Magnetic And Inertial Measurement Units Research Articles

Kinematic stabilization after the Latarjet procedure. Beyond the triple blocking effect

BackgroundThe rationale for the Latarjet procedure was described as the “triple blocking” effect. Satisfactory surgical outcomes have been reported after surgery. However, it has been reported that the “triple blocking” effect increases joint stability, but it does not fully restore it. Moreover, the procedure is nonanatomic and concerns remain regarding the effects. The study of scapulohumeral rhythm, which is a clinical parameter used for the functional evaluation of shoulder kinematics, can offer new perspectives on the rationale for the procedure. This study aimed to compare the shoulder kinematics of patients after the Latarjet procedure to the shoulders of a healthy population using magnetic and inertial measurement units (MIMUs) with a motion analysis system. MethodsA retrospective study with prospective data collection was conducted on 28 patients who underwent the open Latarjet procedure for recurrent shoulder instability. At a minimum 12-month follow-up, each patient was evaluated by assessing the range of motion (ROM), the Rowe score, and the Constant-Murley score (CMS). Patients were examined using the ShowMotion 3D kinematic tracking system (NCS Lab, Modena, Italy), which uses wireless wearable noninvasive MIMUs sensors to assess the three-dimensional kinematics of the shoulder. For each plane of elevation (i.e., flexion and abduction), the scapulohumeral rhythm (SHR) was described by three scapulothoracic rotations (i.e., protraction–retraction, mediolateral rotation and posterior–anterior tilting) as a function of humeral anteflexion or humeral abduction. ResultsThe mean time from first shoulder dislocation to surgery was 6.6 ± 3 years (range, 1-12 years). No intraoperative complications occurred, and CT performed 3 months after surgery showed graft union in all patients. After a mean follow-up time of 32.4±20 months (range, 12-96), the mean CMS and Rowe scores were 94.5±4.8 (range, 84-100) and 96.7±3.5 (range, 90–100), respectively. All patients showed no signs of glenohumeral arthritis on X-ray examination. Scapular posterior tilt and scapular internal rotation were significantly greater in the patient group than in the healthy population for the flexion–extension and abduction–adduction movements along the whole shoulder range of motion (all p < 0.05); no differences were found in upward/downward scapular rotation. ConclusionA greater scapular posterior tilt and scapular internal rotation were observed after the Latarjet procedure. The modified position of the scapula was maintained during the entire ROM, suggesting a shoulder-stabilizing kinematic effect in addition to the bony, sling and bumper effects.

A convenient approach for knee kinematics assessment using wearable inertial sensors during home-based rehabilitation: Validation with an optoelectronic system

Rehabilitation services are among the most severely impacted by the COVID-19 pandemic. This has increased the number of people not receiving the needed rehabilitation care. Home-based rehabilitation becomes alternative support to face this greater need. However, monitoring kinematics parameters during rehabilitation exercises is critical for an effective recovery. This work proposes a detailed framework to estimate knee kinematics using a wearable Magnetic and Inertial Measurement Unit (MIMU). That allows at-home monitoring for knee rehabilitation progress. Two MIMU sensors were attached to the shank and thigh segments respectively. First, the absolute orientation of each sensor was estimated using a sensor fusion algorithm. Second, these sensor orientations were transformed to segments orientations using a functional sensor-to-segment (STS) alignment. Third, the relative orientation between segments, i.e., knee joint angle, was computed and the relevant kinematics parameters were extracted. Then, the validity of our approach was evaluated with a gold-standard optoelectronic system. Seven participants completed three to five Timed-Up-and-Go (TUG) tests. The estimated knee angle was compared to the reference angle. Root-mean-square error (RMSE), correlation coefficient, and Bland-Altman analysis were considered as evaluation metrics. Our results showed reasonable accuracy (RMSE < 8°), strong to very-strong correlation (correlation coefficient > 0.86), a mean difference within 1.1°, and agreement limits from -16° to 14°. In addition, no significant difference was found (p-value > 0.05) in extracted kinematics parameters between both systems. The proposed approach might represent a suitable alternative for the assessment of knee rehabilitation progress in a home context.

