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Inertial Sensors and Applications

A topical collection in Sensors (ISSN 1424-8220). This collection belongs to the section "Physical Sensors".

Viewed by 45584

Editors

Dr. Young Soo Suh

E-Mail Website
Collection Editor
Department of Electrical Engineering, University of Ulsan, 93 Daehak-ro, Nam-gu, Ulsan (44610), Korea
Interests: attitude and motion estimation using inertial and vision sensors; personal navigation systems
Dr. Angelo Maria Sabatini

E-Mail Website
Collection Editor
The BioRobotics Institute, Scuola Superiore Sant’Anna, Piazza Martiri della Libertà 33, 56124 Pisa, Italy
Interests: wearable sensor systems for human motion capture; magneto-inertial measurement units; computational methods for wearable sensor systems; multisensor fusion
Special Issues, Collections and Topics in MDPI journals

Topical Collection Information

Dear Colleagues,

In the past, inertial sensors had limited use, e.g., in military applications, since they are bulky and expensive. Mainly thanks to micro-electro-mechanical systems (MEMS) technology, inertial sensors are becoming smaller and cheaper. This is leading to the widespread use of inertial sensor to estimate attitude and motion in many fields, such as healthcare, sports, and entertainment. Since almost every person has a smartphone or a smartwatch which contain inertial sensors, the application of inertial sensors is expected to increase rapidly.

Regarding recent research on inertial sensors, classical filtering algorithms (which are used in missiles and satellites) have been successfully used for many applications such as attitude estimation of UAV, human gait analysis, sport motion estimation, and personal navigation systems. Then, new algorithms have been proposed to handle specific problems. Recently, machine learning-based algorithms have been increasingly used. Fusion with other sensors (in particular vision sensors) is also a hot research topic.

The aim of this Special Issue is to collect new research and developments in the field of inertial sensor-based algorithms and applications. We invite original contributions, so that current research trends can be presented in this collection. 

Dr. Young Soo Suh
Dr. Angelo Maria Sabatini
Guest Editors

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Published Papers (19 papers)

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2024

Jump to: 2023, 2022, 2021, 2020

13 pages, 3906 KiB  
Article
High-Precision Atom Interferometer-Based Dynamic Gravimeter Measurement by Eliminating the Cross-Coupling Effect
by Yang Zhou, Wenzhang Wang, Guiguo Ge, Jinting Li, Danfang Zhang, Meng He, Biao Tang, Jiaqi Zhong, Lin Zhou, Runbing Li, Ning Mao, Hao Che, Leiyuan Qian, Yang Li, Fangjun Qin, Jie Fang, Xi Chen, Jin Wang and Mingsheng Zhan
Sensors 2024, 24(3), 1016; https://0-doi-org.brum.beds.ac.uk/10.3390/s24031016 - 04 Feb 2024
Viewed by 726
Abstract
A dynamic gravimeter with an atomic interferometer (AI) can perform absolute gravity measurements with high precision. AI-based dynamic gravity measurement is a type of joint measurement that uses an AI sensor and a classical accelerometer. The coupling of the two sensors may degrade [...] Read more.
A dynamic gravimeter with an atomic interferometer (AI) can perform absolute gravity measurements with high precision. AI-based dynamic gravity measurement is a type of joint measurement that uses an AI sensor and a classical accelerometer. The coupling of the two sensors may degrade the measurement precision. In this study, we analyzed the cross-coupling effect and introduced a recovery vector to suppress this effect. We improved the phase noise of the interference fringe by a factor of 1.9 by performing marine gravity measurements using an AI-based gravimeter and optimizing the recovery vector. Marine gravity measurements were performed, and high gravity measurement precision was achieved. The external and inner coincidence accuracies of the gravity measurement were ±0.42 mGal and ±0.46 mGal after optimizing the cross-coupling effect, which was improved by factors of 4.18 and 4.21 compared to the cases without optimization. Full article
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2023

