I have 4 sensors capturing signal data. Signal distribution speed is constant and known. I have sensors positions in 3d space. Also, I have an amplitude/frequency decomposition for data received by each sensor over time (imagine a 3d terrain). Sensors capture signal from 2 moving sources.
Here on the image: blue dots are the sensors; red solid Capsules are emmiting objects; transparent red capsules are here to show signal wave propagation pattern; yellow cubes show projections from objects onto a plane formed by sensors; green "points" are desired positions on a plane.
- In real life emitters have pill-shaped form emitting in all directions, yet we can assume that they are points emitting spherical waves.
- In my particular case, we discuss audio waves via air to microphones (but I hoped for a general solution).
- We do not know the exact signal being transmitted from any of the emitters, yet we do know that there are only two signal sources with not equal positions in space and noise is filtered and extremely low.
- We can perform any kinds of transformations on top of received signals and we have exact time-data correlation per each sensor.
- Sensors form a square with side of length $l$
So how to triangulate sources positions on a 2d plane formed by 4 sensors - what is the algorithm?