Magnetic, Angular Rate, And Gravity Sensors Research Articles

Simplification of calibration of low-cost MARG sensors without high-precision laboratory equipment

AbstractIn mechatronic-related applications, estimating orientation from a magnetic, angular rate, and gravity (MARG) sensor array is a significant topic. Representing attitude orientation is a well-known topic in the aerospace industry, where it plays a critical role in airplanes and unmanned aerial vehicles (UAVs), but it has also gained relevance in other sectors. However, most of the sensors utilized are quite expensive, heavy, and large, making them unsuitable for modest applications. This paper examines the performance of several sensors in low-cost hardware and high-acceleration environments. A theorical method was adopted to estimate Euler angles by using accelerometer, gyroscope and magnetometer, and a robust and easy to implement method calibration was proposed to calibrate the MARG sensor without any external equipment. An experimental verification of the proposed calibration method was completed. The experimental results are then interpreted to provide an insight to advantages and disadvantages for using each sensor separately.

An Observation Model From Linear Interpolation for Quaternion-Based Attitude Estimation

This article aims to solve multiple problems associated with attitude estimation; the complexity of Kalman filter (KF) calculations in the attitude and heading reference system (AHRS), the interference sensitivity of magnetic, angular rate, and gravity (MARG) sensors, and the low accuracy of the factored quaternion algorithm (FQA). It presents a two-layer linear KF using MARG sensors to obtain attitude estimation in quaternions. First, data from a triaxial accelerometer and magnetometer is processed by a novel algorithm, which fuses the quaternion estimator (QUEST) algorithm and FQA by the linear interpolation (LERP) to obtain an observation model. Second, the process model in the two-layer KF was obtained by using LERP to fuse an optimum quaternion obtained from a gyroscope and FQA. The LERP can eliminate gyro bias drift, and integral error, and compensate for unexpected conditions, such as fast rotation and temporary strong magnetic disturbances. The proposed algorithm presents higher accuracy and lower computational load than QUEST or FQA used with a KF alone. The performance of the proposed algorithm is verified through simulation and experiments.

Device Attitude and Real-Time 3D Visualization: An Interface for Elderly Care

Objectivethis paper presents an innovative graphical user interface to visualize the attitude of a sensing device in a three-dimensional space, serving a wide-range of medical applications. Material and methodsbased on inertial measurement units (IMU) or on magnetic, angular rate and gravity (MARG) sensors, a processing unit provides Euler angles using a sensor fusion technique to display the orientation of the device relative to the Earth frame in real-time. The device is schematized by linking six polygonal regions, and is subject to sequential rotations by updating the graph each 350 ms. We conduct comparative studies between the two sensing devices, i.e. IMUs and MARGs, as well as two orientation filters, namely Madgwick's algorithm and Mahony's algorithm. Resultsthe accuracy of the system is reported as a function of (i) the sampling frequency, (ii) the sensing unit, and (iii) the orientation filter, following two elderly care applications, namely fall risk assessment and body posture monitoring. The experiments are conducted using public datasets. The corresponding results show that Madgwick's algorithm is best suited for low sampling rates, whereas MARG sensors are best suited for the detection of postural transitions. Conclusionthis paper addresses the different aspects and discusses the limitations of attitude estimation systems, which are important tools to help clinicians in their diagnosis.

Online calibrated, energy-aware and heading corrected pedestrian navigation with foot-mounted MARG sensors

The objective of this paper is to propose an energy-aware and gait corrected pedestrian dead reckoning (PDR) approach using foot-mounted magnetic, angular rate and gravity (MARG) sensors. Compared with existing algorithms of PDR, the proposed method aims to solve three main problems for real pedestrian applications. First, to avoid limitations of off-line calibration for personal step length parameters, we utilize the zero-velocity-update (ZUPT) aided pedestrian MARG performance to continuously compute one’s pose information. Meanwhile, it accumulates the moving distance for further estimation of one’s step length during the initialization process. Secondly, due to different pedestrian gaits implicating the heading deviation angle between one’s moving direction and heading, there are non-negligible impacts on pedestrian dead reckoning accuracy. The linear Kalman filter (KF) is used to recursively estimate the deviated heading during aforementioned initialization process. The third problem is related to the energy consumption. Following three aspects of adaptive energy saving work are devised: (i) energy-aware strategy for gyroscopes measurements acquisition is adopted to guarantee lower energy consumption. (ii) Modes switching mechanism of navigation computation is applied to the initialization and dead reckoning processes. (iii) De-sampling after initialization process has been invoked. Finally, real-world experiments are carried out to evaluate the performances of developed PDR system. The results show the efficiency of the suggested approach.