An EKF-Based Attitude Estimator for Eliminating the Effect of Magnetometer Measurements on Pitch and Roll Angles

Nowadays, magnetic and inertial measurement units (MIMUs) have become useful tools for determining the attitude of moving objects. An attitude calculation algorithm (ACA) is programed into an MIMU, which determines the attitude by fusing three built-in sensors, namely, gyroscope, accelerometer, and magnetometer. Attitude is often represented by Euler angles, quaternion, or rotation matrix. Despite that great development has been achieved, how to eliminate the negative effect of magnetic disturbance on the pitch and roll estimation is still difficult for an ACA. This article aims to propose an Extended Kalman Filter (EKF)-based approach for problem solving. Inspired by the fact that the Euler angles are computed by using some elements of the rotation matrix, a diagonalizable regulation matrix (DRM) is multiplied to the right half part of the gain matrix (which is multiplied to the residual of the magnetometer measurement in the update stage of EKF). The determination of DRM is based on the principle that these elements can be appropriately regulated by the DRM so as to make the magnetometer measurement only participate in the computation of azimuth. No further revision to EKF is made except the Kalman gain matrix, hence the proposed EKF behaves similar as traditional EKF, except its ability of eliminating the negative effect of magnetic disturbance on the pitch and roll estimation. The superiority of the proposed EKF is validated by comparing it with four other competing algorithms through simulation and experimental experiments.

Measurement of Hand Joint Angle Using Inertial-Based Motion Capture System

The inertial sensor motion capture system has significant advantages over the classical optical motion capture system, including its high versatility, portability, and affordability. However, its accuracy is over one order of magnitude lower than the optical system. The measurement error of the finger joint angle is mainly due to sensor drift and misalignment of sensor to finger segment. In this article, we propose a method that includes both orientation estimation and calibration for accurate joint angle estimation. Specifically, at first, the accuracy of the sensor orientation is greatly improved using the square root cubature Kalman filter (SRCKF) to fuse the magnetic and inertial measurement units (MIMUs) data. Second, the kinematic restrictions of the finger joints are used for initial and in-process calibration to achieve sensor-to-segment (StoS) calibration throughout the process. Finally, the difference between the orientation of the two adjacent segments is the joint angle. Experiments show that our proposed system improves joint measurement accuracy compared with the existing inertial sensor-based systems. Evaluation of ten participants showed that the average root mean square error (RMSE) of finger joint measurements is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5.5^{\circ }(\pm 4.0^{\circ })$ </tex-math></inline-formula> . Our proposed system provides accurate information in measuring hand joint angles and quantifying hand movement function in clinical practice.

A Time-Efficient Complementary Kalman Gain Filter Derived From Extended Kalman Filter and Used for Magnetic and Inertial Measurement Units

Magnetic and inertial measurement units (MIMUs) are mainly used for determining the attitude of moving bodies. The extended Kalman filter (EKF) and the complementary filters (CFs) are the most commonly applied algorithms for calculating the attitude of the body that an MIMU is attached. Despite its much higher accuracy than CFs, the time-consuming EKF may not be competent for the work of attitude calculation if a microcomputer with limited computation power is used. To any attitude calculating algorithm, its posterior attitude (PA) is computed as: PA = prior attitude + gain matrix (GM) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> innovation. The prior attitude and the innovation are derived from the measurements of the gyroscope, the accelerometer, and the magnetometer. The detailed analysis in this study found that the reason for the performance difference between EKF and CFs is their different structures of the GMs, which promotes the authors to construct a new GM. Based on some reasonable assumptions, the GM of EKF is simplified under the principle that the computation accuracy of PA is decreased as little as possible, but its computation burden is reduced as much as possible. After the replacement of the GM of the EKF by the innovatively designed GM, a new CF, named time-efficient complementary Kalman gain filter (TCF), is proposed. The simulation and experimental results show that TCF performs better than two CFs and is close to EKF in terms of attitude estimation accuracy but uses nearly the same computation time as the two CFs and about half of the computation time required by EKF.

