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Re: Triangulation Problem

  • Subject: [mg2976] Re: Triangulation Problem
  • From: hans.steffani at (Hans Steffani)
  • Date: 18 Jan 1996 04:57:45 -0600
  • Approved:
  • Distribution: local
  • Newsgroups: wri.mathgroup
  • Organization: University of Technology Chemnitz, FRG
  • Sender: mj at

techie at (david hoare) writes:

>OK...Here's what should be an easy one - - well not for me...

>I am looking for the trigonometric / algebreic  formulae one would use
>to triangulate an unknown position, knowing 3 fixed points and the
>respective distances to the unknown point. (make sence?)
>Oh - in 3 dimensional space. 

I take it as math problem.

x0 is my position taking 3 komponents.
x1,x2, x3 are the (normalized) direktion vector of the landmarks taken from x0
x1f, x2f, x3f are the positionvektors in worldfixed koordinates.

 x0 + ri xi == xif
for 1<=i<=3 are the 9 equations for the 3 komponents of x0
and the (maybe uninteresting) 3 ri s. 
Oh! 2 landmarks are enough! And we also no the ri. That means
We have to look for least square methods which minimize
\sum_{i=1}^3 (x0 + ri xi - xif)^2

Maybe you ask some achitects or Geodaten (do not know the english
term) as they are used to solve problems like this.

Hans Friedrich Steffani
Hans Friedrich Steffani
Institut fuer Elektrische Maschinen und Antriebe
TU Chemnitz-Zwickau
e-mail: hans.steffani at

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