# JGW-P2213991-v1

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

Document #:
JGW-P2213991-v1
Document type:
P
Submitted by:
Tak Lun Terrence Tsang
Updated by:
Tak Lun Terrence Tsang
Document Created:
16 Mar 2022, 12:26
Contents Revised:
16 Mar 2022, 12:26
DB Info Revised:
16 Mar 2022, 12:26
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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, $\mathcal{H}_\infty$ 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 $\mathcal{H}_\infty$ complementary filters suppress the super sensor noise equally close to the lower bound at all frequencies in logarithmic scale.
The $\mathcal{H}_\infty$ filters also provide better suppression of sensor noises compared to complementary filters pre-designed using traditional methods.
Files in Document:
Notes and Changes:
This version will be submitted for KAGRA CPC review.
The target journal of this paper is Classical and Quantum Gravity.
Referenced by:
• JGW-G2214020: H-infinity optimization of control filters
Publication Information:
The arXiv version is available at https://arxiv.org/abs/2111.14355.
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