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

Abstract

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.

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“…The proprietary filter included with the sensors resulted in more drift for all subjects (Additional file 1 : Figure S5), likely because the filter rejected the distorted magnetometer signal over too long a duration. Recent work has shown that Kalman filters can be formulated to achieve good accuracy over long durations [ 24 ]. Some prior work has shown complementary filters drift with measurement duration [ 23 , 42 ].…”

“…Validation studies applying sensor fusion methods in human movement analysis have reported average RMS differences in the range of 1.7°–8° for joint angles over short durations (on the order of one minute) [ 5 , 19 – 21 ]. Recent work has shown that sensor fusion algorithms [ 22 – 24 ] can produce estimations of sensor orientations with less than 10° RMS difference over five minutes. We extend the work by estimating drift-free physiologically realistic joint angles in new experimental conditions over 10 min.…”

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“…EKFs are used for the sensor fusion of gyroscopes and accelerometers in order to estimate the joints orientation [8], [38], [66], [70], [72], [92], [96], joints orientation and location [55], [76], [79], [88], [108] and segment orientation [77], [78]. Researchers also use EKFs to fuse gyroscope and accelerometer data with magnetometer measurements to estimate the orientation of joints [138], [142] or segments [117], [118], [135], [140], [145]. EKFs are also combined with the Gauss-Newton algorithm to fuse the information of gyroscopes and accelerometers and estimate the orientation of joints [64].…”

“…Other corrections found in the literature that are not related with biomechanical properties include the following: modeling the bias of sensors or including them in the state vector [13], [19], [30], [33], [36], [44], [46], [52], [57], [60]- [63], [70], [75], [82], [83], [95], [117]- [119], [123], [125], [139], [153], [173]; calibrating this bias [30], [44], [46], [97], [104], [105], [121], [124], [133], [150]; low-pass filtering the recorded signals [11], [14], [37], [41], [45], [63], [71], [143], [145]; or optimizing them [67], updating the estimations when a direct observation of gravity is available or with its dynamic compensation [35], [43], [48],…”

“…Other acronyms: BC: biomechanical constraints, ANT: anatomical parameters in use, OC: other constraints, ML learns: refers to that theses ML-based algorithms learn for real motions so they are constraint to anatomical joint limits and EST: refers to the use of anatomical or soft constraints after estimate the required parameters, GS: gyroscope sensor, AS: accelerometer sensor, MS: magnetometer sensor, OS: other sensors for training, EST: type of estimation, ANG: angle, DIS: displacement or position, JNT: joint and SGM: segment. AS MS OS ESTANG DIS JNT SGMA basic study on variable-gain Kalman filter based on angle error calculated from acceleration signals for lower limb angle measurement with inertial sensors[33] Comparison of Three Neural Network Approaches for Estimating Joint Angles and Moments from Inertial Measurement Units[34] quaternion-based orientation optimizer via virtual rotation for human motion tracking[116] State Robust Extended Kalman Filter for Orientation Tracking during Long-Duration Dynamic Tasks Using Magnetic and Inertial Measurement Units[117] to accurate measurement of uniaxial joint angles based on a combination of accelerometers and gyroscopes[37] quaternion-based kalman filter for human body motion tracking using the second estimator of the optimal quaternion algorithm and the joint angle constraint method with inertial and magnetic sensors[120] -based estimator for functional electrical stimulation: Preliminary results from lower-leg extension experiments [degrees of freedom model for upper limb kinematic reconstruction based on wearable sensors[121] AS MS OS ESTANG DIS JNT SGMA novel approach to motion tracking with wearable sensors based on Probabilistic Graphical Models[122] filter for tracking hip angles during cycling using wireless inertial sensors and dynamic acceleration estimation [glove for fingers motion capture using inertial and magnetic measurement units[124] for estimating knee angle using two legmounted gyroscopes for continuous monitoring with mobile health devices sensor-based assessment of lower limb spasticity in children with cerebral palsy[41] of measurement of joint angles and stride length with wireless inertial sensors for wearable gait evaluation system [of gait analysis with a smartphone for measurement of hip joint angle[12] Wearable Magnetometer-Free Motion Capture System: Innovative Solutions for Real-World Applications[44] Accuracy of a custom physical activity and knee angle measurement sensor system for patients with neuromuscular disorders and gait abnormalities[45] AS MS OS EST ANG DIS JNT SGM Ambulatory estimation of knee-joint kinematics in anatomical coordinate system using accelerometers and magnetometers[129] An adaptive complementary filter for inertial sensor based data fusion to track upper body motion[47] An auto-calibrating knee flexion-extension axis estimator using principal component analysis with inertial sensors…”