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Volume 10
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

High-Precision Static Calibration of Capacitive Sensing in Inertial Sensors via Image-Based Displacement Measurement and Bias Modeling

by
Junxiang Li
1,2,3,
Dongxu Liu
4,5,6,
Wenqi Pan
1,2,3,
Shaoxin Wang
5,6,
Keqi Qi
5,6,* and
Peng Dong
1,6,*
1
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Hangzhou 310024, China
2
National Time Service Center, Chinese Academy of Sciences, Xi’an 710600, China
3
University of Chinese Academy of Sciences, Beijing 100049, China
4
School of Engineering Science, University of Science and Technology of China, Hefei 230026, China
5
National Microgravity Laboratory, Center for Gravitational Wave Experiment, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
6
Taiji Laboratory for Gravitational Wave Universe (Beijing/Hangzhou), University of Chinese Academy of Sciences (UCAS), Beijing 100049, China
*
Authors to whom correspondence should be addressed.
Instruments 2026, 10(3), 38; https://doi.org/10.3390/instruments10030038 (registering DOI)
Submission received: 13 May 2026 / Revised: 28 June 2026 / Accepted: 1 July 2026 / Published: 4 July 2026
(This article belongs to the Section Sensing Technologies and Precision Measurement)
Review Reports Versions Notes

Abstract

Space gravitational wave detection missions demand ultra-stable calibration of inertial sensor capacitive sensing. Conventional dynamic methods suffer from mechanical vibration noise and bias separation difficulties, while large-displacement operation introduces pronounced nonlinearity. This work proposes a static calibration method using an image-based displacement measurement system to establish a vibration-free benchmark. A subpixel edge detection algorithm locates the Test Mass and Electrode Housing edges with a repeatability of approximately 0.05 pixels, and the Test Mass geometry is independently calibrated by a Coordinate Measuring Machine (CMM, ±2 µm, k=2) to provide SI traceability. A nonlinear calibration model incorporating higher-order Taylor terms is developed, combined with a forward/reverse connection technique for composite bias modeling. Experimental validation at x0=665 µm (x0/d0≈0.665) demonstrated a gain coefficient repeatability of 0.01658% RMSPER and a combined expanded uncertainty of U≈2.18×10−51/µm (k=2). Intended as a complementary ground-based technique to dynamic calibration, this method avoids dynamic excitation-induced noise while establishing complete SI traceability, offering a reliable solution for ground validation and long-term monitoring of space inertial sensors.
Keywords: capacitive sensing; image-based measurement; static calibration; subpixel edge detection; CMM traceability; gain coefficient; bias model; space gravitational wave detection capacitive sensing; image-based measurement; static calibration; subpixel edge detection; CMM traceability; gain coefficient; bias model; space gravitational wave detection

Share and Cite

MDPI and ACS Style

Li, J.; Liu, D.; Pan, W.; Wang, S.; Qi, K.; Dong, P. High-Precision Static Calibration of Capacitive Sensing in Inertial Sensors via Image-Based Displacement Measurement and Bias Modeling. Instruments 2026, 10, 38. https://doi.org/10.3390/instruments10030038

AMA Style

Li J, Liu D, Pan W, Wang S, Qi K, Dong P. High-Precision Static Calibration of Capacitive Sensing in Inertial Sensors via Image-Based Displacement Measurement and Bias Modeling. Instruments. 2026; 10(3):38. https://doi.org/10.3390/instruments10030038

Chicago/Turabian Style

Li, Junxiang, Dongxu Liu, Wenqi Pan, Shaoxin Wang, Keqi Qi, and Peng Dong. 2026. "High-Precision Static Calibration of Capacitive Sensing in Inertial Sensors via Image-Based Displacement Measurement and Bias Modeling" Instruments 10, no. 3: 38. https://doi.org/10.3390/instruments10030038

APA Style

Li, J., Liu, D., Pan, W., Wang, S., Qi, K., & Dong, P. (2026). High-Precision Static Calibration of Capacitive Sensing in Inertial Sensors via Image-Based Displacement Measurement and Bias Modeling. Instruments, 10(3), 38. https://doi.org/10.3390/instruments10030038

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