Optimal readout scheme for multi-degree-of-freedom seismometers

The low-frequency performance of advanced gravitational-wave detectors is limited by the seismic noise and the associated control noise. A six-degree-of-freedom seismometer has been proposed in (Mow-Lowry and Martynov 2019 Class. Quantum Grav. 36 245006) to improve the active isolation system. The standard readout scheme, which directly inverts the sensing matrix, gives dynamically independent but not statistically independent estimators for different degrees of freedom. This paper studies the optimal readout scheme by using optimal filters to combine the sensor outputs. The improvement is ultimately limited by the sensor noise and the ground motion, which decreases the correlation. For the real-time implementation, we have considered fitting the optimal filters numerically under the passive and causal constraint.