A functional calibration protocol for ankle plantar-dorsiflexion estimate using magnetic and inertial measurement units: Repeatability and reliability assessment

The ankle joint complex presents a tangled functional anatomy, which understanding is fundamental to effectively estimate its kinematics on the sagittal plane. Protocols based on the use of magnetic and inertial measurement units (MIMUs) currently do not take in due account this factor. To this aim, a joint coordinate system for the ankle joint complex is proposed, along with a protocol to perform its anatomical calibration using MIMUs, consisting in a combination of anatomical functional calibrations of the tibiotalar axis and static acquisitions. Protocol repeatability and reliability were tested according to the metrics proposed in Schwartz et al. (2004) involving three different operators performing the protocol three times on ten participants, undergoing instrumented gait analysis through both stereophotogrammetry and MIMUs. Instrumental reliability was evaluated comparing the MIMU-derived kinematic traces with the stereophotogrammetric ones, obtained with the same protocol, through the linear fit method. A total of 270 gait cycles were considered. Results showed that the protocol was repeatable and reliable for what concerned the operators (0.4 ± 0.4 deg and 0.8 ± 0.5 deg, respectively). Instrumental reliability analysis showed a mean RMSD of 3.0 ± 1.3 deg, a mean offset of 9.4 ± 8.4 deg and a mean linear relationship strength of R2 = 0.88 ± 0.08. With due caution, the protocol can be considered both repeatable and reliable. Further studies should pay attention to the other ankle degrees of freedom as well as on the angular convention to compute them.

A Wearable System Based on Multiple Magnetic and Inertial Measurement Units for Spine Mobility Assessment: A Reliability Study for the Evaluation of Ankylosing Spondylitis.

Spinal mobility assessment is essential for the diagnostic of patients with ankylosing spondylitis. BASMI is a routine clinical evaluation of the spine; its measurements are made with goniometers and tape measures, implying systematic errors, subjectivity, and low sensitivity. Therefore, it is crucial to develop better mobility assessment methods. The design, implementation, and evaluation of a novel system for assessing the entire spine’s motion are presented. It consists of 16 magnetic and inertial measurement units (MIMUs) communicated wirelessly with a computer. The system evaluates the patient’s movements by implementing a sensor fusion of the triaxial gyroscope, accelerometer, and magnetometer signals using a Kalman filter. Fifteen healthy participants were assessed with the system through six movements involving the entire spine to calculate continuous kinematics and maximum range of motion (RoM). The intrarater reliability was computed over the observed RoM, showing excellent reliability levels (intraclass correlation >0.9) in five of the six movements. The results demonstrate the feasibility of the system for further clinical studies with patients. The system has the potential to improve the BASMI method. To the best of our knowledge, our system involves the highest number of sensors, thus providing more objective information than current similar systems.

Sensor fusion algorithms for orientation tracking via magnetic and inertial measurement units: An experimental comparison survey

Lightweight and low-cost wearable magnetic and inertial measurement units (MIMUs) have found numerous applications, such as aerial vehicle navigation or human motion analysis, where the 3D orientation tracking of a rigid body is of interest. However, due to the errors in measurements of gyroscope, accelerometer, and/or magnetometer inside a MIMU, numerous studies have proposed sensor fusion algorithms (SFAs) to estimate the 3D orientation accurately and robustly. This paper contributes to these efforts by performing an experimental comparison among a variety of SFAs. Notably, we compared the estimated orientation of 36 SFAs from the complementary filter and linear/extended/complementary/unscented/cubature Kalman filter families with the reference orientation obtained from a camera motion-capture system. The experimental study included data collection with a foot-worn MIMU where nine participants performed various short- and long-duration tasks. We shared the codes and sample of data in https://www.ncbl.ualberta.ca/codes to enable other researchers to compare their works with the literature toward creating a comprehensive online repository for SFAs. To perform a fair comparison, we used the Particle Swarm Optimization routine to find the optimal adaptive gain tuning scheme for each SFAs, as recommended in the literature. Our experimental results showed that gyroscope static bias removal, in general, showed to be effective in reducing the estimation error of SFAs, specifically during long-duration trials. Moreover, our experimental results identified the SFAs with the highest accuracy from each family. We also reported the execution times for the selected SFAs from each family. This paper is among the first experimental comparison studies which provide such breadth of coverage across various SFAs for tracking orientation with MIMUs.

