Levenberg-Marquardt for calibration

*To*: mathgroup at smc.vnet.net*Subject*: [mg24342] Levenberg-Marquardt for calibration*From*: David Lloret <david at cvc.uab.es>*Date*: Sun, 9 Jul 2000 04:52:48 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Dear All, I trying to calibrate a stylus attached to a miniBird tracker. The tracker gives the 3-d position and orientation of a small cube, which I attach to a stylus to make it a pointer device. As far as I know, literature stands for Levenberg-Marquardt to solve the parameters of the calibration, i.e., the transformation from the mobile cube to the stylus. I use several models to calibrate: a plane, a fixed point and a line. The problem is, Mathematica's package does not provide: a) any way to scale parameters, this is, to make 0.1 rad more important than 0.1 mm. b) I can use only 1 equation, xisquare == y - f(x; a), while sometimes I have more than one. Thus, I have to combine them and I am not too sure that e.g. squaring and adding them is the best solution ( f == f1^2 + f2^2) Do you know any easy way to solve this problems? I am prepared to dive into the package, but it is hard for newbiers. Any help will be welcome, because my next step will be to calibrate an echographer attached to the tracker. And that gives quite a few more parameters... With regards, David Lloret Enginyer en Informatica Centre de Visi=F3 per Computador Universitat Autonoma de Barcelona Catalunya (Spain) david at cvc.uab.es