Particle tracks fitted on the Riemann sphere

We present a novel method of fitting trajectories of charged particles in h igh-energy physics particle detectors. The method fits a circular are to tw o-dimensional measurements by mapping the measurements onto the Riemann sph ere and fitting a plane to the transformed coordinates of the measurements. In this way, the non-linear task of circle fitting, which in general requi res the application of some iterative procedure, is turned into a linear pr oblem which can be solved in a fast, direct and non-iterative manner. We il lustrate the usefulness of our approach by stating results from two simulat ion experiments of tracks from the ATLAS Inner Detector Transition Radiatio n Tracker (TRT). The first experiment shows that with a significantly lower execution time, the accuracy of the estimated track parameters is virtuall y as good as the accuracy obtained by applying an optimal, non-linear least -squares procedure. The second experiment focuses on track parameter estima tion in the presence of ambiguous measurements, For this purpose, we have d eveloped a new version of the Elastic Arms algorithm called the Elastic Pla nes algorithm, The algorithm produces results which are almost identical to the results from an optimal version of the Elastic Arms algorithm. The com putational cost of our algorithm, however, is much lower. (C) 2000 Elsevier Science B.V. All rights reserved.