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.
Post by Robert IsraelPost by JonUsing 3 microphones and some electronics, the source and destination of a
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.
--
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada