Auxiliary-channel-assisted cross-talk noise removal in LISA Pathfinder

LISA Pathfinder (LPF) is the technology demonstration mission for the future Laser Interferometer Space Antenna (LISA). Besides the science interferometric channel, LPF is equipped with numerous auxiliary channels that monitor the instrument and environment disturbances, some of which contain information correlated with noise in the science channel. In this work, we investigate cross-talk noise subtraction in LPF using a frequency-domain transfer-function approach, in which the coherence between the science channel and auxiliary channels is used to estimate and remove correlated noise. The effectiveness of this method is first validated using simulated science and auxiliary channel data with a common disturbance. The simulation shows that the subtraction performance strongly depends on the auxiliary-channel noise level, providing a practical framework for determining the auxiliary-channel noise requirement needed to achieve a desired subtraction performance. This method is then used to analyze 9 auxiliary channels in publicly available LPF telemetry data. In the cross-talk dominated frequency band from $1\times10^{-2}$ to $6\times10^{-2}\,\mathrm{Hz}$, this method achieves cross-talk noise suppression comparable to the standard fitting based subtraction. Above $6\times10^{-2}\,\mathrm{Hz}$, it further suppresses the residual noise by avoiding the introduction of auxiliary-channel readout noise associated with the fitting procedure, resulting in better performance than the standard pipeline.