Jump to: 2024, 2022, 2021, 2020

18 pages, 3376 KiB  
Article
Unsupervised Noise Reductions for Gravitational Reference Sensors or Accelerometers Based on the Noise2Noise Method
by Zhilan Yang, Haoyue Zhang, Peng Xu and Ziren Luo
Sensors 2023, 23(13), 6030; https://0-doi-org.brum.beds.ac.uk/10.3390/s23136030 - 29 Jun 2023
Viewed by 1047
Abstract
Onboard electrostatic suspension inertial sensors are important applications for gravity satellites and space gravitational-wave detection missions, and it is important to suppress noise in the measurement signal. Due to the complex coupling between the working space environment and the satellite platform, the process [...] Read more.
Onboard electrostatic suspension inertial sensors are important applications for gravity satellites and space gravitational-wave detection missions, and it is important to suppress noise in the measurement signal. Due to the complex coupling between the working space environment and the satellite platform, the process of noise generation is extremely complex, and traditional noise modeling and subtraction methods have certain limitations. With the development of deep learning, applying it to high-precision inertial sensors to improve the signal-to-noise ratio is a practically meaningful task. Since there is a single noise sample and unknown true value in the measured data in orbit, odd–even sub-samplers and periodic sub-samplers are designed to process general signals and periodic signals, and adds reconstruction layers consisting of fully connected layers to the model. Experimental analysis and comparison are conducted based on simulation data, GRACE-FO acceleration data, and Taiji-1 acceleration data. The results show that the deep learning method is superior to traditional data smoothing processing solutions. Full article
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12 pages, 674 KiB  
Communication
Multi-Harmonic Modulation in a Fiber-Optic Gyroscope
by Martin Miranda, Nobuyuki Takei, Yuki Miyazawa and Mikio Kozuma
Sensors 2023, 23(9), 4442; https://0-doi-org.brum.beds.ac.uk/10.3390/s23094442 - 01 May 2023
Cited by 1 | Viewed by 2192
Abstract
Optimizing the bias modulation of a fiber-optic gyroscope is crucial to improving its precision. In this study, we propose and demonstrate the use of multiple harmonics of sinusoidal modulation as an intermediate alternative to the widely used modulation methods: sinusoidal and square-wave modulation. [...] Read more.
Optimizing the bias modulation of a fiber-optic gyroscope is crucial to improving its precision. In this study, we propose and demonstrate the use of multiple harmonics of sinusoidal modulation as an intermediate alternative to the widely used modulation methods: sinusoidal and square-wave modulation. We show that this alternative integrates the advantages of each modulation method by providing a smooth modulation that produces a clean, spike-free output and a satisfactory signal-to-noise ratio. By using three harmonics of modulation in combination with a high frequency to reduce thermal phase noise, we obtained an angular random walk of 5.2(2)μdeg/h and a bias instability of ∼10μdeg/h. This is the highest performance ever reported for fiber-optic gyroscopes. Full article
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2022