Research on Gradient-Descent Extended Kalman Attitude Estimation Method for Low-Cost MARG.

Aiming at the problem of the weak dynamic performance of the gradient descent method in the attitude and heading reference system, the susceptibility to the interference of accelerometers and magnetometers, and the complex calculation of the nonlinear Kalman Filter method, an extended Kalman filter suitable for a low-cost magnetic, angular rate, and gravity (MARG) sensor system is proposed. The method proposed in this paper is a combination of a two-stage gradient descent algorithm and the extended Kalman filter (GDEKF). First, the accelerometer and magnetometer are used to correct the attitude angle according to the two-stage gradient descent algorithm. The obtained attitude quaternion is combined with the gyroscope measurement value as the observation vector of EKF and the calculated attitude of the gyroscope and the bias of the gyroscope are corrected. The elimination of the bias of the gyroscope can further improve the stability of the attitude observation results. Finally, the MARG sensor system was designed for mathematical model simulation and hardware-in-the-loop simulation to verify the performance of the filter. The results show that compared with the gradient descent method, it has better anti-interference performance and dynamic performance, and better measurement accuracy than the extended Kalman filter.

Improved attitude estimation accuracy by data fusion of a MEMS MARG sensor and a low-cost GNSS receiver

To obtain precise and continuous attitude information, this paper proposed a data fusion scheme that exploits the complementary advantages of a microelectromechanical system (MEMS) magnetic, angular rate, and gravity (MARG) sensor and a low-cost global navigation satellite system (GNSS) receiver. A quaternion-based error state Kalman filter is designed to integrate the different data sources, where the attitude error and gyro bias variation are taken as the error states. The gyro-measured angular rates are continuously integrated to propagate the attitude quaternion, while the accelerometer and magnetometer readings or the GNSS pitch and heading angles estimated by the precise carrier phase observations are utilized to perform the measurement update. The system kinematic model remains constant when the aiding source changes, only the measurement model alternates accordingly. A vehicular dynamical test was conducted to evaluate the proposed algorithm, the test results show that the attitude estimation accuracy of the integrated algorithm is apparently improved.

Robust methods for estimating the orientation and position of IMU and MARG sensors

The inertial measurement unit (IMU) and magnetic, angular rate, and gravity (MARG) sensor orientation and position are widely used in the medical, robotics, and other fields. In general, the orientations can be defined by the integration of angular velocity data, and the positions are also computed from the double integration of acceleration data. However, the acceleration and angular velocity data are often inaccurate due to measurement errors which arise when the sensor moves quickly. Therefore, the orientations and positions significantly differ from the actual values. To address these issues, several techniques are proposed for the accurate measurement of IMU and MARG sensor orientations and positions. The proposed optimization method is applied to raw sensor data to compute faithful orientations by stabilizing and accelerating the convergence of the optimization process. Furthermore, a deep neural network based on 1D convolutional neural network (CNN) layers is proposed to predict the desired velocity from raw acceleration data. The method is validated qualitatively and quantitatively with an optical motion capture (mocap) system. The experimental results show that the proposed method significantly improves orientation and position estimations compared to those of other approaches.

Lightweight Extended Kalman Filter for MARG Sensors Attitude Estimation

Low-power consumption of orientation estimation using low-cost inertial sensors are crucial for all the applications which are resource constrained critically. This paper presents a novel Lightweight quaternion-based Extended Kalman Filter (LEKF) for orientation estimation for magnetic, angular rate and gravity (MARG) sensors. In this filter, with employing the quaternion kinematic equation as the process model, we derived a simplified measurement model to create the lightweight system model for Kalman filtering, where the measurement model works efficiently, and the involved computation of measurement model is reduced. It’s later proved that the proposed filter saves time consumption. Further, observations of the accelerometer and the magnetometer are dealt with the proposed nonlinear measurement model, the good performance should be guaranteed in theory. For the experiments, a commercial sensor for data collection, and an optical system to provide reference measurements of orientation, namely Vicon, are utilized to investigate the performance of the proposed filter. Evaluation for different application scenarios are considered, which primarily includes human motion capture and the drone application. Results indicate that the proposed filter performs well for both applications, and is proved to have a good anti-vibration ability. What’s more, the comparison experiment shows that the proposed filter provides good performance, as same as the basic UKF, but it consumes the least computing time among the compared methods.

