Track fitting with ambiguities and noise: a study of elastic tracking and non-linear filters

We present a study of track fitting in the presence of ambiguous meas urements and noise. We consider four methods for solving the resultin g assignment problem, two elastic arm algorithms and two non-linear f ilters, including a novel development, the Deterministic Annealing Fi lter. We describe their basic features and investigate their relation ships with each other and with other popular estimators, in particula r with the EM algorithm. The performance of the methods is optimized by means of several simulation experiments. We study the influence of the annealing schedule on the performance and show that the applicat ion of advanced minimization methods is required in order to obtain r eliable estimates of the track parameters. We compare the relative ef ficiencies and the computational costs of the four methods both unde r ideal conditions and with noise. A final experiment under realisti c conditions focusses on the robustness of the proposed approach.