Jump to: 2024, 2023, 2021, 2020

21 pages, 6816 KiB  
Article
Identifying the Inertial Properties of a Padel Racket: An Experimental Maneuverability Proposal
by Carlos Blanes, Antonio Correcher, Pablo Beltrán and Martin Mellado
Sensors 2022, 22(23), 9266; https://0-doi-org.brum.beds.ac.uk/10.3390/s22239266 - 28 Nov 2022
Cited by 4 | Viewed by 2805
Abstract
Although the moment of inertia of padel rackets is one of their fundamental properties and of particular interest to the players, hardly any manufacturer specifies the parameter for its rackets. The present paper offers a solution to determine the moment of inertia around [...] Read more.
Although the moment of inertia of padel rackets is one of their fundamental properties and of particular interest to the players, hardly any manufacturer specifies the parameter for its rackets. The present paper offers a solution to determine the moment of inertia around different axes of padel rackets and makes a standardized comparison possible. After a short overview of the physical background of the problem and the existing solutions for inertia testing, the developed concept for a test stand is described in detail. The approach uses the fact that a pendulum swings with its natural frequency, which depends directly on its moment of inertia. The inertia can be calculated by measuring the cycle time of the swing. Two different test stands, a trifilar and a swing pendulum, are designed to enable an oscillation of the rackets with different rotation axes, and an acceleration sensor is used to measure its natural frequency. A user-friendly interface acquires and processes accelerometer data providing inertial moments. A calibration model defines sensor accuracy. Precision is estimated by calculating the influence of the measurement errors and by testing the repeatability. The maneuverability parameter is created, and in the last step, various rackets are evaluated to create a database with the main properties. As a result of the study of the racket population, a maneuverability parameter is proposed to classify the rackets in a comprehensible way for users. The classification method is tested with users to explore the matching between the scientific classification and the player’s feelings. The results are shown and explained. Full article
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27 pages, 1988 KiB  
Article
Equations of Disturbed Motion of the Moving Part of the Gyroscope Suspension
by Igor Korobiichuk, Viktorij Mel’nick, Vera Kosova and Kateryna Maksymenko
Sensors 2022, 22(19), 7442; https://0-doi-org.brum.beds.ac.uk/10.3390/s22197442 - 30 Sep 2022
Cited by 3 | Viewed by 1137
Abstract
The response of the float two-stage angular velocity sensor to the simultaneous perturbation from the rocket body—kinematic perturbation—and the penetrating acoustic radiation from the propulsion engines of the launch vehicle were determined. The solution of two equations was successively analyzed: the first and [...] Read more.
The response of the float two-stage angular velocity sensor to the simultaneous perturbation from the rocket body—kinematic perturbation—and the penetrating acoustic radiation from the propulsion engines of the launch vehicle were determined. The solution of two equations was successively analyzed: the first and second approximations, and the synchronous and asynchronous fuselage pitch. The reaction of the float gyroscope to harmonic oscillations of the base was analyzed. The effect of the zero shift of the device due only to the angular oscillations of the launch vehicle body and the penetrating acoustic radiation was considered. The presented results reveal the nature of the appearance of inertia forces acting on the impedance surface of the gyroscope float suspension. Acoustic radiation that passes into a device generates many vibration modes on the surface and can have a considerable effect on the precision of float two-stage angular velocity sensor and gyro-stabilized platforms. Full article
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22 pages, 1538 KiB  
Article
A Human Gait Tracking System Using Dual Foot-Mounted IMU and Multiple 2D LiDARs
by Huu Toan Duong and Young Soo Suh
Sensors 2022, 22(17), 6368; https://0-doi-org.brum.beds.ac.uk/10.3390/s22176368 - 24 Aug 2022
Cited by 3 | Viewed by 1877
Abstract
This paper proposes a human gait tracking system using a dual foot-mounted IMU and multiple 2D LiDARs. The combining system aims to overcome the disadvantages of each single sensor system (the short tracking range of the single 2D LiDAR and the drift errors [...] Read more.
This paper proposes a human gait tracking system using a dual foot-mounted IMU and multiple 2D LiDARs. The combining system aims to overcome the disadvantages of each single sensor system (the short tracking range of the single 2D LiDAR and the drift errors of the IMU system). The LiDARs act as anchors to mitigate the errors of an inertial navigation algorithm. In our system, two 2D LiDARs are used. LiDAR 1 is placed around the starting point, and LiDAR 2 is placed at the ending point (in straight walking) or at the turning point (in rectangular path walking). Using the LiDAR 1, we can estimate the initial headings and positions of each IMU without any calibration process. We also propose a method to calibrate two LiDARs that are placed far apart. Then, the measurement from two LiDARs can be combined in a Kalman filter and the smoother algorithm to correct the two estimated feet trajectories. If straight walking is detected, we update the current stride heading and the foot position using the previous stride headings. Then, it is used as a measurement update in the Kalman filter. In the smoother algorithm, a step width constraint is used as a measurement update. We evaluate the stride length estimation through a straight walking experiment along a corridor. The root mean square errors compared with an optical tracking system are less than 3 cm. The performance of proposed method is also verified with a rectangular path walking experiment. Full article
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29 pages, 609 KiB  
Systematic Review
Inertial Motion Capture-Based Wearable Systems for Estimation of Joint Kinetics: A Systematic Review
by Chang June Lee and Jung Keun Lee
Sensors 2022, 22(7), 2507; https://0-doi-org.brum.beds.ac.uk/10.3390/s22072507 - 25 Mar 2022
Cited by 15 | Viewed by 3905
Abstract
In biomechanics, joint kinetics has an important role in evaluating the mechanical load of the joint and understanding its motor function. Although an optical motion capture (OMC) system has mainly been used to evaluate joint kinetics in combination with force plates, inertial motion [...] Read more.
In biomechanics, joint kinetics has an important role in evaluating the mechanical load of the joint and understanding its motor function. Although an optical motion capture (OMC) system has mainly been used to evaluate joint kinetics in combination with force plates, inertial motion capture (IMC) systems have recently been emerging in joint kinetic analysis due to their wearability and ubiquitous measurement capability. In this regard, numerous studies have been conducted to estimate joint kinetics using IMC-based wearable systems. However, these have not been comprehensively addressed yet. Thus, the aim of this review is to explore the methodology of the current studies on estimating joint kinetic variables by means of an IMC system. From a systematic search of the literature, 48 studies were selected. This paper summarizes the content of the selected literature in terms of the (i) study characteristics, (ii) methodologies, and (iii) study results. The estimation methods of the selected studies are categorized into two types: the inverse dynamics-based method and the machine learning-based method. While these two methods presented different characteristics in estimating the kinetic variables, it was demonstrated in the literature that both methods could be applied with good performance for the kinetic analysis of joints in different daily activities. Full article
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2021