Cascaded Indirect Kalman Filters for Land-Vehicle Attitude Estimation With MARG Sensors and GNSS Observations

This paper proposes a novel quaternion-based attitude estimation method for land-vehicle applications by fusing the low-cost magnetic, angular rate, and gravity (MARG) sensors and global navigation satellite systems measured velocity (GNSS-V). A structure of three-layer cascaded indirect Kalman filter (IKF) is devised to minimize the interactions of heterogeneous error sources on attitude quaternion solutions. It sequentially fuses the Earth's gravity vector, magnetic vector, and GNSS-V vector pairs with quaternion state constraints from Euler angles in each local filter. To further ensure the robustness of quaternion-based attitude solution, the external acceleration term is adaptively compensated within a sliding window of GNSS-V information. Meanwhile, independent and cross check procedures for observation vectors are also established for excluding individual sensor fault by taking land-vehicle dynamics into account. It is of significant importance that, in this contribution, the GNSS measured velocity is fully utilized in all potential aspects of aiding attitude determination with MARG sensors. Real-world vehicular experiments are carried out to evaluate the performance of our proposed method. The presented results verify the validity and efficiency thus the developed method may be promising for implemention in land-vehicle applications.

Agreement and reliability of magnetic, angular rate, and gravity (MARG) sensors to assess multiple body segment’s external loads during off-road running

The extensive use of wearable sensors in sport medicine, exercise medicine, and health has increased the interest in their study. That is why it is necessary to test these technologies’ efficiency, effectiveness, agreement, and reliability in different settings. Consequently, the purpose of this article was to analyze the magnetic, angular rate, and gravity (MARG) sensor’s test-retest agreement and reliability when assessing multiple body segments’ external loads during off-road running. A total of 18 off-road runners (38.78 ± 10.38 years, 73.24 ± 12.6 kg, 172.17 ± 9.48 cm) ran two laps (1st and 2nd Lap) of a 12 km circuit wearing six MARG sensors. The sensors were attached to six different body segments: left (MPLeft) and right (MPRight) malleolus peroneus, left (VLLeft) and right (VLRight) vastus lateralis, lumbar (L1-L3), and thorax (T2-T4) using a special neoprene suit. After a principal component analysis (PCA) was performed, the total data set variance of all body segments was represented by 44.08%–70.64% for the 1st PCA factor considering two variables, Player LoadRT and Impacts, on L1-L3, respectively. These two variables were chosen among three total accelerometry-based external load indicators (ABELIs) to perform the agreement and reliability tests due to their relevance based on PCAs for each body segment. There were no significant differences between laps in the Player LoadRT or Impacts ( p > 0.05, trivial). The intraclass correlation and lineal correlation showed a substantial to almost perfect over-time test consistency assessed via reliability in both Player LoadRT and Impacts. Bias and t-test assessments showed good agreement between Laps. It can be concluded that MARGs sensors offer significant test re-test reliability and good agreement when assessing off-road kinematics in the six different body segments.

Attitude and Heading Estimation for Indoor Positioning Based on the Adaptive Cubature Kalman Filter.

