  Longitudinal control signals used to keep gravitational wave detectors at a
stable operating point are often affected by modulations from test mass
misalignments leading to an elevated noise floor ranging from 50 to 500 Hz.
Nonstationary noise of this kind results in modulation sidebands and increases
the number of glitches observed in the calibrated strain data. These artifacts
ultimately affect the data quality and decrease the efficiency of the data
analysis pipelines looking for astrophysical signals from continuous waves as
well as the transient events. In this work, we develop a scheme to subtract one
such bilinear noise from the gravitational wave strain data and demonstrate it
at the GEO 600 observatory. We estimate the coupling by making use of
narrow-band signal injections that are already in place for noise projection
purposes and construct a coherent bilinear signal by a two-stage system
identification process. We improve upon the existing filter design techniques
by employing a Bayesian adaptive directed search strategy that optimizes across
the several key parameters that affect the accuracy of the estimated model. The
scheme takes into account the possible nonstationarities in the coupling by
periodically updating the involved filter coefficients. The resulting
postoffline subtraction leads to a suppression of modulation sidebands around
the calibration lines along with a broadband reduction of the midfrequency
noise floor. The observed increase in the astrophysical range and a reduction
in the occurrence of nonastrophysical transients suggest that the above method
is a viable data cleaning technique for current and future generation
gravitational wave observatories.

General Relativity and Quantum Cosmology;Instrumentation and Methods for Astrophysics;Instrumentation and Detectors