  Interferometric gravitational wave detectors operate by sensing the
differential light travel time between free test masses. Correspondingly, they
are sensitive to anything that changes the physical distance between the test
masses, including physical motion of the masses themselves. In ground-based
detectors the test masses are suspended as pendula and, consequently, thermal
or other excitations of the suspension wires' violin modes lead to a strong,
albeit narrow-band, ``signal'' in the detector wave-band that can confound
attempts to observe gravitational waves.
  Here we describe the design of a Kalman filter that determines the
time-dependent vibrational state of a detector's suspension ``violin'' modes
from the detector output. From the estimated state we can predict that
component of the detector output due to suspension excitations, thermal or
otherwise, and subtractively remove those disturbances from the detector
output. We demonstrate the filter's effectiveness both through numerical
simulations and application to real data taken on the LIGO 40 M prototype
detector.
