# LMS

Started by September 7, 2008
```Hi,

I am working on sound localization system. I want to find the co-ordinate
of the sound source  by least mean square method in MATLAB. I have the
co-ordinates of the 4 microphones and the relative distance between mic 1
to the source to mic 2 to the source, i.e. the time delay*speed of sound.

I even have the formulas but I have no clue on how to crack this:
d12=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x2-xs)^2+(y2-ys)^2)
d13=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x3-xs)^2+(y3-ys)^2)
d14=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x4-xs)^2+(y4-ys)^2)

d12, d13, d14 - relative distance bet the mic pairs 1,2 , 1,3 and 1,4
respectively. (x1,y1) - co-ordinates of mic 1 , (x2,y2) - co-ordinates of
mic 2, (x3,y3) - co-ordinates of mic 3, (x4,y4) - co-ordinates of mic 4

Solving these simultaneously will give me (xs,ys)

Any suggestions on how to do this.. ??

```
```On Sep 7, 4:38&#2013266080;am, "maz_p5" <maz...@hotmail.com> wrote:
> Hi,
>
> I am working on sound localization system. I want to find the co-ordinate
> of the sound source &#2013266080;by least mean square method in MATLAB. I have the
> co-ordinates of the 4 microphones and the relative distance between mic 1
> to the source to mic 2 to the source, i.e. the time delay*speed of sound.
>
> I even have the formulas but I have no clue on how to crack this:
> d12=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x2-xs)^2+(y2-ys)^2)
> d13=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x3-xs)^2+(y3-ys)^2)
> d14=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x4-xs)^2+(y4-ys)^2)
>
> d12, d13, d14 - relative distance bet the mic pairs 1,2 , 1,3 and 1,4
> respectively. (x1,y1) - co-ordinates of mic 1 , (x2,y2) - co-ordinates of
> mic 2, (x3,y3) - co-ordinates of mic 3, (x4,y4) - co-ordinates of mic 4
>
> Solving these simultaneously will give me (xs,ys)
>
> Any suggestions on how to do this.. ??

Hire somebody who does have a clue how to crack it.

Dirk
```
```
maz_p5 wrote:

> Hi,
>
> I am working on sound localization system. I want to find the co-ordinate
> of the sound source  by least mean square method in MATLAB. I have the
> co-ordinates of the 4 microphones and the relative distance between mic 1
> to the source to mic 2 to the source, i.e. the time delay*speed of sound.
>
> I even have the formulas but I have no clue on how to crack this:
> d12=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x2-xs)^2+(y2-ys)^2)
> d13=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x3-xs)^2+(y3-ys)^2)
> d14=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x4-xs)^2+(y4-ys)^2)
>
> d12, d13, d14 - relative distance bet the mic pairs 1,2 , 1,3 and 1,4
> respectively. (x1,y1) - co-ordinates of mic 1 , (x2,y2) - co-ordinates of
> mic 2, (x3,y3) - co-ordinates of mic 3, (x4,y4) - co-ordinates of mic 4
>
> Solving these simultaneously will give me (xs,ys)
>
> Any suggestions on how to do this.. ??

Loads of papers on this. Do an IEEE Xplore search on acoustic source
location.
This is a non-linear problem but can be simplified in a number of
ways. There are a good many methods.
```
```>
>
>maz_p5 wrote:
>
>> Hi,
>>
>> I am working on sound localization system. I want to find the
co-ordinate
>> of the sound source  by least mean square method in MATLAB. I have the
>> co-ordinates of the 4 microphones and the relative distance between mic
1
>> to the source to mic 2 to the source, i.e. the time delay*speed of
sound.
>>
>> I even have the formulas but I have no clue on how to crack this:
>> d12=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x2-xs)^2+(y2-ys)^2)
>> d13=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x3-xs)^2+(y3-ys)^2)
>> d14=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x4-xs)^2+(y4-ys)^2)
>>
>> d12, d13, d14 - relative distance bet the mic pairs 1,2 , 1,3 and 1,4
>> respectively. (x1,y1) - co-ordinates of mic 1 , (x2,y2) - co-ordinates
of
>> mic 2, (x3,y3) - co-ordinates of mic 3, (x4,y4) - co-ordinates of mic
4
>>
>> Solving these simultaneously will give me (xs,ys)
>>
>> Any suggestions on how to do this.. ??
>
>Loads of papers on this. Do an IEEE Xplore search on acoustic source
>location.
>This is a non-linear problem but can be simplified in a number of
>ways. There are a good many methods.
>
Hi,
I have done all my search and this is the equation what I have come up
with; but how do i solve it in MATLAB.
Any suggestions on it?

Thank you.
```
```On Sep 7, 8:52&#2013266080;am, "maz_p5" <maz...@hotmail.com> wrote:
> >maz_p5 wrote:
>
> >> Hi,
>
> >> I am working on sound localization system. I want to find the
> co-ordinate
> >> of the sound source &#2013266080;by least mean square method in MATLAB. I have the
> >> co-ordinates of the 4 microphones and the relative distance between mic
> 1
> >> to the source to mic 2 to the source, i.e. the time delay*speed of
> sound.
