Software
Multilateration
The Basics
Multilateration is a method of determining the coordinates of a point in N-dimensions given the distance between that point and N + 1 other points. In our case, working with a roughly 2-dimensional space, we use 3 nodes. Using the equation shown below you can determine the precise location of point in 2d space.
x, y = the coordinates of the audio source
xA, yA= the coordinates of listening node A
xB, yB= the coordinates of listening node B
C = the speed of sound
tA = the time of arrival at listening node A
tB = the time of arrival at listening node B
Implementaiton
Our algorithm is based upon these fundamentals and uses SymPy to calculate a system of these equations and uses Scipy to perform a least squares regression
A Bayesian Regression tool is used to determine the initial guesses for the numeric solution solver.
Signal Processing and TDoA Calculation
The Basics
Using simple magnitude to determine the difference in time of arrive of a sound event at each node is difficult because of noise in the data and drop-off in signal intensity as signals reach more distant microphone nodes.
Instead we use waveform matching to calculate correlation between signals, and assign them appropriate timestamps.
idk how the details of the implementation work Venkat should add some detail
