3D closed-form triangulation solution

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The discussion focuses on finding a closed-form solution for determining the coordinates of a target point in 3D space using known distances from three reference points. The user has established that the problem involves nonlinear equations derived from these distances. They seek a straightforward method to solve for the target point's coordinates without resorting to complex numerical methods. A key distinction is made between triangulation, which involves angles, and trilateration, which relies solely on distance measurements. The conversation highlights the need for resources or methods specifically addressing trilateration in 3D space.
Lagomorph
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Hi,
I have 3 points in 3D space whose positions are known to me and a third target point, whose position I am trying to find. I can obtain the distance between each of the 3 points and the target point. I can easily get 3 equations to obtain the 3 coordinate variables, but these equations are nonlinear.

Do you guys know how I could get a simple, closed-form solution for each of the coordinate variables defining the target point? I figured that this would be a fairly standard problem, but I'm having finding anything written about it.

Thanks in advance.
 
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This isn't triangulation. Triangulation involves angles. You want something involving distance ... trilateration. See this wiki article on http://en.wikipedia.org/wiki/Trilateration" .
 
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