Micro Inertial Sensors: Calibration Methods, Technologies and Application

A special issue of Micromachines (ISSN 2072-666X). This special issue belongs to the section "E:Engineering and Technology".

Deadline for manuscript submissions: closed (30 November 2022) | Viewed by 23479

Special Issue Editor

Berkeley Sensor & Actuator Center, University of California, Berkeley, CA 94720, USA
Interests: analog and mixed-signal integrated circuit design; background calibration techniques for mems inertial sensors; frequency modulated gyroscopes

Special Issue Information

Dear Colleagues,

In the field of micro-inertial sensors, there have been significant efforts in both academia and industry, pushing boundaries of the technology for high-performance applications such as driverless cars and low-cost applications such as mobile and IoT devices. High performance micro-inertial sensors have recently reached navigation-grade performance thanks to novel fabrication techniques and new transducer topologies. Advances in MEMS and silicon photonics have produced novel inertial devices promising paradigm-shift in the future. In addition, consumer electronics have leveraged micro-inertial sensor technology with low-cost batch fabrication techniques, which has made inertial sensors one of the most prominent technologies in our everyday life. New system and circuit techniques enable ultra-low-power solutions for mobile devices and IoT applications. Background calibration techniques provide performance improvements without compromising size, cost, and power. This Special Issue seeks research papers and review articles covering the recent advances in inertial sensors with emphasis on calibration methods, novel system and circuit techniques, new transducer technologies, and applications.

Dr. Burak Eminoglu
Guest Editor

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Keywords

  • Inertial sensors
  • MEMS
  • Gyroscopes
  • Accelerometers
  • Magnetometers
  • Background calibration

Published Papers (10 papers)

