《粒子物理与核物理实验方法（二）》track_fit_rf.pdf

Computer munications 131 (2000) 95–108ate/cpcParticle tracks ?tted on the Riemann sphereA. Strandliea,b,?,,1,ühwirthc,2, B. Lillekjendliea,d,3aFaculty of Technology, Gj?vik College, . Box 191, N-2802 Gj?vik, NorwaybDepartment of Physics, University of Oslo, Oslo, NorwaycInstitute for High Energy Physics of the Austrian Academy of Sciences, Vienna, AustriadSINTEF, Oslo, NorwayReceived 18 January 2000AbstractWe present a novel method of ?tting trajectories of charged particles in high-energy physics particle detectors. The method?ts a circular arc to two-dimensional measurements by mapping the measurements onto the Riemann sphere and ?tting aplane to the transformed coordinates of the measurements. In this way, the non-linear task of circle ?tting, which in generalrequires the application of some iterative procedure, is turned into a linear problem which can be solved in a fast, direct andnon-iterative manner. We illustrate the usefulness of our approach by stating results from two simulation experiments of tracksfromthe ATLAS Inner Detector Transition Radiation Tracker (TRT). The ?rst experiment shows that with a signi?cantly lowerexecution time, the accuracy of the estimated track parameters is virtually as good as the accuracy obtained by applying anoptimal, non-linear least-squares procedure. The second experiment focuses on track parameter estimation in the presence ofambiguous measurements. For this purpose, we have developed a new version of the Elastic Arms algorithm called the ElasticPlanes algorithm. The algorithmproduces results which are almost identical to the results froman optimal version of the ElasticArms algorithm. putational cost of our algorithm, however, is much lower.?2000 Elsevier Science . All . IntroductionThe task of ?tting circular arcs to a set of measure-ments is of vital importance in high-energy physicsexperiments. This is due to the fact that many of thetracking systems in collider experiments are pu