Re: Triangulation Problem

• To: mathgroup at smc.vnet.net
• Subject: [mg2976] Re: Triangulation Problem
• From: hans.steffani at e-technik.tu-chemnitz.de (Hans Steffani)
• Date: Thu, 18 Jan 1996 02:56:40 -0500
• Organization: University of Technology Chemnitz, FRG

techie at io.org (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.

now:
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 e-technik.tu-chemnitz.de

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