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Research

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12 pages, 4843 KiB  
Article
Simulations and Experiments on the Vibrational Characteristics of Cylindrical Resonators with First Three Harmonic Errors
by Chen Liang, Kaiyong Yang, Yao Pan, Yunfeng Tao, Jingyu Li, Shilong Jin and Hui Luo
Micromachines 2022, 13(10), 1679; https://0-doi-org.brum.beds.ac.uk/10.3390/mi13101679 - 06 Oct 2022
Viewed by 1174
Abstract
A cylindrical resonator gyroscope is a kind of Coriolis gyroscope, which measures angular velocity or angle via processing of the standing wave. The symmetry of a cylindrical resonator is destroyed by different degrees of geometric nonuniformity and structural damage in the machining process. [...] Read more.
A cylindrical resonator gyroscope is a kind of Coriolis gyroscope, which measures angular velocity or angle via processing of the standing wave. The symmetry of a cylindrical resonator is destroyed by different degrees of geometric nonuniformity and structural damage in the machining process. The uneven mass distribution caused by the asymmetry of the resonator can be expressed in the form of a Fourier series. The first three harmonics will reduce the anti-interference ability of the resonator to the external vibration, as well as increase the angular random walk and zero-bias drift of the gyroscope. In this paper, the frequency split of different modes caused by the first three harmonic errors and the displacement of the center of the cylindrical resonator bottom plate are obtained by simulation, and the relationship between them is explored. The experimental results on five fused silica cylindrical resonators are consistent with the simulation, confirming the linear relationship between the n = 1 frequency split and second harmonic error. A method for evaluating the first three harmonic errors of fused silica cylindrical resonators is provided. Full article
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14 pages, 4053 KiB  
Article
Pedestrian Dead Reckoning with Low-Cost Foot-Mounted IMU Sensor
by Shunsei Yamagishi and Lei Jing
Micromachines 2022, 13(4), 610; https://0-doi-org.brum.beds.ac.uk/10.3390/mi13040610 - 13 Apr 2022
Cited by 5 | Viewed by 1920
Abstract
In this paper, we researched Pedestrian Dead Reckoning (PDR) with one foot-mounted IMU sensor. The issues of PDR are magnetism noise and accumulated error due to the noise included in acceleration and gyro data. Two methods are proposed in this paper. First is [...] Read more.
In this paper, we researched Pedestrian Dead Reckoning (PDR) with one foot-mounted IMU sensor. The issues of PDR are magnetism noise and accumulated error due to the noise included in acceleration and gyro data. Two methods are proposed in this paper. First is the gait-phase-estimation method with pitch angle for the Zero Velocity Update algorithm. Second is a method for avoiding accumulated errors by updating the roll and pitch angles with acceleration. The two experiments were conducted to examine the error of gait-phase estimation and distance estimations. The relative error of distance was about 7.40% in the case of walking straight and about 12.27% in the case of a shifting travel direction. Full article
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15 pages, 6090 KiB  
Article
Effect of Quadrature Control Mode on ZRO Drift of MEMS Gyroscope and Online Compensation Method
by Feng Bu, Shuwen Guo, Bo Fan and Yiwang Wang
Micromachines 2022, 13(3), 419; https://0-doi-org.brum.beds.ac.uk/10.3390/mi13030419 - 08 Mar 2022
Cited by 6 | Viewed by 2340
Abstract
The quadrature coupling error is an important factor that affects the detection output of microelectromechanical system (MEMS) gyroscopes. In this study, two quadrature error control methods, quadrature force-to-rebalance control (Mode I) and quadrature stiffness control (Mode II) were analyzed. We obtained the main [...] Read more.
The quadrature coupling error is an important factor that affects the detection output of microelectromechanical system (MEMS) gyroscopes. In this study, two quadrature error control methods, quadrature force-to-rebalance control (Mode I) and quadrature stiffness control (Mode II) were analyzed. We obtained the main factors affecting the zero-rate output (ZRO) under force-to-rebalance (FTR) closed-loop detection. The analysis results showed that the circuit phase delay in Mode I caused the quadrature channel to leak into the in-phase channel. However, in Mode II, the quadrature coupling stiffness was corrected in real time, which effectively improved the stability of the ZRO. The changes in the vibration displacement and Q-factor were the main factors for the ZRO drift in Mode II. Therefore, we propose an online compensation method for ZRO drift based on multiparameter fusion. The experimental results on a cobweb-like disk resonator gyroscope (CDRG) with a 340 k Q-factor showed that the bias instability (BI) of Mode II was significantly better than that of Mode I. After online compensation, the BI reached 0.23°/h, and the bias repeatability reached 3.15°/h at room temperature. Full article
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19 pages, 5241 KiB  
Article
Cold Starting Temperature Drift Modeling and Compensation of Micro-Accelerometer Based on High-Order Fourier Transform
by Yi Wang, Xinglin Sun, Tiantian Huang, Lingyun Ye and Kaichen Song
Micromachines 2022, 13(3), 413; https://0-doi-org.brum.beds.ac.uk/10.3390/mi13030413 - 05 Mar 2022
Cited by 5 | Viewed by 1743
Abstract
The traditional temperature modeling method is based on the full heating of the accelerometer to achieve thermal balance, which is not suitable for the cold start-up phase of the micro-accelerometer. For decreasing the complex temperature drift of the cold start-up phase, a new [...] Read more.
The traditional temperature modeling method is based on the full heating of the accelerometer to achieve thermal balance, which is not suitable for the cold start-up phase of the micro-accelerometer. For decreasing the complex temperature drift of the cold start-up phase, a new temperature compensation method based on a high-order Fourier transform combined model is proposed. The system structure and repeatability test of the micro digital quartz flexible accelerometer are provided at first. Additionally, we analyzed where the complex temperature drift of the cold start-up phase comes from based on the system structure and repeatability test. Secondly, a high-order temperature compensation model combined with K-means clustering and the symbiotic organisms search (SOS) algorithm is established with repeatability test data as training data. To verify the proposed temperature compensation model, a test platform was built to transmit the measured values before and after compensation with the proposed Fourier-related model and the other time-related model, which is also a model aiming at temperature compensation in the cold start-up phase. The experimental results indicate that the proposed method achieves better compensation accuracy compared with the traditional temperature compensation methods and the time-related compensation model. Furthermore, the compensation for the cold start-up phase has no effect on the original accuracy over the whole temperature range. The stability of the accelerometer can be significantly improved to about 30 μg in the start-up phase of different temperatures after compensation. Full article
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16 pages, 2572 KiB  
Article
Effects of Structural Dimension Variation on the Vibration of MEMS Ring-Based Gyroscopes
by Zhipeng Ma, Xiaoli Chen, Xiaojun Jin, Yiming Jin, Xudong Zheng and Zhonghe Jin
Micromachines 2021, 12(12), 1483; https://0-doi-org.brum.beds.ac.uk/10.3390/mi12121483 - 29 Nov 2021
Cited by 5 | Viewed by 1513
Abstract
This study investigated the effects of structural dimension variation arising from fabrication imperfections or active structural design on the vibration characteristics of a (100) single crystal silicon (SCS) ring-based Coriolis vibratory gyroscope. A mathematical model considering the geometrical irregularities and the anisotropy of [...] Read more.
This study investigated the effects of structural dimension variation arising from fabrication imperfections or active structural design on the vibration characteristics of a (100) single crystal silicon (SCS) ring-based Coriolis vibratory gyroscope. A mathematical model considering the geometrical irregularities and the anisotropy of Young’s modulus was developed via Lagrange’s equations for simulating the dynamical behavior of an imperfect ring-based gyroscope. The dynamical analyses are focused on the effects on the frequency split between two vibration modes of interest as well as the rotation of the principal axis of the 2θ mode pair, leading to modal coupling and the degradation of gyroscopic sensitivity. While both anisotropic Young’s modulus and nonideal deep trench verticality affect the frequency difference between two vibration modes, they have little contribution to deflecting the principal axis of the 2θ mode pair. However, the 4θ variations in the width of both the ring and the supporting beams cause modal coupling to occur and the degenerate 2θ mode pair to split in frequency. To aid the optimal design of MEMS ring-based gyroscopic sensors that has relatively high robustness to fabrication tolerance, a geometrical compensation based on the developed model is demonstrated to identify the geometries of the ring and the suspension. Full article
