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Topical Collection "Inertial Sensors and Applications"

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

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
Scuola Superiore Sant'Anna di Studi Universitari e di Perfezionamento, Pisa, Italy
Interests: wearable sensor systems for human motion capture; magneto-inertial measurement units; computational methods for wearable sensor systems; multisensor fusion
Special Issues and Collections 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

Manuscript Submission Information

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Published Papers (11 papers)

2021

Jump to: 2020

Open AccessCommunication
Improved Single Inertial-Sensor-Based Attitude Estimation during Walking Using Velocity-Aided Observation
by and
Sensors 2021, 21(10), 3428; https://doi.org/10.3390/s21103428 (registering DOI) - 14 May 2021
Viewed by 122
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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Open AccessArticle
Error Analysis of Accelerometer- and Magnetometer-Based Stationary Alignment
Sensors 2021, 21(6), 2040; https://doi.org/10.3390/s21062040 - 14 Mar 2021
Viewed by 440
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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Open AccessLetter
Treadmill-to-Overground Mapping of Marker Trajectory for Treadmill-Based Continuous Gait Analysis
Sensors 2021, 21(3), 786; https://doi.org/10.3390/s21030786 - 25 Jan 2021
Cited by 1 | Viewed by 464
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: 2021

Open AccessCommunication
The Sensitive Element of Acoustic Sensor on Circular Polarized Waves: From Theoretical Considerations towards Perspective Rotation Rate Sensors Design
Sensors 2021, 21(1), 32; https://doi.org/10.3390/s21010032 - 23 Dec 2020
Viewed by 497
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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Open AccessArticle
Nonlinear Vibration Study Based on Uncertainty Analysis in MEMS Resonant Accelerometer
Sensors 2020, 20(24), 7207; https://doi.org/10.3390/s20247207 - 16 Dec 2020
Cited by 1 | Viewed by 367
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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Open AccessArticle
Interference Torque of a Gas-Dynamic Bearing Gyroscope Subject to a Uniform Change of the Specific Force and the Carrier Angular Velocity
Sensors 2020, 20(23), 6852; https://doi.org/10.3390/s20236852 - 30 Nov 2020
Viewed by 407
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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Open AccessArticle
Development and Validation of Open-Source Activity Intensity Count and Activity Intensity Classification Algorithms from Raw Acceleration Signals of Wearable Sensors
Sensors 2020, 20(23), 6767; https://doi.org/10.3390/s20236767 - 26 Nov 2020
Viewed by 386
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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Open AccessArticle
A Novel Alignment Method for SINS with Large Misalignment Angles Based on EKF2 and AFIS
Sensors 2020, 20(21), 5975; https://doi.org/10.3390/s20215975 - 22 Oct 2020
Cited by 1 | Viewed by 689
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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Open AccessArticle
Cylindrical Shell Vibration Gyroscope Excited and Detected by High-Temperature-Sintered Piezoelectric Ceramic Electrodes
Sensors 2020, 20(21), 5972; https://doi.org/10.3390/s20215972 - 22 Oct 2020
Viewed by 430
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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Open AccessArticle
Magnetic Field Gradient-Based EKF for Velocity Estimation in Indoor Navigation
Sensors 2020, 20(20), 5726; https://doi.org/10.3390/s20205726 - 09 Oct 2020
Cited by 1 | Viewed by 562
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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Open AccessArticle
Design of Readout Circuit with Quadrature Error and Auxiliary PLL for MEMS Vibratory Gyroscope
Sensors 2020, 20(16), 4564; https://doi.org/10.3390/s20164564 - 14 Aug 2020
Viewed by 749
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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