A Full-State Robust Extended Kalman Filter for Orientation Tracking During Long-Duration Dynamic Tasks Using Magnetic and Inertial Measurement Units.

Accurate and robust orientation estimation using magnetic and inertial measurement units (MIMUs) has been a challenge for many years in long-duration measurements of joint angles and pedestrian dead-reckoning systems and has limited several real-world applications of MIMUs. Thus, this research aimed at developing a full-state Robust Extended Kalman Filter (REKF) for accurate and robust orientation tracking with MIMUs, particularly during long-duration dynamic tasks. First, we structured a novel EKF by including the orientation quaternion, non-gravitational acceleration, gyroscope bias, and magnetic disturbance in the state vector. Next, the a posteriori error covariance matrix equation was modified to build a REKF. We compared the accuracy and robustness of our proposed REKF with four filters from the literature using optimal filter gains. We measured the thigh, shank, and foot orientation of nine participants while performing short- and long-duration tasks using MIMUs and a camera motion-capture system. REKF outperformed the filters from literature significantly (p < 0.05) in terms of accuracy and robustness for long-duration tasks. For example, for foot MIMU, the median RMSE of (roll, pitch, yaw) were (6.5, 5.5, 7.8) and (22.8, 23.9, 25) deg for REKF and the best filter from the literature, respectively. For short-duration trials, REKF achieved significantly (p < 0.05) better or similar performance compared to the literature. We concluded that including non-gravitational acceleration, gyroscope bias, and magnetic disturbance in the state vector, as well as using a robust filter structure, is required for accurate and robust orientation tracking, at least in long-duration tasks.

A Simplified Extended Kalman Filter Used for Magnetic and Inertial Measurement Units

As a sensor unit, a magnetic and inertial measurement unit (MIMU) is mainly composed of a tri-axis gyroscope, a tri-axis accelerometer and a tri-axis magnetometer. The Extended Kalman Filter (EKF) is the currently preferred algorithm used to fuse the outputs of the MIMU sensor in order to determine the attitude of the MIMU's carrier platform. One of the main problems of the EKF is its high computational cost, which is largely due to solving the matrix inversion in the Kalman gain. This article simplifies the Kalman gain by ensuring it does not contain any matrices that would require an inversion operation. This is achieved by simplifying the linearized measurement matrix (the Jacobian matrix) through orthogonalizing the observation and reference vectors. The inversion of the matrix contained in the Kalman gain can then be mathematically derived and the derived matrix can eventually replace the matrix inversion, in order to avoid the inversion operation when the EKF is executed. The simplified EKF is compared to the traditional EKF experimentally and the results show that the simplified method has similar accuracy to the traditional method, but with a faster execution time.

40 years of sensor fusion for orientation tracking via magnetic and inertial measurement units: Methods, lessons learned, and future challenges

Technological developments over the past two decades have resulted in the development of more accurate and lightweight low-cost magnetic and inertial measurement units (MIMUs). These developments have allowed the extensive application of MIMUs in various fields, specifically tracking the 3D orientation of a rigid body. Despite recent technological improvements, measurements from a tri-axial gyroscope, accelerometer, and/or magnetometer inside the MIMU are characterized by uncertainties. Numerous studies have been conducted to address these uncertainties and develop sensor fusion algorithms (SFAs) to estimate the 3D orientation accurately and robustly. This paper contributes to these efforts by providing a survey of the state-of-the-art SFAs for orientation estimation. We surveyed +250 publications, categorized the SFAs with various structures, identified the modifications proposed to improve their performance, and discussed the strengths and weaknesses of these approaches. We found that, while early SFAs were mostly a vector observation algorithm or an extended Kalman filter, to improve the computational efficiency, more recent works have developed SFAs with a complementary filter or complementary Kalman filter structure. At the same time, to improve the performance of the SFAs, several research teams have proposed various modifications to the basic structure of these filters, such as adaptive gain tuning or imperfect measurement rejection. We also provided an outlook on the lessons learned as well as the main challenges related to SFAs and discussed the practical steps toward developing an effective SFA. We have identified the need for benchmarking studies as the main challenge at the moment. This paper is among the first surveys which provide such breadth of coverage across different SFAs for tracking orientation with MIMUs.

