Track element merging strategy and vertex fitting in complex modular detectors

For the purpose of this paper it is assumed that the problem of associating the many hundreds and often ambiguous coordinates to particle track candidates has already been solved. Then it turns out that the requirements of track fitting, i.e. estimation of track parameters, are met best by the least-squares estimate, being rather fast, flexible and relatively robust. In practice, it turns out that a tree-like hierarchical strategy is the best one to assemble coordinates or track elements from many particles to a common vertex. Therefore sect. 2 discusses different attempts to assemble individual track elements to complete tracks in the context of a complex detector with possibly radically different modules. It should clarify the precise meaning, advantages and disadvantages of all methods discussed. Sect. 3 describes a novel algorithm to evaluate the common vertex in the presence of high track multiplicities. Its main advantage is the fact that the number of required arithmetic operations is proportional to n (number of tracks) if only the estimate and the chi2 are computed and proportional to n2 if the covariance matrix of the estimate is computed as well. (orig./HSI)