  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.
