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Levenberg-Marquardt for calibration

  • To: mathgroup at
  • Subject: [mg24342] Levenberg-Marquardt for calibration
  • From: David Lloret <david at>
  • Date: Sun, 9 Jul 2000 04:52:48 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

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 +

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

With regards,

David Lloret
Enginyer en Informatica
Centre de Visi=F3 per Computador
Universitat Autonoma de Barcelona
Catalunya (Spain)
david at

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