The demands for indoor positioning in location-based services (LBS) and applications grow rapidly. It is beneficial for indoor positioning to combine attitude and heading information. Accurate attitude and heading estimation based on magnetic, angular rate, and gravity (MARG) sensors of micro-electro-mechanical systems (MEMS) has received increasing attention due to its high availability and independence. This paper proposes a quaternion-based adaptive cubature Kalman filter (ACKF) algorithm to estimate the attitude and heading based on smart phone-embedded MARG sensors. In this algorithm, the fading memory weighted method and the limited memory weighted method are used to adaptively correct the statistical characteristics of the nonlinear system and reduce the estimation bias of the filter. The latest step data is used as the memory window data of the limited memory weighted method. Moreover, for restraining the divergence, the filter innovation sequence is used to rectify the noise covariance measurements and system. Besides, an adaptive factor based on prediction residual construction is used to overcome the filter model error and the influence of abnormal disturbance. In the static test, compared with the Sage-Husa cubature Kalman filter (SHCKF), cubature Kalman filter (CKF), and extended Kalman filter (EKF), the mean absolute errors (MAE) of the heading pitch and roll calculated by the proposed algorithm decreased by 4–18%, 14–29%, and 61–77% respectively. In the dynamic test, compared with the above three filters, the MAE of the heading reduced by 1–8%, 2–18%, and 2–21%, and the mean of location errors decreased by 9–22%, 19–31%, and 32–54% respectively by using the proposed algorithm for three participants. Generally, the proposed algorithm can effectively improve the accuracy of heading. Moreover, it can also improve the accuracy of attitude under quasistatic conditions.

Attitude Estimation Using Low-Cost MARG Sensors With Disturbances Reduction

Attitude information obtained from low-cost magnetic, angular rate, and gravity (MARG) sensors is prone to be deteriorated by disturbances such as external acceleration and magnetic anomaly in operational environments. To address the problem, a robust attitude estimation algorithm using low-cost MARG sensors is proposed. An error state Kalman filter (ESKF) is used for data fusing, in which the attitude errors are interpreted as a small rotation vector, and the gyro bias variation is also estimated. The nominal state and the error state are propagated with unit quaternion and rotation vector, respectively. An attitude correction is followed which combines the nominal and error parts by quaternion multiplication. The robustness of the proposed algorithm is embodied in resisting accuracy degradation of the attitude estimation caused by both external acceleration and magnetic anomalies. While external accelerations and magnetic disturbances are detected online, the accuracy reduction in attitude estimation is prevented by adaptively adjusting the related measurement noise covariance matrix. Besides, a two-step measurement update strategy is designed to guarantee that the roll and pitch update is separated from the yaw update. Various rotation and land vehicle dynamic tests have been conducted to validate the effectiveness and robustness of the proposed algorithm.

Potential Use of Wearable Sensors to Assess Cumulative Kidney Trauma in Endurance Off-Road Running.

(1) Background: This study aimed to explore wearable sensors′ potential use to assess cumulative mechanical kidney trauma during endurance off-road running. (2) Methods: 18 participants (38.78 ± 10.38 years, 73.24 ± 12.6 kg, 172.17 ± 9.48 cm) ran 36 k off-road race wearing a Magnetic, Angular Rate and Gravity (MARG) sensor attached to their lower back. Impacts in g forces were recorded throughout the race using the MARG sensor. Two blood samples were collected immediately pre- and post-race: serum creatinine (sCr) and albumin (sALB). (3) Results: Sixteen impact variables were grouped using principal component analysis in four different principal components (PC) that explained 90% of the total variance. The 4th PC predicted 24% of the percentage of change (∆%) of sCr and the 3rd PC predicted the ∆% of sALB by 23%. There were pre- and post-race large changes in sCr and sALB (p ≤ 0.01) and 33% of participants met acute kidney injury diagnosis criteria. (4) Conclusions: The data related to impacts could better explain the cumulative mechanical kidney trauma during mountain running, opening a new range of possibilities using technology to better understand how the number and magnitude of the g-forces involved in off-road running could potentially affect kidney function.

A Novel Fuzzy-Adaptive Extended Kalman Filter for Real-Time Attitude Estimation of Mobile Robots.

