I.

Three timbers of known length are set in the ground at known locations and 
meet at a calculated apex of an irregular triangular pyramid.  This formula 
also finds the two common points of intersection of three intersecting 
spheres.  It is also used to find GPS coordinates for a receiver from three 
satellites.  I have worked out the solution in this Excel 97 workbook:

http://www.geocities.com/jongiff2000/GPS_math.xls

II.

A gun is fired and the bullet swiped out a conical shock wave that is picked 
up by three microphones.  From the shock wave's arrival time differences 
between the microphones, both the source and destination of the bullet are 
calculated.  This solution is worked out in the Excel 97 workbook at:

http://www.geocities.com/jongiff2000/mach708.xls

Notes.

To view the different worksheets, click on the tabs in the lower left hand 
corner.  These Excel calculation engines can be embedded in other programs 
to give virtually real-time solutions to constantly changing inputs.

Illegal inputs generate corrupt results.  An illegal input requires the 
formula to calculate an impossible scenarion, such as a bullet at Mach 4 
arriving at each of the 3 microphones an hour apart when the microphones are 
only 10 feet apart.  The same is true for the GPS solution.  If it is 
impossible for the 3 legs of the pyramid to meet, such as distances of 100 
feet, 2 feet and 3 feet, the solution will be corrupt.  Legal data must be 
input for reasonable results.