# Sound Source Localisation...HELP!!!!

Started by December 18, 2008
```Hi.. I needed a few tips on 2-D localisation of a sound source using 2
microphones (COLLINEAR WITH THE SOURCE). The source is assumed to be a
single frequency source and in-accessible with the only known
characteristics being the ones measured from an oscilloscope.
Oh, and I'm a Mechanical Engineer with ABSOLUTELY NO PRIOR EXPOSURE TO DSP
so please be kind enough to elaborate those "few tips"...Thanks :-)

```
```FordPrefect wrote:
> Hi.. I needed a few tips on 2-D localisation of a sound source using 2
> microphones (COLLINEAR WITH THE SOURCE). The source is assumed to be a
> single frequency source and in-accessible with the only known
> characteristics being the ones measured from an oscilloscope.
> Oh, and I'm a Mechanical Engineer with ABSOLUTELY NO PRIOR EXPOSURE
> TO DSP so please be kind enough to elaborate those "few
> tips"...Thanks :-)

You already have half the problem solved because the microphones are
colinear with the source.  That means they all lie on the same line.

After that, I think it's impossible to know the source location ON the line.
Let's see:

You know the frequency.  This means you know the wavelength / can calculate
it.

If the microphones are exactly one wavelength apart (or an integer number of
wavelengths apart) and colinear, then their outputs will add perfectly.  It
doesn't matter where the source is located for this to be the case.

If the microphoness are spaced 1/2 wavelength (or 1/2 wavelength plus an
integer number of wavelengths) and colinear, then they will add to perfectly
cancel.  It doesn't matter where the source is located for this to be the
case.

But, you did say "an oscilloscope" so there may be other information
available.
*IF* you had a time base for the source signal then you could measure the
time delay from the source to the microphones.  Knowing the delay and
knowing the speed of sound will give you the location on the line.

*IF* the colinearity is not really part of the picture then there's more to
be said.
In fact, having the source more *perpendicular* to the line on which the
microphones lie might be advantageous.  Consider this:
The microphones are on a line (this will always be true).
This is still 2D so it's all on an imaginary plane that is of known
orientation.
Choose a spacing value for the microphones.  1/2 wavelength might be a good
starting point.
Rotate the microphone array.
When the microphone array is broadside to the source, the output will be
maximum.
When the microphone array is colinear to the source, the output will be
zero.
Now you're back to the original colinearity situation - you know the
direction of the source.  You've measured an angle.

Keeping the same spacing, move the microphones along a line (let us say that
the line orientation is perpendicular to the angle measured above).
Remeasure the angle to the source.  Two angles from the line will give you
the location.

I don't think you can do this without moving at least one of the microphones
and without making two measurements.

PS: All of this is  purely mechanical.  :-)

A mechanical engineer's trick for reducing machinery noise:
Make the number of rotating elements a prime number (such as pistons in an
engine).  They will radiate in phase that is related by the prime number (we
assume they are close together relative to a wavelength).  The sum of the
sinusoids will be a minimum compared to having more (nonprime) elements or
fewer (nonprime) elements.

Fred

```
```"Fred Marshall" <fmarshallx@remove_the_x.acm.org> writes:

> A mechanical engineer's trick for reducing machinery noise:
> Make the number of rotating elements a prime number (such as pistons in an
> engine).  They will radiate in phase that is related by the prime number (we
> assume they are close together relative to a wavelength).  The sum of the
> sinusoids will be a minimum compared to having more (nonprime) elements or
> fewer (nonprime) elements.

Why don't we see more 5- and 7- cylinder cars, then?
--
%  Randy Yates                  % "Maybe one day I'll feel her cold embrace,
%% Fuquay-Varina, NC            %                    and kiss her interface,
%%% 919-577-9882                %            til then, I'll leave her alone."
%%%% <yates@ieee.org>           %        'Yours Truly, 2095', *Time*, ELO
http://www.digitalsignallabs.com
```
```On Dec 19, 10:33 am, "Fred Marshall" <fmarshallx@remove_the_x.acm.org>
wrote:

.> ...
