Improvements in the optics measurement resolution for the LHC

Optics measurement algorithms which are based on the measurement of beam position monitor (BPM) turn-by-turn data are currently being improved in preparation for the commissioning of the LHC at higher energy. The turn-by-turn data of one BPM may be used more than once, but the implied correlations were not considered in the final error bar. In this paper the error propagation including correlations is studied for the statistical part of the uncertainty. The confidence level of the measurement is investigated analytically and with simulations.