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16 pages, 5295 KiB  
Article
Real-Time Built-In Self-Test of MEMS Gyroscope Based on Quadrature Error Signal
by Rui Feng, Jiong Wang, Wei Qiao, Fu Wang, Ming Zhou, Xinglian Shang, Lei Yu, Liuhui Zhou and Shuwen Guo
Micromachines 2021, 12(9), 1115; https://0-doi-org.brum.beds.ac.uk/10.3390/mi12091115 - 16 Sep 2021
Cited by 3 | Viewed by 2794
Abstract
In high-reliability applications, the health condition of the MEMS gyroscope needs to be known in real time to ensure that the system does not fail due to the wrong output signal. Because the MEMS gyroscope self-test based on the principle of electrostatic force [...] Read more.
In high-reliability applications, the health condition of the MEMS gyroscope needs to be known in real time to ensure that the system does not fail due to the wrong output signal. Because the MEMS gyroscope self-test based on the principle of electrostatic force cannot be performed during the working state. We propose that by monitoring the quadrature error signal of the MEMS gyroscope in real time, an online self-test of the MEMS gyroscope can be realized. The correlation between the gyroscope’s quadrature error amplitude signal and the gyroscope scale factor and bias was theoretically analyzed. Based on the sixteen-sided cobweb-like MEMS gyroscope, the real-time built-in self-test (BIST) method of the MEMS gyroscope based on the quadrature error signal was verified. By artificially setting the control signal of the gyroscope to zero, we imitated several scenarios where the gyroscope malfunctioned. Moreover, a mechanical impact table was used to impact the gyroscope. After a 6000 g shock, the gyroscope scale factor, bias, and quadrature error amplitude changed by −1.02%, −5.76%, and −3.74%, respectively, compared to before the impact. The gyroscope failed after a 10,000 g impact, and the quadrature error amplitude changed −99.82% compared to before the impact. The experimental results show that, when the amplitude of the quadrature error signal seriously deviates from the original value, it can be determined that the gyroscope output signal is invalid. Full article
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11 pages, 6332 KiB  
Article
The Design, Simulation and Fabrication of an Omnidirectional Inertial Switch with Rectangular Suspension Spring
by Wenguo Chen, Rui Wang, Huiying Wang and Shulei Sun
Micromachines 2021, 12(4), 440; https://0-doi-org.brum.beds.ac.uk/10.3390/mi12040440 - 15 Apr 2021
Cited by 2 | Viewed by 1822
Abstract
An omnidirectional inertial switch with rectangular spring is proposed in this paper, and the prototype has been fabricated by surface micromachining technology. To evaluate the threshold consistency and stability of omnidirectional inertia switch, the stiffness of rectangular suspension springs is analyzed. The simulation [...] Read more.
An omnidirectional inertial switch with rectangular spring is proposed in this paper, and the prototype has been fabricated by surface micromachining technology. To evaluate the threshold consistency and stability of omnidirectional inertia switch, the stiffness of rectangular suspension springs is analyzed. The simulation result shows that the coupling stiffness of the rectangular spring suspension system in the non-sensitive direction is a little more than that in the sensitive direction, which indicated that the omnidirectional switching system’s stability is reinforced, attributed to the design of rectangular springs. The dynamic response simulation shows that the threshold of the omnidirectional inertial switch using the rectangular suspension spring has high consistency in the horizontal direction. The prototype of an inertial switch is fabricated and tested successfully. The testing results indicate even threshold distribution in the horizontal direction. The threshold acceleration of the designed inertial switch is about 58 g in the X direction and 37 g in the Z direction; the contact time is about 18 μs. Full article
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15 pages, 6014 KiB  
Article
A Novel Method for Estimating and Balancing the Second Harmonic Error of Cylindrical Fused Silica Resonators
by Yunfeng Tao, Yao Pan, Jianping Liu, Yonglei Jia, Kaiyong Yang and Hui Luo
Micromachines 2021, 12(4), 380; https://0-doi-org.brum.beds.ac.uk/10.3390/mi12040380 - 01 Apr 2021
Cited by 4 | Viewed by 1901
Abstract
The cylindrical resonator gyroscope (CRG) is a type of Coriolis vibratory gyroscope which measures the angular velocity or angle through the precession of the elastic wave of the cylindrical resonator. The cylindrical fused silica resonator is an essential component of the CRG, the [...] Read more.
The cylindrical resonator gyroscope (CRG) is a type of Coriolis vibratory gyroscope which measures the angular velocity or angle through the precession of the elastic wave of the cylindrical resonator. The cylindrical fused silica resonator is an essential component of the CRG, the symmetry of which determines the bias drift and vibration stability of the gyroscope. The manufacturing errors breaking the symmetry of the resonator are usually described by Fourier series, and most studies are only focusing on analyzing and reducing the fourth harmonic error, the main error source of bias drift. The second harmonic error also is one of the obstacles for CRG towards high precision. Therefore, this paper provides a chemical method to evaluate and balance the second harmonic error of cylindrical fused silica resonators. The relation between the frequency split of the n = 1 mode and the second harmonic error of the resonator is obtained. Simulations are performed to analyze the effects of the first three harmonic errors on the frequency splits. The relation between the location of the low-frequency axis of n = 1 mode and the heavy axis of the second harmonic error is also analyzed by simulation. Chemical balancing experiments on two fused silica resonators demonstrate the feasibility of this balancing procedure, and show good consistency with theoretical and simulation analysis. The second harmonic error of the two resonators is reduced by 86.6% and 79.8%, respectively. Full article
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22 pages, 15210 KiB  
Article
Multi-Function Microelectromechanical Systems Implementation with an ASIC Compatible CMOS 0.18 μm Process
by Chih-Hsuan Lin, Chao-Hung Song and Kuei-Ann Wen
Micromachines 2021, 12(3), 314; https://0-doi-org.brum.beds.ac.uk/10.3390/mi12030314 - 17 Mar 2021
Cited by 6 | Viewed by 1757
Abstract
A multi-function microelectromechanical system (MEMS) with a three-axis magnetometer (MAG) and three-axis accelerometer (ACC) function was implemented with an application-specific integrated circuit (ASIC)-compatible complementary metal-oxide-semiconductor (CMOS) 0.18 μm process. The readout circuit used the nested chopper, correlated double-sampling (CDS), noise reduction method; the [...] Read more.
A multi-function microelectromechanical system (MEMS) with a three-axis magnetometer (MAG) and three-axis accelerometer (ACC) function was implemented with an application-specific integrated circuit (ASIC)-compatible complementary metal-oxide-semiconductor (CMOS) 0.18 μm process. The readout circuit used the nested chopper, correlated double-sampling (CDS), noise reduction method; the frequency division multiplexing method; the time-division multiplexing method; and the calibration method. Sensing was performed by exciting the MEMS three-axis magnetometer at X/Y/Z axes mechanical resonant frequencies of 3.77/7.05/7.47 kHz, respectively. A modest die-level vacuum packaging resulted in in-plane and out-of-plane mechanical quality factors of 471–500 and 971–1000, respectively. The sensitivities of both the three-axis magnetometer with 2 mA driving current and the three-axis accelerometer were 7.1–10.7 uV/uT and 58.37–88.87 uV/ug. The resolutions of both the three-axis magnetometer with 2 mA driving current and three-axis accelerometer resolution were 44.06–87.46 nT/√Hz and 5.043–7.5 ng/√Hz. The resolution was limited by circuit noise equivalent acceleration (CNEM) and Brownian noise equivalent magnetic field (BNEM). Full article
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Review

