  The inner silicon detector of the Compact Muon Solenoid experiment (CMS) at
CERN's LHC consists of 16588 modules. Charged-particle tracks in the detector
are used to improve the accuracy to which the position and orientation of the
modules is known. This contribution focuses on the Millepede-II algorithm, one
of the two alignment algorithms used by CMS. Recently an advanced track model
has been introduced into the CMS alignment procedure, which is based on the
"Broken Lines" model and is able to take multiple Coulomb scattering in the
detector material properly into account. We show the unique approach needed for
solving the alignment problem in a reasonable amount of time. Emphasis is given
to the mathematical treatment of the problem.
