Sound localisation - multilateration or triangulation?

[gibbs-909]

Hello. I'm working on a project, where I'm trying to locate the position of a sound source. I've got an array of 4 microphones, 3 in a triangle and one out of plane. The microphones are all connected to a micro-controller which can accurately time stamp the incoming signals. Since the time the signal was produced is unknown, the system calculates the Time Difference of Arrival (TDoA) for each microphone, relative to the first mic that detected the signal. I know what microphones were triggered and the order they were triggered in, and they are at known positions. How can I use this information to get the x,y,z coordinates of the sound source? I've been looking into triangulation and multilateration but can't seem to figure it out. Any help is greatly appreciated.

[JohnyElloy]

To determine the coordinates of the sound source using time-of-arrival measurements from multiple microphones, you can employ the multilateration method. This involves determining the time differences of arrival of the signal at each microphone, converting them into distances, and forming a system of equations describing the geometric relationships between the sound source and the microphones. After that, you can solve this system of equations to obtain the coordinates of the sound source.