《粒子物理与核物理实验方法（二）》track_rf_helix.pdf

Nuclear Instruments and Methods in Physics Research A 490 (2002) 366–378Helix ?tting by an extended Riemann ?tR. ,*, A. Strandlieb, W. WaltenbergeraaInstitute for High Energy Physics of the Austrian Academy of Sciences, Nikolsdorfer Gasse 18, A-1050 Vienna, AustriabEP Division, CERN, CH-1211 Gen"eve 23, SwitzerlandReceived 4 February 2002; received in revised form 5 April 2002; accepted 5 April 2002AbstractWe present an extension of the Riemann circle ?t to a helix ?t in space. The method is studied both in barrel- anddisk-type detectors. We show results from two simulation experiments, including parison to linear regression andto the Kalman ?lter. An implementation in C++ is Elsevier Science . All rights :; .+cKeywords:Circle ?t; Helix ?t; Riemann ?t; Kalman ?lter; Global least-squares ?t1. IntroductionThe ?tting of observations to a helical trackmodel will be a task of considerable importance inthe data analysis chain of the future LHCexperiments. As long as the ic ?eld in theinner tracker is suf?ciently homogeneous the trackmodel can be assumed to be a perfect helix. Thishas clear advantages over a more general trackmodel if the tracks are ?tted by (linearized) least-squares estimators like global regression [1] or theextended Kalman ?lter [2]. For simple detectorshapes (cylinders or planes), the track model puted explicitly, and so can the Jacobiansthat are needed to build the linear model for theglobal regression or to propagate the track statesand the associated covariance matrices in theKalman ?lter. For this reason, the helical track ?tis faster than a ?t with a more general track modelwhich requires numerical track-and-error propa-gation, for instance by a Runge–Kutta-typealgorithm [1,3].There are, however, certain drawbacks tolinearized least-squares estimators, the main onebeing that in many cases an approximate knowl-edge of the track is required in order to ?nd anexpansion point of suf?cient quali