This paper proposes a novel fuzzy-adaptive extended Kalman filter (FAEKF) for the real-time attitude estimation of agile mobile platforms equipped with magnetic, angular rate, and gravity (MARG) sensor arrays. The filter structure employs both a quaternion-based EKF and an adaptive extension, in which novel measurement methods are used to calculate the magnitudes of system vibrations, external accelerations, and magnetic distortions. These magnitudes, as external disturbances, are incorporated into a sophisticated fuzzy inference machine, which executes fuzzy IF-THEN rules-based adaption laws to consistently modify the noise covariance matrices of the filter, thereby providing accurate and robust attitude results. A six-degrees of freedom (6 DOF) test bench is designed for filter performance evaluation, which executes various dynamic behaviors and enables measurement of the true attitude angles (ground truth) along with the raw MARG sensor data. The tuning of filter parameters is performed with numerical optimization based on the collected measurements from the test environment. A comprehensive analysis highlights that the proposed adaptive strategy significantly improves the attitude estimation quality. Moreover, the filter structure successfully rejects the effects of both slow and fast external perturbations. The FAEKF can be applied to any mobile system in which attitude estimation is necessary for localization and external disturbances greatly influence the filter accuracy.

A Novel Joint Angle Estimation Method for Serial Manipulator Using Micro-Electromechanical Systems Sensors

This article focuses on the use of low-cost micro-electromechanical systems (MEMS) magnetic, angular rate, and gravity (MARG) sensors in the field of estimating the joint angles of revolute serial manipulators. In particular, an easy-to-install joint angle estimation method, named the incremental decomposition method (IDM), is proposed. It allows the MEMS MARG sensors to be mounted in any attitude on any position of the manipulator's links, with at least one attitude measurement unit on the output side of each joint. The IDM is completely independent from the encoder-based joint angle estimator. Hence, it can work as an assistant fault-detection criterion for the economical robotic arms. A robotic arm with six degrees of freedom is used as the experimental setup. The IDM can estimate the manipulator's joint angles by fusing the attitude quaternion output by the MARG sensors. To validate the performances and limitations of this method, five experiments have been accomplished in this article. The experimental results are reported in order, in comparison with the high-resolution encoders.

A decision-tree based multiple-model UKF for attitude estimation using low-cost MEMS MARG sensor arrays

Micro-electronic-mechanical system (MEMS) is widely used in various applications, especially as a low-cost and small size system for attitude estimation which requires high accuracy and fast response. This work proposes a novel decision-tree based multiple-model unscented Kalman filter (DTMM-UKF) for attitude estimation. It is a quaternion-based attitude estimator that fuses related strap-down magnetic, angular rate, and gravity (MARG) sensor arrays. A set of novel criteria for testing whether the magnetometer and accelerometer are reliable is developed. To improve the anti-interference performance, we define four different filter models for the UKF. Particularly, a decision tree is established to automatically switch filter model based on these reliability test criteria. The priori attitude estimation is obtained from the process model using gyroscope data. Fusing the accelerometer and magnetometer data together, the observation attitude could be solved based on corresponding objective function and Jacobian matrix determined by the filter model. Under the UKF frame, the final optimal attitude could be determined by fusing priori estimation and observed attitude. Experimental tests show that the DTMM-UKF algorithm has better robustness and higher real-time estimation accuracy.

An instrumented glove for monitoring hand function.

The measurement of hand kinematics is important for the assessment and rehabilitation of the paralysed hand. The traditional method of hand function assessment uses a mechanical or electronic goniometer placed across the joint of interest to measure the range of joint movement. Mechanical goniometers are imprecise and lack the ability to provide a dynamic measurement; electronic goniometers are expensive and cumbersome to use during therapy. An alternative to the goniometric based assessment is to use inertial motion sensors to monitor the hand movement-these can be incorporated in a glove. In this paper, we present the design of an instrumented glove equipped with Magnetic, Angular Rate and Gravity (MARG) sensors for the objective evaluation of hand function. The instrumented glove presented in this paper is designed to assess the range of movement of the hand and also monitor the hand function during the course of hand rehabilitation. Static and dynamic calibrations were performed for the Euler angles calculated from the MARG sensors. The results are also presented for physiological flexion/extension of the wrist (relative roll), flexion/extension of elbow (relative pitch), and internal rotation/external rotation (relative yaw). The static calibration results gave mean absolute errors of 4.1° for roll, 4.0° for pitch, and 4.6° for yaw. From the dynamic calibration, the speed of response to a step change gave a convergence time of 0.4 s; sinusoidally oscillating movement gave good tracking at 0.2 Hz but exhibits overshoot errors at higher frequencies which were tested to be 1 Hz. We present the results of the calibration of the instrumented glove (one sensor pair measuring one joint angle) measuring anatomical joint angles-mean absolute errors during static calibration: 6.3° for a relative roll (wrist flexion/extension), 5.0° for relative pitch (elbow flexion/extension), and 4.5° for relative yaw (shoulder internal rotation/external rotation). The experimental results from the instrumented glove are promising, and it can be used as an alternative to the traditional goniometer based hand function assessments.

