In conventional beam-based alignment (BBA) procedures, the relative alignment of a quadrupole to a nearby beam-position monitor is determined by finding a beam position in the quadrupole at which the closed orbit does not change when the quadrupole field is varied. The final focus magnets of the interaction regions (IR) of circular colliders often have some specialized properties that make it difficult to perform conventional beam-based alignment procedures. At the HERA interaction points, for example, these properties are the following: (a) the quadrupoles are quite strong and long. Therefore a thin lens approximation is quite imprecise. (b) The effects of angular magnet offsets become significant. (c) The possibilities to steer the beam are limited as long as the alignment is not within specifications. (d) The beam orbit has design offsets and design angles with respect to the axis of the low-beta quadrupoles. (e) Often quadrupoles do not have a beam-position monitor in their vicinity. Here we present a beam-based alignment procedure that determines the relative offset of the closed orbit from a quadrupole center without requiring large orbit changes or monitors next to the quadrupole. Taking into account the alignment angle allows us to reduce the sensitivity to optical errors by 1 to 2 orders of magnitude. We also show how the BBA measurements of all IR quadrupoles can be used to determine the global position of the magnets. The sensitivity to errors of this method is evaluated and its applicability to HERA is shown.
