. There is no reference such as light to attach to this sound, however, the time difference of arrival (TDOA) of this sound between two pairs AB and AC of microphones is known, as is the speed of sound and the precise location of the microphones relative to each other. However, the absolute time of transmission is unknown, therefore c=d/T is not possible.

我正在寻找一种算法，可以让我找到此声源的x，y坐标.我已经在Google上搜索了很多次答案，但是我发现的结果并不暗示如何使用TDOA数据来得出相交的双曲线，他们只是说可以.感谢您提出的任何建议或建议，

I am looking for an algorithm that allows me to find the x,y coordinates of this sound source. I have searched Google for the answer many times, however the results I have found do not suggest how to use this TDOA data to derive intersecting hyperbolas, they merely say you can. I'm grateful for any pointers or suggestions, thanks

推荐答案

让我们指定与麦克风A，B，C，D da，db，dc，dd和TOF ta，tb，tc，td的距离.声音的速度是c.

Lets denominate the distances from microphone A,B,C,D da,db,dc,dd and the TOF ta,tb,tc,td. The speed of sound is c.

很容易看到:

|ta-tb|*c= |(da-db)| (1)
|tc-td|*c= |(dc-dd)| (2)

可以将双曲线定义为点的轨迹，对于每个点，到两个给定焦点的距离之差的绝对值是恒定的.这正是方程式左侧的内容:时间差是一个(测量的)常数，而c也是常数:因此声源的可能位置在双曲线上，其两个焦点是两个麦克风.我们有两个方程，因此我们有两个双曲线.两个双曲线通常在多个点处相交(因为它们具有二次方程式)，因此，如果您计算相交点，则会有多个可能的声源位置.麦克风的特殊星座可能会有帮助.

A hyperbola can be defined as the locus of points for each of which the absolute value of the difference between the distances to two given foci is a constant. That is precisely what we have on the left side of our equations: the time difference is a (measured) constant, and c is also constant: so the possible location for the sound source is on a hyperbola, whose two foci is the two microphones. We have two equations therefore we have two hyperbolas. Two hyperbolas normally intersect in multiple points (because they have quadratic equation), so if you calculate the point of intersection you will have multiple possible sound source locations. Special constellation of the microphones might help.

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