If the three microphones are wired in parallel to feed the input, a single trace digital storage 1kHz oscilloscope can be used instead of a three trace. The analog input goes to an ADC (Analgog-to-Digital Converter), which is fed to a Parallel-to-Serial multiplexer, which goes into the pipeline of a USB port and the signal analyzed by code to extract the time differences between peaks from the microphone signals.
The signal is compared to a database of projectile signatures for various types of bullets and their speeds. This is used to estimate the speed of the bullet which is necessary for calculations. In addition the distance from the gun to the plane of the microphones is estimated from topographical maps of the vicinity. If the microphones are mounted on a helicopter and the gunman is on the ground, this distance would be the altitude of the helicopter.
The math determines the point on the plane of the 3 microphones where the bullet intersects and the unit vector of the line of fire. If you go to that point and aim in the opposite direction of the unit vector, you can send return fire and hit the shooter.
The mathematical development is given in the form of an Excel 97 worksheet downloadable for free at,
You have to have Excel installed on your computer for the browser to open up the worksheet. Once you have it opened, clik File and Save As on the browser and you can have a copy of your own. If you don't have Excel but would like to see the math behind the Excel equations, you can it them at the web page,
Excel can do many Linear Algebra operations like Inverse, Transpose and Multiply of matrixes and is pretty handy at it.
Also refere to the Triangulation Solver at
in relationship with this problem. 3 laser beams located at the microphones can trace the line of fire from the plane of the microphones where the bullet intersects to the gunman and return fire. The Triangulation Solver is also useful for GPS tracking.
I personally derived all of these solutions and they are under no patent or copyright by me. I only ask that if you use them, that you do nothing for me in return.
Jon Giffen