Jump to: 2024, 2023, 2022, 2020

22 pages, 7905 KiB  
Article
A Systematic Design Optimization Approach for Multiphysics MEMS Devices Based on Combined Computer Experiments and Gaussian Process Modelling
by Shayaan Saghir, Muhammad Mubasher Saleem, Amir Hamza, Kashif Riaz, Sohail Iqbal and Rana Iqtidar Shakoor
Sensors 2021, 21(21), 7242; https://0-doi-org.brum.beds.ac.uk/10.3390/s21217242 - 30 Oct 2021
Cited by 5 | Viewed by 2526
Abstract
This paper presents a systematic and efficient design approach for the two degree-of-freedom (2-DoF) capacitive microelectromechanical systems (MEMS) accelerometer by using combined design and analysis of computer experiments (DACE) and Gaussian process (GP) modelling. Multiple output responses of the MEMS accelerometer including natural [...] Read more.
This paper presents a systematic and efficient design approach for the two degree-of-freedom (2-DoF) capacitive microelectromechanical systems (MEMS) accelerometer by using combined design and analysis of computer experiments (DACE) and Gaussian process (GP) modelling. Multiple output responses of the MEMS accelerometer including natural frequency, proof mass displacement, pull-in voltage, capacitance change, and Brownian noise equivalent acceleration (BNEA) are optimized simultaneously with respect to the geometric design parameters, environmental conditions, and microfabrication process constraints. The sampling design space is created using DACE based Latin hypercube sampling (LHS) technique and corresponding output responses are obtained using multiphysics coupled field electro–thermal–structural interaction based finite element method (FEM) simulations. The metamodels for the individual output responses are obtained using statistical GP analysis. The developed metamodels not only allowed to analyze the effect of individual design parameters on an output response, but to also study the interaction of the design parameters. An objective function, considering the performance requirements of the MEMS accelerometer, is defined and simultaneous multi-objective optimization of the output responses, with respect to the design parameters, is carried out by using a combined gradient descent algorithm and desirability function approach. The accuracy of the optimization prediction is validated using FEM simulations. The behavioral model of the final optimized MEMS accelerometer design is integrated with the readout electronics in the simulation environment and voltage sensitivity is obtained. The results show that the combined DACE and GP based design methodology can be an efficient technique for the design space exploration and optimization of multiphysics MEMS devices at the design phase of their development cycle. Full article
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19 pages, 2030 KiB  
Communication
Improved Single Inertial-Sensor-Based Attitude Estimation during Walking Using Velocity-Aided Observation
by Duc Cong Dang and Young Soo Suh
Sensors 2021, 21(10), 3428; https://0-doi-org.brum.beds.ac.uk/10.3390/s21103428 - 14 May 2021
Viewed by 1977
Abstract
This paper presents a Kalman filter-based attitude estimation algorithm using a single body-mounted inertial sensor consisting of a triaxial accelerometer and triaxial gyroscope. The proposed algorithm has been developed for attitude estimation during dynamic conditions such as walking and running. Based on the [...] Read more.
This paper presents a Kalman filter-based attitude estimation algorithm using a single body-mounted inertial sensor consisting of a triaxial accelerometer and triaxial gyroscope. The proposed algorithm has been developed for attitude estimation during dynamic conditions such as walking and running. Based on the repetitive properties of the velocity signal of human gait during walking, a novel velocity-aided observation is used as a measurement update for the filter. The performance has been evaluated in comparison to two standard Kalman filters with different measurement update methods and a smoother algorithm which is formulated in the form of a quadratic optimization problem. Whereas two standard Kalman filters give maximum 5 degrees in both pitch and roll error for short walking case, their performance gradually decrease with longer walking distance. The proposed algorithm shows the error of about 3 degrees in 15 m walking case, and indicate the robustness of the method with the same performance in 75 m trials. As far as the accuracy of the estimation is concerned, the proposed method achieves advantageous results due to its periodic error correction capability in both short and long walking cases at varying speeds. In addition, in terms of practicality and stability, with simple parameter settings and without the need of all-time data, the algorithm can achieve smoothing-algorithm-performance level with lower computational resources. Full article
