Optimal sensor fusion method for active vibration isolation systems in ground-based gravitational-wave detectors

Abstract

Sensor fusion is a technique used to combine sensors with different noise characteristics into a super sensor that has superior noise performance. To achieve sensor fusion, complementary filters are used in current gravitational-wave detectors to combine relative displacement sensors and inertial sensors for active seismic isolation. Complementary filters are a set of digital filters, which have transfer functions that are summed to unity. Currently, complementary filters are shaped and tuned manually rather than being optimized. They can be sub-optimal and hard to reproduce for future detectors. In this paper, optimization is proposed for synthesizing optimal complementary filters. The complementary filter design problem is converted into an optimization problem that seeks minimization of an objective function equivalent to the maximum difference between the super sensor noise and the lower bound in logarithmic scale. The method is exemplified with three cases, which simulate the sensor fusion between a relative displacement sensor and an inertial sensor. In all cases, the complementary filters suppress the super sensor noise equally close to the lower bound at all frequencies in logarithmic scale. The filters also provide better suppression of sensor noises compared to complementary filters pre-designed using traditional methods.