  This article presents a method that uses turn-by-turn beam position data and
k-modulation data to measure the calibration factors of beam position monitors
in high energy accelerators. In this method, new algorithms have been developed
to reduce the effect of coupling and other sources of uncertainty, allowing
accurate estimates of the calibration factors. Simulations with known sources
of errors indicate that calibration factors can be recovered with an accuracy
of 0.7% rms for arc beam position monitors and an accuracy of 0.4% rms for
interaction region beam position monitors. The calibration factors are also
obtained from LHC experimental data and are used to evaluate the effect this
calibration has on a quadrupole correction estimated with the action and phase
jump method for a interaction region of the LHC.
