Track Fitting

Track fitting is an application of established statistical estimation procedures with well-known properties. For a long time, estimators based on the least-squares principle were—with some notable exceptions—the principal methods for track fitting. More recently, robust and adaptive methods have found their way into the reconstruction programs. The first section of the chapter presents least-squares regression, the extended Kalman filter, regression with breakpoints, general broken lines and the triplet fit. The following section discusses robust regression by the M-estimator, the deterministic annealing filter, and the Gaussian-sum filter for electron reconstruction. The next section deals with linearized fits of space points to circles and helices. The chapter concludes with a section on track quality and shows how to test the track hypothesis, how to detect outliers, and how to find kinks in a track.