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28 pages, 915 KiB  
Review
MEMS Inertial Sensor Calibration Technology: Current Status and Future Trends
by Xu Ru, Nian Gu, Hang Shang and Heng Zhang
Micromachines 2022, 13(6), 879; https://0-doi-org.brum.beds.ac.uk/10.3390/mi13060879 - 31 May 2022
Cited by 36 | Viewed by 4899
Abstract
A review of various calibration techniques of MEMS inertial sensors is presented in this paper. MEMS inertial sensors are subject to various sources of error, so it is essential to correct these errors through calibration techniques to improve the accuracy and reliability of [...] Read more.
A review of various calibration techniques of MEMS inertial sensors is presented in this paper. MEMS inertial sensors are subject to various sources of error, so it is essential to correct these errors through calibration techniques to improve the accuracy and reliability of these sensors. In this paper, we first briefly describe the main characteristics of MEMS inertial sensors and then discuss some common error sources and the establishment of error models. A systematic review of calibration methods for inertial sensors, including gyroscopes and accelerometers, is conducted. We summarize the calibration schemes into two general categories: autonomous and nonautonomous calibration. A comprehensive overview of the latest progress made in MEMS inertial sensor calibration technology is presented, and the current state of the art and development prospects of MEMS inertial sensor calibration are analyzed with the aim of providing a reference for the future development of calibration technology. Full article
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