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I've been trying to find the distance $d$ in this system where I only can know the distances $a0, a1, b0, b1, c0, c1$ but not the position of $A, B, C, P0, P1$. I tried 2D trilateration using nonlinear least squares method but I'm not being able to solve it.

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Is it possible to solve it? If it is, how can I do that?

Thanks in advance!

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up vote 1 down vote accepted

It seems to me that the only restriction you have is that the distance $d$ you are looking for has to be the third side of triangles with sides $a_0,a_1,d$; $b_0,b_1,d$; $c_0,c_1,d$.

But these constraints mean that $|a_0-a_1|\leq d\leq a_0+a_1$ and equivalent for $b$ and $c$. So you can only restrict $d$ to an interval, and with $d$ in that interval, you will be able to construct triangles (possibly degenerate) on a base of length $d$ which satisfy the constraints.

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I see your point, thanks! I cant upvote you because I don't have enough reputation. –  Eudald Sep 2 '12 at 20:59
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