Investigation of Orientation Estimation of Multiple IMUs

Inertial Measurement Units (IMUs) were first applied to aircraft navigation and large devices in the 1930s. At that time their application was restricted because of constraints such as size, cost, and power consumption. In recent years, however, Micro-electromechanical (MEMS) IMUs were introduced with very favorable features such as low cost, compactness, and low processing power. One of the disadvantages of these low cost IMU sensors is that the accuracy is lower compared to high-end sensors. However, past experimental results have shown that redundant Magnetic and Inertial Measurement Units (MIMUs) improve navigation performance such as for unmanned air vehicles. Even though past simulation and experimental results demonstrated that redundant sensors improve the navigation performance, however, none of the current research work offers information as to how many sensors are required in order to meet a certain accuracy. This paper evaluates different numbers of sensor configurations of an MIMU sensor array using a simulation environment. Differently rotated MIMU sensors are incrementally added and the Madgwick filter is used to estimate the Euler angles of foot mounted MIMU data. The evaluation measure used is the root mean square error (RMSE) based on the Euler angles as compared to the ground truth. During the experiments it was noticed that the execution time with increasing number of sensors increases exponentially, and thus, the parallelization of the code was designed and implemented, and run on a multi-core machine. Thus, the speedup of the parallel implementation was evaluated. The findings using the parallel version with 16 sensors are that the execution time is less than twice the execution time of having only 1 sensor and 24 times less than using the sequential version with the added benefit of a 26% increase in accuracy.

Adaptive Gain Regulation of Sensor Fusion Algorithms for Orientation Estimation with Magnetic and Inertial Measurement Units

Magnetic and inertial measurement units (MIMUs) proved to be an accurate alternative for optic, electromagnetic, or acoustic measurement technologies. While the orientation of the MIMU could be estimated using accelerometer, gyroscope, or magnetometer sensors alone, many studies proposed sensor fusion algorithms (SFAs) to overcome the drawbacks that appear when each sensor is used individually. However, the performance of such SFAs highly depends on their gains, and poor initialization or incorrect adjustment of the gains would degrade the SFAs’ performance. Therefore, this article proposes a general framework to find the optimal adaptive gain tuning scheme for Kalman filters and complementary filters to achieve accurate and robust orientation estimation with MIMUs. To this end, we proposed an innovative optimization framework to find the fixed optimal gain of an SFA or the optimal adaptive gain regulation scheme. Also, we demonstrated that the designed adaptive gain regulation scheme (a hard switch with two or three levels or a fuzzy inference system) is essential for orientation tracking with various SFAs. We measured the thigh, shank, and foot motion of nine participants while performing various activities using MIMUs and a camera motion-capture system to calculate the MIMUs’ error in 3-D angle estimations. Gain regulation by hard switch was significantly ( $p ) more accurate and robust than it was for innovation adaptive estimation. Also, for all tested SFAs, hard switching for shank and foot MIMUs was significantly more accurate or robust than that for fixed optimal gain. Our experimental results showed that the adaptive gain tuning of SFAs using optimized gains is crucial, regardless of the algorithm structure or complexity.