An Improved Yaw Estimation Algorithm for Land Vehicles Using MARG Sensors.

This paper presents a linear Kalman filter for yaw estimation of land vehicles using magnetic angular rate and gravity (MARG) sensors. A gyroscope measurement update depending on the vehicle status and constraining yaw estimation is introduced. To determine the vehicle status, the correlations between outputs from different sensors are analyzed based on the vehicle kinematic model and Coriolis theorem, and a vehicle status marker is constructed. In addition, a two-step measurement update method is designed. The method treats the magnetometer measurement update separately after the other updates and eliminates its impact on attitude estimation. The performances of the proposed algorithm are tested in experiments and the results show that: the introduced measurement update is an effective supplement to the magnetometer measurement update in magnetically disturbed environments; the two-step measurement update method makes attitude estimation immune to errors induced by magnetometer measurement update, and the proposed algorithm provides more reliable yaw estimation for land vehicles than the conventional algorithm.

Criterion Validity of a MARG Sensor to Assess Countermovement Jump Performance in Elite Basketballers.

Staunton, CA, Stanger, JJ, Wundersitz, DW, Gordon, BA, Custovic, E, and Kingsley, MI. Criterion validity of a MARG sensor to assess countermovement jump performance in elite basketballers. J Strength Cond Res 35(3): 797-803, 2021-This study assessed the criterion validity of a magnetic, angular rate, and gravity (MARG) sensor to measure countermovement jump (CMJ) performance metrics, including CMJ kinetics before take-off, in elite basketballers. Fifty-four basketballers performed 2 CMJs on a force platform with data simultaneously recorded by a MARG sensor located centrally on the player's back. Vertical accelerations recorded from the MARG sensor were expressed relative to the direction of gravity. Jumps were analyzed by a blinded assessor and the best jump according to the force platform was used for comparison. Pearson correlation coefficients (r) and mean bias with 95% ratio limits of agreement (95% RLOA) were calculated between the MARG sensor and the force platform for jumps performed with correct technique (n = 44). The mean bias for all CMJ metrics was less than 3%. Ninety-five percent RLOA between MARG- and force platform-derived flight time and jump height were 1 ± 7% and 1 ± 15%, respectively. For CMJ performance metrics before takeoff, impulse displayed less random error (95% RLOA: 1 ± 13%) when compared with mean concentric power and time to maximum force displayed (95% RLOA: 0 ± 29% and 1 ± 34%, respectively). Correlations between MARG and force platform were significant for all CMJ metrics and ranged from large for jump height (r = 0.65) to nearly perfect for mean concentric power (r = 0.95). Strong relationships, low mean bias, and low random error between MARG and force platform suggest that MARG sensors can provide a practical and inexpensive tool to measure impulse and flight time-derived CMJ performance metrics.

Adaptive EKF Based on HMM Recognizer for Attitude Estimation Using MEMS MARG Sensors

This paper addresses the intractable problem of attaining precise attitude estimation efficiently using MEMS MARG (magnetic, angular rate, and gravity) sensors for 3-D motion tracking, which is called attitude and heading reference system (AHRS). The performance of AHRS is adversely affected by sensor noise and measurement disturbances. To overcome this problem, we propose a novel adaptive extended Kalman filter (AEKF) in this paper, including a multiplicative extended Kalman filter (MEKF) and a hidden Markov Model (HMM) recognizer. MEKF is built on sensor noise model. An HMM recognizer is developed to identify the measurement disturbance caused by motion or environmental interference and then to adjust the noise covariance of MEKF adaptively. The proposed AEKF was assessed with a high-precision test platform by using a high-caliber commercial AHRS. Experimental results indicate that the proposed method achieves a higher level of stability and accuracy in comparison to other attitude estimators, especially in dynamic tests, which demonstrates the availability of 3-D motion tracking.