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21 pages, 1335 KiB  
Article
Error Analysis of Accelerometer- and Magnetometer-Based Stationary Alignment
by Felipe O. Silva, Lucas P. S. Paiva and Gustavo S. Carvalho
Sensors 2021, 21(6), 2040; https://0-doi-org.brum.beds.ac.uk/10.3390/s21062040 - 14 Mar 2021
Cited by 5 | Viewed by 2940
Abstract
This paper revisits the stationary attitude initialization problem, i.e., the stationary alignment, of Attitude and Heading Reference Systems (AHRSs). A detailed and comprehensive error analysis is proposed for four of the most representative accelerometer- and magnetometer-based stationary attitude determination methods, namely, the Three-Axis [...] Read more.
This paper revisits the stationary attitude initialization problem, i.e., the stationary alignment, of Attitude and Heading Reference Systems (AHRSs). A detailed and comprehensive error analysis is proposed for four of the most representative accelerometer- and magnetometer-based stationary attitude determination methods, namely, the Three-Axis Attitude Determination (TRIAD), the QUaternion ESTimator (QUEST), the Factored Quaternion Algorithm (FQA), and the Arc-TANgent (ATAN). For the purpose of the error analysis, constant biases in the accelerometer and magnetometer measurements are considered (encompassing, hence, the effect of hard-iron magnetism), in addition to systematic errors in the local gravity and Earth magnetic field models (flux density magnitude, declination angle, and inclination angle). The contributions of this paper are novel closed-form formulae for the residual errors (normality, orthogonality, and alignment errors) developed in the computed Direction Cosine Matrices (DCM). As a consequence, analytical insight is provided into the problem, allowing us to properly compare the performance of the investigated alignment formulations (in terms of ultimate accuracy), as well as to remove some misleading conclusions reported in previous works. The adequacy of the proposed error analysis is validated through simulation and experimental results. Full article
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13 pages, 3178 KiB  
Letter
Treadmill-to-Overground Mapping of Marker Trajectory for Treadmill-Based Continuous Gait Analysis
by Woo Chang Jung and Jung Keun Lee
Sensors 2021, 21(3), 786; https://0-doi-org.brum.beds.ac.uk/10.3390/s21030786 - 25 Jan 2021
Cited by 3 | Viewed by 2402
Abstract
A treadmill was used to perform continuous walking tests in a limited space that can be covered by marker-based optical motion capture systems. Most treadmill-based gait data are analyzed based on gait cycle percentage. However, achieving continuous walking motion trajectories over time without [...] Read more.
A treadmill was used to perform continuous walking tests in a limited space that can be covered by marker-based optical motion capture systems. Most treadmill-based gait data are analyzed based on gait cycle percentage. However, achieving continuous walking motion trajectories over time without time normalization is often required, even if tests are performed under treadmill walking conditions. This study presents a treadmill-to-overground mapping method of optical marker trajectories for treadmill-based continuous gait analysis, by adopting a simple concept of virtual origin. The position vector from the backward moving virtual origin to a targeted marker within a limited walking volume is the same as the position vector from the fixed origin to the forward moving marker over the ground. With the proposed method, it is possible (i) to observe the change in physical quantity visually during the treadmill walking, and (ii) to obtain overground-mapped gait data for evaluating the accuracy of the inertial-measurement-unit-based trajectory estimation. The accuracy of the proposed method was verified from various treadmill walking tests, which showed that the total travel displacement error rate was 0.32% on average. Full article
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2020

