Microelectromechanical systems (MEMS) gyroscopes are valued for low cost, compact size, light weight, and low power consumption, which has made them important in drones, smart devices, autonomous vehicles, and navigation systems. Among their measurement schemes, force-to-rebalance (FTR) mode is widely used because of its precision and stability. But phase errors can emerge in excitation circuits, pickoff circuits, and digital processing, altering frequency locking, scale factor, and zero-rate output (ZRO). Earlier studies often corrected only part of the problem and did not fully distinguish between error locations or mechanisms. Based on these challenges, there is a need to carry out in-depth research on how phase errors affect different control loops in MEMS gyroscopes and how they can be accurately calibrated.
Researchers from Jiangsu University of Science and Technology, Southeast University, Beijing Institute of Aerospace Control Devices, Nanjing Institute of Technology, the Shanghai Institute of Microsystem and Information Technology of the Chinese Academy of Sciences, the University of Chinese Academy of Sciences, and Beijing Institute of Technology reported (DOI: 10.1038/s41378-025-01144-6) in 2026 in Microsystems & Nanoengineering that phase errors in MEMS gyroscopes do not contribute equally to performance loss. Their work on FTR rate measurement shows that some errors mainly disturb drive-frequency locking, while others directly degrade scale factor and ZRO in the sense loop.
The team analyzed three key loops: the drive modal control loop, the FTR rate control loop, and the quadrature stiffness correction loop. In drive mode, they found that phase errors in the feedback and forward paths shift the locking point away from the true resonant frequency and increase excitation amplitude. However, with feedthrough suppressed, those drive-mode errors had little discernible influence on FTR rate performance, regardless of whether compensation was applied. The more consequential findings came from sense mode. There, the feedback-path phase error strongly affected scale factor and ZRO, while the forward-path phase error had a much smaller effect. Bandwidth changed little in either case. The researchers also showed that these errors vary with temperature from -20 °C to 50 °C, meaning calibration must be reconsidered across operating conditions rather than fixed once and assumed stable forever.
“This study makes one point especially clear: better gyroscopes will not come from correcting everything in the same way, but from identifying which phase errors actually damage the signal,” the findings suggest. “Once those dominant errors are isolated, engineers can focus compensation where it matters most—improving scale factor, protecting zero-rate stability, and avoiding unnecessary correction effort elsewhere.” Framed this way, the work offers not just a diagnosis of error sources, but a more practical roadmap for designing gyroscopes that remain reliable when real-world conditions begin to shift.
The study has clear practical relevance for compact navigation, intelligent vehicles, and other precision electronics that rely on stable angular-rate sensing. By ranking the influence of different phase errors and pairing that analysis with calibration procedures, the work provides a useful strategy for improving MEMS gyroscope performance without demanding major hardware redesign. It also highlights the importance of temperature-aware compensation in real deployment. As MEMS devices move deeper into autonomous systems and high-performance sensing platforms, this kind of targeted error analysis could help push miniature gyroscopes toward greater reliability in the field.
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Referneces
DOI
10.1038/s41378-025-01144-6
Original Source URL
https://doi.org/10.1038/s41378-025-01144-6
Funding information
This work was supported in part by Basic Science (Natural Science) Research Project of Higher Education Institutions in Jiangsu Province of China under Grant 23KJB590001, in part by Foundation of Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, China under Grant SEU-MIAN-202403, in part by National Key Research and Development Program of China under Grant No.2022YFB3205000, in part by National Natural Science Foundation of China under Grant No.52475586 and U2230206.
About Microsystems & Nanoengineering
Microsystems & Nanoengineering is an online-only, open access international journal devoted to publishing original research results and reviews on all aspects of Micro and Nano Electro Mechanical Systems from fundamental to applied research. The journal is published by Springer Nature in partnership with the Aerospace Information Research Institute, Chinese Academy of Sciences, supported by the State Key Laboratory of Transducer Technology.