Software alignment for tracking detectors

Tracking detectors in high-energy physics experiments require an accurate determination of a large number of alignment parameters in order to allow a precise reconstruction of tracks and vertices. In addition to the initial optical survey and corrections for electronics and mechanical effects the use of tracks in a special software alignment is essential. A number of different methods is in use, ranging from simple residual-based procedures to complex fitting systems with many thousands of parameters. The methods are reviewed with respect to their mathematical basis and accuracy, and to aspects of the practical realization.