Jump to: 2024, 2023, 2022, 2021

14 pages, 4241 KiB  
Communication
The Sensitive Element of Acoustic Sensor on Circular Polarized Waves: From Theoretical Considerations towards Perspective Rotation Rate Sensors Design
by Michail Shevelko, Andrey Lutovinov, Aleksandr Peregudov, Ekaterina Popkova, Yasemin Durukan and Sergey Shevchenko
Sensors 2021, 21(1), 32; https://0-doi-org.brum.beds.ac.uk/10.3390/s21010032 - 23 Dec 2020
Cited by 1 | Viewed by 1911
Abstract
In this paper, the perspectives of using the features of acoustic wave propagation to design rotation rate sensors (RRS) are discussed. The possibility of developing the solid-state sensitive elements (SE) of RRS on acoustic waves of circular polarization is shown. The theoretical basis [...] Read more.
In this paper, the perspectives of using the features of acoustic wave propagation to design rotation rate sensors (RRS) are discussed. The possibility of developing the solid-state sensitive elements (SE) of RRS on acoustic waves of circular polarization is shown. The theoretical basis of bulk acoustic wave propagation under rotation is given. The direct excitation of circularly polarized acoustic wave (CPAW) is considered, the design of the CPAW emitting transducer is offered. The results of experimental studies that indicated the circular nature of the particle motions in the radiated wave are discussed. The principally new concept of the RRS SE design on CPAW, being able to operate under high vibration and acceleration, is proposed. The experimental results revealed a high correlation with theoretical and numerical predictions and confirmed RRS on CPAW operability. Full article
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19 pages, 1828 KiB  
Article
Nonlinear Vibration Study Based on Uncertainty Analysis in MEMS Resonant Accelerometer
by Yan Li, Linke Song, Shuai Liang, Yifeng Xiao and Fuling Yang
Sensors 2020, 20(24), 7207; https://0-doi-org.brum.beds.ac.uk/10.3390/s20247207 - 16 Dec 2020
Cited by 6 | Viewed by 2022
Abstract
This paper aims to develop a resonant accelerometer for high-sensitivity detection and to investigate the nonlinear vibration of the MEMS resonant accelerometer driven by electrostatic comb fingers. First, a nonlinear vibration model of the resonator with comb fingers in a MEMS resonant accelerometer [...] Read more.
This paper aims to develop a resonant accelerometer for high-sensitivity detection and to investigate the nonlinear vibration of the MEMS resonant accelerometer driven by electrostatic comb fingers. First, a nonlinear vibration model of the resonator with comb fingers in a MEMS resonant accelerometer is established. Then, the nonlinear and nonlinear stiffness coefficients are calculated and analyzed with the Galérkin principle. The linear natural frequency, tracking error, and nonlinear frequency offset are obtained by multi-scale method. Finally, to further analyze the nonlinear vibration, a sample-based stochastic model is established, and the uncertainty analysis method is applied. It is concluded from the results that nonlinear vibration can be reduced by reducing the resonant beam length and increasing the resonant beam width and thickness. In addition, the resonant beam length and thickness have more significant effects, while the resonant beam width and the single concentrated mass of comb fingers have little effect, which are verified by experiments. The results of this research have proved that uncertainty analysis is an effective approach in nonlinear vibration analysis and instructional in practical resonant accelerometer design. Full article
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14 pages, 4416 KiB  
Article
Interference Torque of a Gas-Dynamic Bearing Gyroscope Subject to a Uniform Change of the Specific Force and the Carrier Angular Velocity
by Yan Li, Desheng Zhang and Fuhai Duan
Sensors 2020, 20(23), 6852; https://0-doi-org.brum.beds.ac.uk/10.3390/s20236852 - 30 Nov 2020
Cited by 1 | Viewed by 2404
Abstract
The work is devoted to an analysis of interference torque of a gas-dynamic bearing gyroscope, while a condition with uniformly changed specific force and carrier angular velocity are taken into account. A five-degrees-of-freedom (5-DOF) model is established considering the translation and tilt of [...] Read more.
The work is devoted to an analysis of interference torque of a gas-dynamic bearing gyroscope, while a condition with uniformly changed specific force and carrier angular velocity are taken into account. A five-degrees-of-freedom (5-DOF) model is established considering the translation and tilt of the rotor, which solves dynamic rotor equations and the Reynolds equation simultaneously. The model makes it possible to obtain the rotor trajectory under time-transient specific force and carrier angular velocity. The interference torque of the gyroscope is analyzed based on the rotor trajectory. Results indicate that the gas-dynamic bearings show a significant hysteresis effect with a perturbation of bearing force or bearing moment, which indicates the necessity of transient research. Interference torque is large when the carrier angular velocity starts to change or stops to change, and when the specific force stops to change. When the specific force change rate is less than 8.4 km/s3 with no change of the carrier angular velocity, the condition could be simplified as a steady state, which is consistent with the previous study. Full article
