Data conditioning for gravitational wave detectors: A Kalman filter for regressing suspension violin modes

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, in order that they be approximately “free” above the pendulumn frequency. Still, thermal or other excitations of the suspension wires’ violin modes do impart a force on the masses that appears as a strong, albeit narrow-band, “signal” in the detectors waveband. Gravitational waves, on the other hand, change the distance between the test masses without disturbing the suspensions. Consequently, violin modes can confound attempts to observe gravitational waves since “signals” that are correlated with a disturbance of the suspension violin modes are not likely due to a passing gravitational wave. Here we describe the design of a Kalman filter that determines the time-dependent vibrational state of a detector’s suspension “violin” modes from time dependent observations of the detector output. From the estimated state we can predict that component of the detector output due to suspension excitations, thermal or otherwise. The wire state can be examined for evidence of suspension disturbances that might, in the absence of such a diagnostic, be mistaken for gravitational wave signals. Additionally, from the wire state we can subtractively remove the contribution from suspension disturbances, thermal or otherwise, from the detector output, leaving a residual free from this instrumental artifact. We demonstrate the filter’s effectiveness both through numerical simulations and application to real data taken on the LIGO 40 M prototype detector.