.> A mechanical engineer's trick for reducing machinery noise:
.> Make the number of rotating elements a prime number (such as
pistons in an
.> engine).  They will radiate in phase that is related by the prime
number (we
.> assume they are close together relative to a wavelength).  The sum
of the
.> sinusoids will be a minimum compared to having more (nonprime)
elements or
.> fewer (nonprime) elements.
.>
.> Fred

Aside from certain types of engines sometimes found in aircraft:

http://en.wikipedia.org/wiki/Rotary_engine

I was not aware that pistons were rotating elements.

Dale B. Dalrymple

```
```Randy Yates <yates@ieee.org> wrote:
> "Fred Marshall" <fmarshallx@remove_the_x.acm.org> writes:

>> A mechanical engineer's trick for reducing machinery noise:
>> Make the number of rotating elements a prime number (such as pistons in an
>> engine).  They will radiate in phase that is related by the prime number
>> (we assume they are close together relative to a wavelength).
>> The sum of the sinusoids will be a minimum compared to having more
>> (nonprime) elements or fewer (nonprime) elements.

> Why don't we see more 5- and 7- cylinder cars, then?

The radial engines they used to use on airplanes were usually
an odd number.  For V engines, two pistons on each crank, it
has to be even.  It might be that you could do a V design with
all but the last having two, and still arrange the phase.

A V8 fires every 90 degrees of crankshaft rotation
(on a four stroke/cycle engine), a V6 every 120 degrees.

I believe there are three cylinder engines in some small cars.

-- glen
```
```On Thu, 18 Dec 2008 17:02:32 -0600, FordPrefect <altermyego42@gmail.com> wrote:
> Hi.. I needed a few tips on 2-D localisation of a sound source using 2
> microphones (COLLINEAR WITH THE SOURCE). The source is assumed to be a
> single frequency source and in-accessible with the only known
> characteristics being the ones measured from an oscilloscope.
> Oh, and I'm a Mechanical Engineer with ABSOLUTELY NO PRIOR EXPOSURE TO DSP
> so please be kind enough to elaborate those "few tips"...Thanks :-)

Ford,

Just to make sure we're working with the same impression, I'm
interpreting your phrase "COLLINEAR WITH THE SOURCE" this way:

S: source
M1,M2: microphones

A-----M1---------M2---------S-----B

As Fred has pointed out, as stated this is a 1-D localization
problem, not a 2-D problem.

And I'm assuming this is a "mathematical" problem (Oscilloscope has
infinite bandwidth and values can be read from it with infinite
precision, microphones are omnidirectional and infinitely small and
can be placed with infinite accuracy, instantaneous measurements,
etc.)

S is a "single-frequency source" -- a simple sine wave with
frequency "F".  You can measure F with the 'scope, which, with the
speed of sound in air will yield wavelength -- the length of one
full compression-rarefaction cycle from S.

But...  unless you have some way of causing a recognizable "hiccup"
from S -- starting and stopping it, for example -- I think I have to
go along with Fred:  it's insoluble, at least as stated.  You need
more information, such as "the position of S is known within a
one-wavelength distance", or "S starts and stops", or something
else.

The problem is the periodicity of the (assumed) signal from S.

Imagine that the location of S along AB is chosen as the origin, the
0 point for measuring displacements.

Now imagine that M1 and M2 are placed anywhere along the line and
you observe the signal from both (it's an imaginary 'scope, so I can
imagine it's a two-channel 'scope <grin!>).  Now imagine placing the
mocrophones at any other locations and measuring again.

Now imagine that I move S exactly one wavelength to the left, or to
the right, and that you repeat the same set of measurements.  Your
'scope traces will be identical...  but your distances from S will
be different.  Oops!

