# Trilateration in 3D with signal strengths

I'm having a hard time getting my head around the maths to locate a target in 3D given a number of known points (4 or more) and a value that indicates the signal strength (range 0–100).

I've looked at the simpler answer in the 2D case but I'm unsure how to generalise the idea of normalising the signal strengths for the 3D case. It might even be that this answer is too simple for my requirements. I know that in my case the signal strength is proportional to distance-2 but do not know the propagation constant.

I've also seen this question, but it's not quite what I'm after as I want to use the signal strengths from a larger number of nodes to improve the estimate.

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Sorry, no answer, but I think if you're trying to improve the estimate (in the overdetermined case), you're going to have to include some form of per-measurement error. Good luck with it. – BradHards Aug 4 '12 at 22:47
You could try to post the same question in math.stackexchange.com. – Chau Aug 5 '12 at 9:44

The solution here was a simple one. I have a number of signal values, `S`, which are proportional to the distance `d`:
The function `f` is known, and the constant `k` cancels out in the interpolation, so all that's needed is to apply the inverse of the function to each of the magnitudes before normalisation.