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28 pages, 3685 KiB  
Article
Development and Validation of Open-Source Activity Intensity Count and Activity Intensity Classification Algorithms from Raw Acceleration Signals of Wearable Sensors
by Isabelle Poitras, Jade Clouâtre, Laurent J. Bouyer, François Routhier, Catherine Mercier and Alexandre Campeau-Lecours
Sensors 2020, 20(23), 6767; https://0-doi-org.brum.beds.ac.uk/10.3390/s20236767 - 26 Nov 2020
Cited by 2 | Viewed by 2166
Abstract
Background: A popular outcome in rehabilitation studies is the activity intensity count, which is typically measured from commercially available accelerometers. However, the algorithms are not openly available, which impairs long-term follow-ups and restricts the potential to adapt the algorithms for pathological populations. The [...] Read more.
Background: A popular outcome in rehabilitation studies is the activity intensity count, which is typically measured from commercially available accelerometers. However, the algorithms are not openly available, which impairs long-term follow-ups and restricts the potential to adapt the algorithms for pathological populations. The objectives of this research are to design and validate open-source algorithms for activity intensity quantification and classification. Methods: Two versions of a quantification algorithm are proposed (fixed [FB] and modifiable bandwidth [MB]) along with two versions of a classification algorithm (discrete [DM] vs. continuous methods [CM]). The results of these algorithms were compared to those of a commercial activity intensity count solution (ActiLife) with datasets from four activities (n = 24 participants). Results: The FB and MB algorithms gave similar results as ActiLife (r > 0.96). The DM algorithm is similar to a ActiLife (r ≥ 0.99). The CM algorithm differs (r ≥ 0.89) but is more precise. Conclusion: The combination of the FB algorithm with the DM results is a solution close to that of ActiLife. However, the MB version remains valid while being more adaptable, and the CM is more precise. This paper proposes an open-source alternative for rehabilitation that is compatible with several wearable devices and not dependent on manufacturer commercial decisions. Full article
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25 pages, 26049 KiB  
Article
A Novel Alignment Method for SINS with Large Misalignment Angles Based on EKF2 and AFIS
by Yanming Zhao, Gongmin Yan, Yongyuan Qin and Qiangwen Fu
Sensors 2020, 20(21), 5975; https://0-doi-org.brum.beds.ac.uk/10.3390/s20215975 - 22 Oct 2020
Cited by 3 | Viewed by 2380
Abstract
In order to achieve the fine alignment of strapdown inertial navigation (SINS) under large misalignment angles, a novel filtering alignment method is proposed based on the second-order extended Kalman filter (EKF2) and adaptive fuzzy inference system (AFIS). Firstly, the quaternion is employed to [...] Read more.
In order to achieve the fine alignment of strapdown inertial navigation (SINS) under large misalignment angles, a novel filtering alignment method is proposed based on the second-order extended Kalman filter (EKF2) and adaptive fuzzy inference system (AFIS). Firstly, the quaternion is employed to represent the attitude errors of SINS. A second-order nonlinear state equation is made based on the nonlinear velocity error model and attitude error model, and the linear measurement equation is based on the velocity outputs from SINS. Then, the filtering scheme is designed based on EKF2 and AFIS. The error estimation and fine alignment can be achieved by using the proposed filtering scheme. The results of Monte Carlo Simulation show that the errors of pitch, roll and yaw misalignment angles quickly decrease to about 14″, 15″ and 7.62′ respectively in 350 s under the condition of any misalignment angles with pitch error from −40° to 40°, roll error from −40° to 40°, and yaw error from −50° to 50°. Even when the initial misalignment angles are all very large such as (80°, 120°, 170°), the proposed nonlinear alignment method still can converge normally by utilizing the adaptive fuzzy inference system (AFIS) to adjust the covariance matrix Pk/k−1. Finally, the turntable experiment was performed, and the effectiveness and superiority of the proposed method were further verified by compared with other nonlinear methods. Full article
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18 pages, 8316 KiB  
Article
Cylindrical Shell Vibration Gyroscope Excited and Detected by High-Temperature-Sintered Piezoelectric Ceramic Electrodes
by Tianliang Qu, Guanqing Zhou, Xiaoming Xue and Junhua Teng
Sensors 2020, 20(21), 5972; https://0-doi-org.brum.beds.ac.uk/10.3390/s20215972 - 22 Oct 2020
Cited by 1 | Viewed by 2360
Abstract
