Automatic cross-talk removal from multi-channel data

TL;DR

This paper introduces a method to remove environmental interference from a primary signal in multi-channel data, improving the extraction of the true signal by estimating and subtracting unknown linear environmental couplings.

Contribution

It presents a novel technique to estimate unknown linear transfer functions for environmental noise removal in multi-channel signals, demonstrated on gravitational-wave detector data.

Findings

Effective removal of environmental noise from the primary channel

Estimation of unknown transfer functions improves signal clarity

Method reduces variance of the residual noise

Abstract

A technique is described for removing interference from a signal of interest ("channel 1") which is one of a set of N time-domain instrumental signals ("channels 1 to N"). We assume that channel 1 is a linear combination of "true" signal plus noise, and that the "true" signal is not correlated with the noise. We also assume that part of this noise is produced, in a poorly-understood way, by the environment, and that the environment is monitored by channels 2 to N. Finally, we assume that the contribution of channel n to channel 1 is described by an (unknown!) linear transfer function R_n(t-t'). Our technique estimates the R_i and provides a way to subtract the environmental contamination from channel 1, giving an estimate of the "true" signal which minimizes its variance. It also provides some insights into how the environment is contaminating the signal of interest. The method is illustrated with data from a prototype interferometric gravitational-wave detector, in which the channel of interest (differential displacement) is heavily contaminated by environmental noise (magnetic and seismic noise) and laser frequency noise but where the coupling between these signals is not known in advance.