Feasibility of quantifying the physical exposure of materials handlers in the workplace with magnetic and inertial measurement units

Handling tasks can expose workers to risk factors. The objective was to describe the feasibility of using magnetic and inertial measurement units (MIMUs) to quantify the physical exposure of materials handlers in the workplace. Full-body kinematics were obtained with MIMUs on 10 handlers gathering products ordered by retailers with a pallet truck. An observer classified the visual difference (VD) of segment orientation between a MIMUs avatar and video recordings in three categories (none, minor and major) for each product transfer. The feet, arms, shoulders and head were considered similar for ≥97% of observations. The trunk segment obtained the most differences with 9% of minor VD and 5% of major VD, which were related to the duration of the magnetic disturbances of the MIMUs. Estimating parameters of the physical exposure of handlers in the workplace is feasible with kinematics and an order list, but visual verification remains important for scientific rigour.Practitioner Summary: The feasibility of measuring physical exposure with magnetic and inertial measurement units was evaluated on materials handlers in the workplace. Visual observation of the postures indicated that most of the data is considered acceptable. Magnetic disturbances can increase the measurement error, so data must be verified to ensure validity.

Sensor to segment calibration for magnetic and inertial sensor based motion capture systems

This study aims to propose a novel sensor to segment calibration method for magnetic and inertial measurement unit (M-IMU) based human motion capture systems. The calibration procedure is designed to be easily performed by the subject, which can calibrate the whole body segments with only three predefined postures. Firstly, the orientation measurements for each body segment are collected during calibration process. Secondly, a segmentation procedure based on a moving average window algorithm and double-threshold technique is introduced to recognize and segment the calibration postures automatically. To suppress the shaking during the calibration process, an intrinsic average algorithm is presented to smooth the orientation measurements. Finally, an iteration hand-eye calibration approach is utilized to retrieve the sensor to segment calibration matrices. The error due to the ungraded calibration postures can be reduced observably, and we also define an indicator to evaluate the quality of the performed calibration postures. The calibration procedure has been validated on several subjects using a wearable M-IMU based motion capture system. Experiment results show that the proposed calibration method can suppress the shaking disturbances effectively, and has good repeatability.

Sensor-to-body calibration procedure for clinical motion analysis of lower limb using magnetic and inertial measurement units

Magnetic and Inertial measurement units (MIMUs) have become exceedingly popular for ambulatory human motion analysis during the past two decades. However, measuring anatomically meaningful segment and joint kinematics requires virtual alignment of the MIMU frame with the anatomical frame of its corresponding segment. Therefore, this paper presents a simple calibration procedure, based on MIMU readouts, to align the inertial frame of the MIMU with the anatomical frames, as recommended by ISB. The proposed calibration includes five seconds of quiet standing in a neutral posture followed by ten consecutive hip flexions/extensions. This procedure will independently calibrate MIMUs attached to the pelvis, thigh, shank, and foot. The accuracy and repeatability of the calibration procedure and the 3D joint angle estimation were validated against the gold standard motion capture system by an experimental study with ten able-bodied participants. The procedure showed high test-retest repeatability in aligning the MIMU frame with its corresponding anatomical frame, i.e., the helical angle between the MIMU and anatomical frames did not significantly differ between the test and retest sessions (except for thigh MIMU). Compared to previously introduced procedures, this procedure attained the highest inter-participant repeatability (inter-participant coefficient of variations of the helical angle: 20.5–42.2%). Further, the proposed calibration would reduce the offset errors of the 3D joint angle estimation (up to 12.8 degrees on average) compared to joint angle estimation without calibration (up to 26.3 degrees on average). The proposed calibration enables MIMU to measure clinically meaningful gait kinematics.

Computationally Efficient Adaptive Error-State Kalman Filter for Attitude Estimation

