3D closed-form triangulation solution

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SUMMARY

The discussion centers on finding a closed-form solution for determining the coordinates of a target point in 3D space using trilateration. The user has three known points and the distances to the target point, resulting in three nonlinear equations. The solution requires understanding the mathematical principles of trilateration rather than triangulation, which involves angles. The user is seeking a straightforward method to solve these equations.

PREREQUISITES
  • Understanding of 3D coordinate systems
  • Knowledge of nonlinear equations
  • Familiarity with trilateration principles
  • Basic algebra and geometry skills
NEXT STEPS
  • Research closed-form solutions for trilateration in 3D space
  • Study methods for solving nonlinear equations
  • Explore mathematical modeling techniques for distance-based problems
  • Examine existing algorithms for trilateration, such as the least squares method
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Mathematicians, engineers, computer scientists, and anyone involved in 3D modeling or spatial analysis will benefit from this discussion.

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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