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.
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