The degree of knowns is equivalent to the degree of unknowns, however you 
put it.  A fourth mike is needed but only to determine which side of the 
plane of the first three mikes that the shot originated.

This problem was solved 25 years ago for the military, and it is patented. 
The solution exists and the system is used on choppers to return gunfire. 
It's also used by law enforcement to predict where a bullet will hit before 
it gets there.  It's already been done.  I only thought I'd try to solve it 
on my own.

George Sjoke, Polish, Vector & Tensor Analysis, University of Akron, 1983.

Look at another solution on my web site for GPS math.  It's a problem of 
determining the intersection of three spheres.  They intersect at two 
points, one on either side of the plane of the 3 satellites.

I guess there always has to be someone to refute the answer.  Dimensional 
Analysis checks out on all equations.


"Robert Israel" <israel@math.MyUniversitysInitials.ca> wrote in message 
news:rbisrael.20081231205256$2fcc@news.acm.uiuc.edu...
>
>> Using 3 microphones and some electronics, the source and destination of a
>> flying bullet can be calculated.  Here's how:
>>
>> http://mypeoplepc.com/members/jon8338/math/id21.html
>>
>
> Nope.   Too many variables and two few data points.  You really only have
> two degrees of freedom in the data (Delta t_{12} and Delta t_{13} in your
> notation, since Delta t_{23} = Delta t_{13} - Delta t_{12}), and there
> are four degrees of freedom in the result you want (two for the unit 
> direction
> vector of the bullet, and another two for where the path intersects
> a plane normal to that vector).  And all this is under the doubtful 
> assumption
> that you know the speed of the bullet.
> -- 
> Robert Israel              israel@math.MyUniversitysInitials.ca
> Department of Mathematics        http://www.math.ubc.ca/~israel
> University of British Columbia            Vancouver, BC, Canada