A geometrically intuitive quaternion-based complementary attitude and heading reference system (CAHRS) proposed in our previous work estimated the attitude of a magnetic and inertial measurement unit (MIMU). The method used two correction factors, $\mu _{_{a}}$ that determined the rate at which the accelerometer corrected the inclination angle, and $\mu _{_{m}}$ that governed the rate at which the magnetometer corrected the yaw angle. Improvements to the filter have been made by embedding each correction factor within an error-state Kalman filter (KF), enabling the correction rates to behave adaptively. The revised filter only estimates the error in two variables, thus remaining computationally efficient (65 addition, 88 subtraction, and 214 multiplication operations) compared with established algorithms in the literature for attitude estimation that utilize a KF or extended KF. The accuracy of the attitude estimated (i.e., the pitch, roll, and yaw angle errors $\theta _{\text {RMSE}_{_{}}}^{\circ }$ , $\phi _{\text {RMSE}}^{\circ }$ , and $\psi _{\text {RMSE}}^{\circ }$ ) by the adaptive error-state KF was compared with the CAHRS algorithm and a cascaded KF that is representative of state-of-the-art methods. Each algorithm was assessed using a publicly available data set in which the attitude of a foot-worn magnetic and inertial measurement units was recorded by a motion capture system while participants walked and ran around a room for one or three minutes ( $\phi _{\text {RMSE}}^{\circ } = 2.08^\circ $ , $\theta _{\text {RMSE}}^{\circ } = 1.98^\circ $ , and $\psi _{\text {RMSE}}^{\circ }= 5.25^\circ $ ).

Adaptive regulation of the weights of REQUEST used to magnetic and inertial measurement unit based on hidden Markov model

An attitude algorithm is used by a given magnetic and inertial measurement unit (MIMU) for weight fusion of the outputs of gyroscope and the outputs of the subunit constructed by accelerometer and magnetometer for attitude calculation of a rigid body. It has been proved that the weight assigned to the outputs of gyroscope determines the overall performances of attitude algorithm. A new weight adaptive regulation method based on Kalman filter and hidden Markov model is proposed, and then a new attitude algorithm is constructed by the integration of that method with recursive quaternion estimation algorithm. The authors’ attitude algorithm is compared with some other related attitude algorithms in their experiments. With the outputs of the sensors in MTi as the inputs of the new attitude algorithm, the maximum attitude estimation errors in response to three-dimensional random movements and the changes of their amplitudes are 2.85° and 6.82°, respectively, and the Allan variance of attitude drift in response to motionless conditions is 2.1×10−4°. Other attitude algorithms cannot simultaneously achieve similar dynamic and similar static performances comparing to their attitude algorithm. The results validate the overall performance improvement of their attitude algorithm.

Adaptive-Gain Regulation of Extended Kalman Filter for Use in Inertial and Magnetic Units Based on Hidden Markov Model

Magnetic and inertial measurement units (MIMUs) are promising tools for attitude tracking of moving bodies without location restriction. An extended Kalman filter (EKF) is a commonly used attitude algorithm for MIMUs, and its Kalman gain is usually regulated according to the measurements of the accelerometer for the best integrated performance, i.e., the best performance for both when the carrier is motionless and when the carrier is moving. A hidden Markov model (HMM) is introduced, and then trained using static measurements of the accelerometer. Once the body has a movement, the match probability between the dynamic measurements of the accelerometer and the trained HMM will decrease, which is then used for the timely regulation of the Kalman gain to make the EKF rely more on the measurements of the gyroscope for attitude calculation. A slight revision to the introduced HMM is given for the improvement of the smoothness of the outputs of the HMM when the carrier is motionless. A relationship between the Kalman gain and the output of the HMM is also given, and the value range of the outputs of the HMM is readjusted in order to fit that relationship. Six competitive methods are compared with our method, and simulation and experiment tests validate the superiority of our method.

Concurrent validation of magnetic and inertial measurement units in estimating upper body posture during gait

We assessed the concurrent validity of commercially available magnetic and inertial measurement units (MIMUs) for estimating mean postural angles for head flexion, thorax flexion and shoulder girdle elevation during gait in seven healthy individuals. Postural angles estimated with the MIMUs were compared with angles calculated using marker data from a gold standard motion capture system. Coefficients of determination of mean postural angles between measurement systems were 0.82 for head flexion, 0.58 for thorax flexion, and 0.77 for shoulder girdle elevation. Bland–Altman analysis showed good agreement between measurement systems. Intraclass correlation coefficients were 0.9 for head flexion, 0.73 for thorax flexion, and 0.87 for shoulder girdle elevation. Root mean square errors were less than 3° between measurement systems for all body segments. The present findings suggest that the MIMUs tested in this study are valid for estimating head flexion, thorax flexion and shoulder girdle elevation during gait.