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Old Mar 14th 2018, 08:01 AM   #1
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Sound Localization using multilateration?

Hello. I'm working on a project, where I'm trying to locate the position of a sound source. I've got an array of 4 microphones, 3 in a triangle and one out of plane. The microphones are all connected to a micro-controller which can accurately time stamp the incoming signals. Since the time the signal was produced is unknown, the system calculates the Time Difference of Arrival (TDoA) for each microphone, relative to the first mic that detected the signal. I know what microphones were triggered and the order they were triggered in, and they are at known positions. How can I use this information to get the x,y,z coordinates of the sound source? I've been looking into triangulation and multilateration but can't seem to figure it out. Any help is greatly appreciated.
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Old Mar 14th 2018, 10:58 AM   #2
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Why 4 mikes?

You only need 3 for 3 dimensions.

You obviously know that time difference can be converted to distances?
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Old Mar 14th 2018, 11:25 AM   #3
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How can it be done with 3 mics?
Since I don't know the time the signal was generated time TDoAs are all relative to the first mic that detected it. So with 4 mics there are only 3 TDoAs.
If the start time of the signal was known then yes obviously it would be easy to work out the distance of the source from each mic and it then locating it would be very simple. Without knowing when the signal started it's much less trivial.
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Old Mar 14th 2018, 12:35 PM   #4
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I used to work on something similar which uses a similar concept, i.e. over-the-horizon (OTH) radar. Specifically I worked on the software which processed the raw data. Unfortunately that was 28 years ago and I'm a bit rusty. Not to mention that you're doing something a bit different.

Search the internet on the terms phased array and beam forming and you may get something useful. You won't get something easy though. Then again you want something a bit different.

That you only need three comes from the fact that with three microphones you can detect where it comes from. To explain why takes some effortif you don't know the math. How much math do you know? Do you know trigonometry and geometry?

Last edited by Pmb; Mar 14th 2018 at 12:55 PM.
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Old Mar 14th 2018, 01:07 PM   #5
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Originally Posted by gibbs909 View Post
How can it be done with 3 mics?
Since I don't know the time the signal was generated time TDoAs are all relative to the first mic that detected it. So with 4 mics there are only 3 TDoAs.
If the start time of the signal was known then yes obviously it would be easy to work out the distance of the source from each mic and it then locating it would be very simple. Without knowing when the signal started it's much less trivial.
But surely all the mikes are detecting the same signal?

There used to be a system manufactured by US Motorola called TRisponder, which worked in the manner you seek, along with another called Syledis from a French manufacturer, Sercel. The only difference is that they were EM wave pulses not sound.

They were called rho-rho systems (or range-range) systems. PMB may be able to confirm if this is old radar technology, I used them for marine geopositioning systems.

For undersea positioning ultrasonic beacon transponders are used in the same way.


Old fashioned surveyors and navigators called the problem the resection problem. That of acquiring position on a plane table or boat by position lines from known observed stations.

A position line is a line of constant distance from a known point.
The intersection of two such lines from different points gives position in 2D and 3 such points give position in 3D.

Usually extra stations are used because errors can be accoutned for in the redundancy.

Tienstra is one mathematical technique for solving the resection.

This book should help you with the maths

https://www.amazon.co.uk/Underwater-.../dp/0419121005

Last edited by studiot; Mar 14th 2018 at 01:10 PM.
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Old Mar 14th 2018, 01:29 PM   #6
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I dug out the book here is an extract from a similar system.

Please note that accuracy of space measurements with acoustic waves depends upon the size of the wave, so you need very short wavelengths (ultrasonics) to get centimetric accuracy.

There are also many other accuracy considerations.
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Sound Localization using multilateration?-acousticpos1.jpg  
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Old Mar 14th 2018, 02:59 PM   #7
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Originally Posted by gibbs909 View Post
How can I use this information to get the x,y,z coordinates of the sound source? I've been looking into triangulation and multilateration but can't seem to figure it out.
Try this. Set up a Cartesian coordinate system. Arrange the microphones in a plane in an equilateral triangle with one mike at x = 0 and the center of triangle at the center of the Cartesian coordinate system. Then write down the equations which represent the system. To do this note that the sound travels at 343 m/s at standard temperature and pressure (STP). Then once that is down correctly solve for x, y and z.

Do you think you can take it from there?
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Old Mar 14th 2018, 03:00 PM   #8
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Originally Posted by gibbs909 View Post
How can I use this information to get the x,y,z coordinates of the sound source? I've been looking into triangulation and multilateration but can't seem to figure it out.
Try this. Set up a Cartesian coordinate system. Arrange the microphones in a plane in an equilateral triangle with one mike at x = 0 and the center of triangle at the center of the Cartesian coordinate system. Then write down the equations which represent the system. To do this note that the sound travels at 343 m/s at standard temperature and pressure (STP). Then once that is down correctly solve for x, y and z.

Do you think you can take it from there?

I myself never try to reinvent the wheel so if I were you I'd do an internet search and see if someone has already done this. It might help.
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