K-Modulation Developments via Simultaneous Beam Based Alignment in the LHC

A parasitic effect of k-modulation is that if the modulated quadrupole has an offset the modulation results in a dipole like kick forcing the beam on a new orbit. This paper presents a new method using the orthonormality of singular value decomposition that uses this new orbit to estimate the offset. This could be used to measure misalignments or crossing angles but could also help improve k-modulation \beta measurements by predicting the parasitic tune change caused by the new orbit not passing through the centre of the sextupoles.