Re: Triangulation Problem

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

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