>
> >> I even have the formulas but I have no clue on how to crack this:
> >> d12=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x2-xs)^2+(y2-ys)^2)
> >> d13=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x3-xs)^2+(y3-ys)^2)
> >> d14=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x4-xs)^2+(y4-ys)^2)
>
> >> d12, d13, d14 - relative distance bet the mic pairs 1,2 , 1,3 and 1,4
> >> respectively. (x1,y1) - co-ordinates of mic 1 , (x2,y2) - co-ordinates
> of
> >> mic 2, (x3,y3) - co-ordinates of mic 3, (x4,y4) - co-ordinates of mic
> 4
>
> >> Solving these simultaneously will give me (xs,ys)
>
> >> Any suggestions on how to do this.. ??
>
> >Loads of papers on this. Do an IEEE Xplore search on acoustic source
> >location.
> >This is a non-linear problem but can be simplified in a number of
> >ways. There are a good many methods.
>
> Hi,
> I have done all my search and this is the equation what I have come up
> with; but how do i solve it in MATLAB.
> Any suggestions on it?
>
> Thank you. &#2013266080;

Look up "GPS equations," good books that describe how the GPS
system works should have the solution.

Julius
```
```On Sep 7, 6:52&#2013266080;pm, "maz_p5" <maz...@hotmail.com> wrote:
> >maz_p5 wrote:
>
> >> Hi,
>
> >> I am working on sound localization system. I want to find the
> co-ordinate
> >> of the sound source &#2013266080;by least mean square method in MATLAB. I have the
> >> co-ordinates of the 4 microphones and the relative distance between mic
> 1
> >> to the source to mic 2 to the source, i.e. the time delay*speed of
> sound.
>
> >> I even have the formulas but I have no clue on how to crack this:
> >> d12=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x2-xs)^2+(y2-ys)^2)
> >> d13=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x3-xs)^2+(y3-ys)^2)
> >> d14=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x4-xs)^2+(y4-ys)^2)
>
> >> d12, d13, d14 - relative distance bet the mic pairs 1,2 , 1,3 and 1,4
> >> respectively. (x1,y1) - co-ordinates of mic 1 , (x2,y2) - co-ordinates
> of
> >> mic 2, (x3,y3) - co-ordinates of mic 3, (x4,y4) - co-ordinates of mic
> 4
>
> >> Solving these simultaneously will give me (xs,ys)
>
> >> Any suggestions on how to do this.. ??
>
___________________________________________________________________
> Hi,
> I have done all my search and this is the equation what I have come up
> with; but how do i solve it in MATLAB.
> Any suggestions on it?
>
> Thank you. &#2013266080;
______________________________________________________________________

nonlinear equations, which is what I think you want to do..

http://www.mathworks.com/support/solutions/data/1-15NRJ.html?product=OP&solution=1-15NRJs
```
```On Sep 8, 7:36 am, Mandar Gokhale <stallo...@gmail.com> wrote:
> On Sep 7, 6:52 pm, "maz_p5" <maz...@hotmail.com> wrote:
>
> > >maz_p5 wrote:
>
> > >> Hi,
>
> > >> I am working on sound localization system. I want to find the
> > co-ordinate
> > >> of the sound source  by least mean square method in MATLAB. I have the
> > >> co-ordinates of the 4 microphones and the relative distance between mic
> > 1
> > >> to the source to mic 2 to the source, i.e. the time delay*speed of
> > sound.
>
> > >> I even have the formulas but I have no clue on how to crack this:
> > >> d12=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x2-xs)^2+(y2-ys)^2)
> > >> d13=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x3-xs)^2+(y3-ys)^2)
> > >> d14=sqrt((x1-xs)^2+(y1-ys)^2)-sqrt((x4-xs)^2+(y4-ys)^2)
>
> > >> d12, d13, d14 - relative distance bet the mic pairs 1,2 , 1,3 and 1,4
> > >> respectively. (x1,y1) - co-ordinates of mic 1 , (x2,y2) - co-ordinates
> > of
> > >> mic 2, (x3,y3) - co-ordinates of mic 3, (x4,y4) - co-ordinates of mic
> > 4
>
> > >> Solving these simultaneously will give me (xs,ys)
>
> > >> Any suggestions on how to do this.. ??
>
> ___________________________________________________________________> Hi,
> > I have done all my search and this is the equation what I have come up
> > with; but how do i solve it in MATLAB.
> > Any suggestions on it?
>
> > Thank you.
>
> ______________________________________________________________________
>
> nonlinear equations, which is what I think you want to do..
>
> http://www.mathworks.com/support/solutions/data/1-15NRJ.html?product=...

Actually you obviously have not done a good enough search. the one
thing you don't want to do is just go ahead and try and solve these
equation as they stand.
They need to be linearized first and there are numerous papers on
this.

For example Smith and Abel Closed-Form Least-Squares source location
estimation from range difference measurements.

IEEE Trans ASSP 35,12 Dec 1987. Loads more
```