A cylindrical shell piezoelectric vibration gyroscope is a kind of Coriolis vibration gyroscope. Its core components are the cylindrical quartz resonator (CQR) and the piezoelectric ceramic electrodes (PCEs). In order to develop a high-precision Cylindrical shell piezoelectric vibration gyroscope, it is very important [...] Read more.
A cylindrical shell piezoelectric vibration gyroscope is a kind of Coriolis vibration gyroscope. Its core components are the cylindrical quartz resonator (CQR) and the piezoelectric ceramic electrodes (PCEs). In order to develop a high-precision Cylindrical shell piezoelectric vibration gyroscope, it is very important to reduce the influence of the PCEs and obtain a high-quality-factor CQR. To achieve this goal, a novel high-temperature sintering method is proposed to combine the CQR and the PCEs, and the corresponding sintered resonators are fabricated. After sintering, results of the acoustic excitation experiment and piezoelectric excitation experiment are tested, and the influence of the sintered PCEs on the CQR is determined. A complete gyroscope is obtained by vacuum packaging the sintered resonator. Through the open-loop and closed-loop tests, the performance parameters of gyroscope are obtained. The feasibility of the high-temperature sintering method is proved by experiments. Full article
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17 pages, 2178 KiB  
Article
Magnetic Field Gradient-Based EKF for Velocity Estimation in Indoor Navigation
by Makia Zmitri, Hassen Fourati and Christophe Prieur
Sensors 2020, 20(20), 5726; https://0-doi-org.brum.beds.ac.uk/10.3390/s20205726 - 09 Oct 2020
Cited by 13 | Viewed by 2642
Abstract
This paper proposes an advanced solution to improve the inertial velocity estimation of a rigid body, for indoor navigation, through implementing a magnetic field gradient-based Extended Kalman Filter (EKF). The proposed estimation scheme considers a set of data from a triad of inertial [...] Read more.
This paper proposes an advanced solution to improve the inertial velocity estimation of a rigid body, for indoor navigation, through implementing a magnetic field gradient-based Extended Kalman Filter (EKF). The proposed estimation scheme considers a set of data from a triad of inertial sensors (accelerometer and gyroscope), as well as a determined arrangement of magnetometers array. The inputs for the estimation scheme are the spatial derivatives of the magnetic field, from the magnetometers array, and the attitude, from the inertial sensors. As shown in the literature, there is a strong relation between the velocity and the measured magnetic field gradient. However, the latter usually suffers from high noises. Then, the novelty of the proposed EKF is to develop a specific equation to describe the dynamics of the magnetic field gradient. This contribution helps to filter, first, the magnetic field and its gradient and second, to better estimate the inertial velocity. Some numerical simulations that are based on an open source database show the targeted improvements. At the end of the paper, this approach is extended to position estimation in the case of a foot-mounted application and the results are very promising. Full article
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16 pages, 3867 KiB  
Article
Design of Readout Circuit with Quadrature Error and Auxiliary PLL for MEMS Vibratory Gyroscope
by Hua Chen and Yanqing Zhong
Sensors 2020, 20(16), 4564; https://0-doi-org.brum.beds.ac.uk/10.3390/s20164564 - 14 Aug 2020
Cited by 2 | Viewed by 3864
Abstract
Traditional MEMS gyroscope readout eliminates quadrature error and relies on the phase relationship between the drive displacement and the Coriolis position to accomplish a coherent demodulation. This scheme shows some risk, especially for a mode-matching gyro. If only a slight resonant frequency deviation [...] Read more.
Traditional MEMS gyroscope readout eliminates quadrature error and relies on the phase relationship between the drive displacement and the Coriolis position to accomplish a coherent demodulation. This scheme shows some risk, especially for a mode-matching gyro. If only a slight resonant frequency deviation between the drive and sense mode occurs, a dramatic change in the phase relationship follows, which leads to a wrong demodulation. To solve this, this paper proposes a new readout based on the quadrature error and an auxiliary phase-locked loop (PLL). By tuning the phase shifter in the sense-mode circuit, letting the quadrature error and the carrier of the mixer be in 90° phase alignment, the Coriolis was simultaneously in phase with the carrier. Hence, the demodulation was accomplished. The carrier comes from the PLL output of the drive-mode circuit due to its low jitter and independence of the work mode of the gyro. Moreover, an auxiliary PLL is used to filter the quadrature error to enhance the phase alignment accuracy. Through an elaborate design, a printed circuit board was used to verify the proposed idea. The experimental results show the readout circuit functioned well. The scale factor of the gyro was 6.8 mV/°/s, and the bias instability was 204°/h. Full article
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