However, if you drop the collinearity assumption, you can get a
_direction_ to S by putting M1 and M2 on a bracket and rotating them
until the sine waves from 'scope channel 1 and 'scope channel 2 line
up.  Move perpendicular to this direction and repeat, then plot the
bearings; and if you're working on a plane (flat surface) you have
the location of S through "triangulation".  (On a globe that will
still leave you two possible locations for S, so you'll need at
least one more measurement to pin it down; on other surfaces YMMV.
<grin!>)

(You'll see this approach used in all the "Find The Hidden Radio
Transmitter" scenes of any spy movie.  <grin!>)

But, again, to do this violates the problem-as-originally-stated.

down incorrectly, or it really is impossible to solve. Or meybe
there's a "gotcha" we've overlooked somewhere?

Frank McKenney
--
I am Boris of Borg.  Assimilate moose and squirrel.
--
Frank McKenney, McKenney Associates
Richmond, Virginia / (804) 320-4887
Munged E-mail: frank uscore mckenney ayut mined spring dawt cahm (y'all)
```
```On Sat, 20 Dec 2008 03:08:06 +0000 (UTC), glen herrmannsfeldt
<gah@ugcs.caltech.edu> wrote:

>Randy Yates <yates@ieee.org> wrote:
>> "Fred Marshall" <fmarshallx@remove_the_x.acm.org> writes:
>
>>> A mechanical engineer's trick for reducing machinery noise:
>>> Make the number of rotating elements a prime number (such as pistons in an
>>> engine).  They will radiate in phase that is related by the prime number
>>> (we assume they are close together relative to a wavelength).
>>> The sum of the sinusoids will be a minimum compared to having more
>>> (nonprime) elements or fewer (nonprime) elements.
>
>> Why don't we see more 5- and 7- cylinder cars, then?
>
>The radial engines they used to use on airplanes were usually
>an odd number.  For V engines, two pistons on each crank, it
>has to be even.  It might be that you could do a V design with
>all but the last having two, and still arrange the phase.
>
>A V8 fires every 90 degrees of crankshaft rotation
>(on a four stroke/cycle engine), a V6 every 120 degrees.
>
>I believe there are three cylinder engines in some small cars.
>
>-- glen

Even in-line engines usually have even numbers of cylinders.   It's
harder to manage vibration in a 3-, 5- or 7- cylinder engine than it
is with an even number of cylinders.   Sometimes symmetry is a good
thing.

I can see how Fred's point makes sense, and pistons aren't always
easily treated as "rotating machinery".   I don't think the same
principle applies with cylinders as it would with, say, keeping
vibration down in the shafts of a transmission.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org

Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php
```
```On Thu, 18 Dec 2008 17:02:32 -0600, "FordPrefect"
<altermyego42@gmail.com> wrote:

>Hi.. I needed a few tips on 2-D localisation of a sound source using 2
>microphones (COLLINEAR WITH THE SOURCE). The source is assumed to be a
>single frequency source and in-accessible with the only known
>characteristics being the ones measured from an oscilloscope.
>Oh, and I'm a Mechanical Engineer with ABSOLUTELY NO PRIOR EXPOSURE TO DSP
>so please be kind enough to elaborate those "few tips"...Thanks :-)
>

As others have mentioned, strictly getting position in general is
going to be difficult as you've described it.    It gets easier if S
moves at a constant rate, since then you can use the Doppler to
estimate range (with some constraints).   Since that's a pretty
limiting assumption, it's probably not very useful.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org

Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php
```
```Frnak McKenney wrote:

...

> So either your professor stated the problem badly, you copied it
> down incorrectly, or it really is impossible to solve. Or meybe
> there's a "gotcha" we've overlooked somewhere?

I think that the OP meant "coplanar" and is embarrassed to 'fess up.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```"Frnak McKenney" <frnak@far.from.the.madding.crowd.com> wrote in message
> On Thu, 18 Dec 2008 17:02:32 -0600, FordPrefect <altermyego42@gmail.com>
> wrote:
>> Hi.. I needed a few tips on 2-D localisation of a sound source using 2
>> microphones (COLLINEAR WITH THE SOURCE). The source is assumed to be a
>> single frequency source and in-accessible with the only known
>> characteristics being the ones measured from an oscilloscope.
