Apr 1, 2000
Track Fitting on the Riemann Sphere
- Department of Technology, Gjøvik College, and Department of Physics, University of Oslo.
- Department of Technology, Gjøvik College.
We present a novel method of fitting trajectories of charged particles in
high-energy physics particle detectors. The method fits a circular arc to
two-dimensional measurements by mapping the measurements onto the Riemann
sphere and fit a plane to the transformed coordinates of the measurements.
In this way, the non-linear task of circle fitting, which in general requires
the application of some iterative procedure, is turned into a linear problem
which can be solved in a fast, direct and non-iterative manner.
We illustrate the usefulness of our approach by stating results from
simulation experiments of tracks from the ATLAS Inner Detector Transition
Radiation Tracker (TRT). The experiments show that the accuracy of the estimated
track parameters is virtually as good as the accuracy obtained by applying an
optimal, non-linear least-squares procedure. The computational cost of our
method, however, is significantly lower.
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