>> Oh, and I'm a Mechanical Engineer with ABSOLUTELY NO PRIOR EXPOSURE TO
>> DSP
>> so please be kind enough to elaborate those "few tips"...Thanks :-)
>
> Ford,
>
> Just to make sure we're working with the same impression, I'm
> interpreting your phrase "COLLINEAR WITH THE SOURCE" this way:
>
> S: source
> M1,M2: microphones
>
>   A-----M1---------M2---------S-----B
>
> As Fred has pointed out, as stated this is a 1-D localization
> problem, not a 2-D problem.
>
> And I'm assuming this is a "mathematical" problem (Oscilloscope has
> infinite bandwidth and values can be read from it with infinite
> precision, microphones are omnidirectional and infinitely small and
> can be placed with infinite accuracy, instantaneous measurements,
> etc.)
>
> S is a "single-frequency source" -- a simple sine wave with
> frequency "F".  You can measure F with the 'scope, which, with the
> speed of sound in air will yield wavelength -- the length of one
> full compression-rarefaction cycle from S.
>
> But...  unless you have some way of causing a recognizable "hiccup"
> from S -- starting and stopping it, for example -- I think I have to
> go along with Fred:  it's insoluble, at least as stated.  You need
> more information, such as "the position of S is known within a
> one-wavelength distance", or "S starts and stops", or something
> else.
>
Well, the intensity of a sound falls off as 1/(distance^2).  Assuming that
both microphones are on the same side of the sound source, let the amplitude
of the sound as measured at the mics be A1 and A2 and the distance between
the source and the mics be d1 and d2.  Let the distance between the mics be
d, and to simplify the math let A1 >A2 (and therefore d1 < d2).  Call the
amplitude of the sound at unit distance A.
A1 = A/(d1^2)
A2 = A/(d2^2) = (A/((d1+d)^2)
so A1/A2 = (d1+d)^2/d1^2)
(d1+d)/d1 = sqrt(A1/A2) = R
d1+d = R* d1
d = (R-1)* d1
d1 = d/(R-1) = d(sqrt(A1/A2)-1)

>problem is the periodicity of the (assumed) signal from S.
>
> Imagine that the location of S along AB is chosen as the origin, the
> 0 point for measuring displacements.
>
> Now imagine that M1 and M2 are placed anywhere along the line and
> you observe the signal from both (it's an imaginary 'scope, so I can
> imagine it's a two-channel 'scope <grin!>).  Now imagine placing the
> mocrophones at any other locations and measuring again.
>
> Now imagine that I move S exactly one wavelength to the left, or to
> the right, and that you repeat the same set of measurements.  Your
> 'scope traces will be identical...  but your distances from S will
> be different.  Oops!
>
> However, if you drop the collinearity assumption, you can get a
> _direction_ to S by putting M1 and M2 on a bracket and rotating them
> until the sine waves from 'scope channel 1 and 'scope channel 2 line
> up.  Move perpendicular to this direction and repeat, then plot the
> bearings; and if you're working on a plane (flat surface) you have
> the location of S through "triangulation".  (On a globe that will
> still leave you two possible locations for S, so you'll need at
> least one more measurement to pin it down; on other surfaces YMMV.
> <grin!>)
>
> (You'll see this approach used in all the "Find The Hidden Radio
> Transmitter" scenes of any spy movie.  <grin!>)
>
> But, again, to do this violates the problem-as-originally-stated.
>
> So either your professor stated the problem badly, you copied it
> down incorrectly, or it really is impossible to solve. Or meybe
> there's a "gotcha" we've overlooked somewhere?
>
>
> Frank McKenney
> --
>    I am Boris of Borg.  Assimilate moose and squirrel.
> --
> Frank McKenney, McKenney Associates
> Richmond, Virginia / (804) 320-4887
> Munged E-mail: frank uscore mckenney ayut mined spring dawt cahm (y'all)

** Posted from http://www.teranews.com **
```