Strapdown Integration Research Articles

Validation of algorithms for calculating spatiotemporal gait parameters during continuous turning using lumbar and foot mounted inertial measurement units

Spatiotemporal gait parameters such as step time and walking speed can be used to quantify gait performance and determine physical function. Inertial measurement units (IMUs) allow for the measurement of spatiotemporal gait parameters in unconstrained environments but must be validated against a gold standard.While many IMU systems and algorithms have been validated during treadmill walking and overground walking in a straight line, fewer studies have validated algorithms during more complex walking conditions such as continuous turning in different directions.This study explored the concurrent validity in a population of healthy adults (range 26–52 years) of three different algorithms using lumbar and foot mounted IMUs to calculate spatiotemporal gait parameters: two methods utilizing an inverted pendulum model, and one method based on strapdown integration. IMU data was compared to a Vicon twelve-camera optoelectronic system, using data collected from 9 participants performing straight walking and continuous walking trials at different speeds, resulting in 162 walking trials in total. Intraclass correlation coefficients (ICCA,1) for absolute agreement were calculated between the algorithm outputs and Vicon output.Temporal parameters were comparable in all methods and ranged from moderate to excellent, except double support time which was poor. Strapdown integration performed better for estimating spatial parameters than pendulum models during straight walking, but worse during turning. Selecting the most appropriate model should take into consideration both speed and walking condition.

Convolutional Neural Network for Estimating Spatiotemporal and Kinematic Gait Parameters using a Single Inertial Sensor.

Lower limb disability severely impacts gait, thus requiring clinical interventions. Inertial sensor systems offer the potential for objective monitoring and assessment of gait in and out of the clinic. However, it is imperative such systems are capable of measuring important gait parameters while being minimally obtrusive (requiring few sensors). This work used convolutional neural networks to estimate a set of six spatiotemporal and kinematic gait parameters based on raw inertial sensor data. This differs from previous work which either was limited to spatiotemporal parameters or required conventional strap-down integration techniques to estimate kinematic parameters. Additionally, we investigated a data segmentation method which does not rely on gait event detection, further supporting its applicability in real-world settings.Preliminary results demonstrate our model achieved high accuracy on a mix of spatiotemporal and kinematic gait parameters, either meeting or exceeding benchmarks based on literature. We achieved 0.04 ± 0.03 mean absolute error for stance-time symmetry ratio and an absolute error of 4.78 ± 4.78, 4.50 ± 4.33, and 6.47 ± 7.37cm for right and left step length and stride length, respectively. Lastly, errors for knee and hip ranges of motion were 2.31 ± 4.20 and 1.73 ± 1.93°, respectively. The results suggest that machine learning can be a useful tool for long-term monitoring of gait using a single inertial sensor to estimate measures of gait quality.

Magnetometer-free Kalman filter for motor-based assessment of prodromal Parkinson's disease.

Observing the kinematics of specific motor tasks, such as finger tapping (FT), provides an objective and consistent quantification of the severity of neurodegenerative diseases. However, the current clinical practice mostly relies on visual observations performed by the clinician. Thus, the assessment is subjective. In this paper, we propose a magnetometer-free Kalman filter (KF) to assess FT features using wearable, inertial sensors. The KF was used to assess features during two different FT tasks, namely forefinger tapping (FTAP) and thumb-forefinger tapping (THFF). The proposed KF was validated against a camera-based reference and compared with a strap-down integration-based method. Comparison between KF method and camera reference showed low discrepancies in terms of root mean square error (RMSE) for considered features: namely number of repetitions (RMSE < 0.7), tapping frequency (RMSE < 0.1 Hz), and amplitude (RMSE < 2.6 deg). An high correlation coefficient between amplitudes was also obtained. The proposed KF performed better than the strap-down integration method on both FT tasks, showing lower RMSE on every feature as well as a higher correlation coefficient. Clinical Relevance- The wearable setup, as well as the proposed magnetometer-free KF, may provide a low-cost, easyto- use, non-invasive motion tracking system for protocols aimed to assess motor performances in neurodegenerative disorders.

Running Speed Estimation Using Shoe-Worn Inertial Sensors: Direct Integration, Linear, and Personalized Model.

The overground speed is a key component of running analysis. Today, most speed estimation wearable systems are based on GNSS technology. However, these devices can suffer from sparse communication with the satellites and have a high-power consumption. In this study, we propose three different approaches to estimate the overground speed in running based on foot-worn inertial sensors and compare the results against a reference GNSS system. First, a method is proposed by direct strapdown integration of the foot acceleration. Second, a feature-based linear model and finally a personalized online-model based on the recursive least squares' method were devised. We also evaluated the performance differences between two sets of features; one automatically selected set (i.e., optimized) and a set of features based on the existing literature. The data set of this study was recorded in a real-world setting, with 33 healthy individuals running at low, preferred, and high speed. The direct estimation of the running speed achieved an inter-subject mean ± STD accuracy of 0.08 ± 0.1 m/s and a precision of 0.16 ± 0.04 m/s. In comparison, the best feature-based linear model achieved 0.00 ± 0.11 m/s accuracy and 0.11 ± 0.05 m/s precision, while the personalized model obtained a 0.00 ± 0.01 m/s accuracy and 0.09 ± 0.06 m/s precision. The results of this study suggest that (1) the direct estimation of the velocity of the foot are biased, and the error is affected by the overground velocity and the slope; (2) the main limitation of a general linear model is the relatively high inter-subject variance of the bias, which reflects the intrinsic differences in gait patterns among individuals; (3) this inter-subject variance can be nulled using a personalized model.

Estimation of Human Center of Mass Position through the Inertial Sensors-Based Methods in Postural Tasks: An Accuracy Evaluation.

The estimation of the body’s center of mass (CoM) trajectory is typically obtained using force platforms, or optoelectronic systems (OS), bounding the assessment inside a laboratory setting. The use of magneto-inertial measurement units (MIMUs) allows for more ecological evaluations, and previous studies proposed methods based on either a single sensor or a sensors’ network. In this study, we compared the accuracy of two methods based on MIMUs. Body CoM was estimated during six postural tasks performed by 15 healthy subjects, using data collected by a single sensor on the pelvis (Strapdown Integration Method, SDI), and seven sensors on the pelvis and lower limbs (Biomechanical Model, BM). The accuracy of the two methods was compared in terms of RMSE and estimation of posturographic parameters, using an OS as reference. The RMSE of the SDI was lower in tasks with little or no oscillations, while the BM outperformed in tasks with greater CoM displacement. Moreover, higher correlation coefficients were obtained between the posturographic parameters obtained with the BM and the OS. Our findings showed that the estimation of CoM displacement based on MIMU was reasonably accurate, and the use of the inertial sensors network methods should be preferred to estimate the kinematic parameters.

Instrumented triple single-leg hop test: A validated method for ambulatory measurement of ankle and knee angles using inertial sensors

BackgroundHop tests are commonly used in clinical environments to measure function after sport-related knee injuries. Joint angle measurement during hopping is feasible in research-based environments equipped with motion-capture systems. Employing these systems in clinical research settings is inefficient, given the associated cost, preparation time, and expertise required to administer and interpret the findings. Therefore, this study aimed to introduce a wearable system comprising three inertial measurement units for 3D joint angular measurement during horizontal hop tests, validate the joint angles against a camera-based system, and evaluate its applicability in clinical research environments. MethodsTen able-bodied participants were outfitted with three inertial measurement units during triple single-leg hop trials. 3D knee and ankle angles were calculated using the strap-down integration method, and results were compared with camera-based joint angles. Additionally, knee and ankle range of motions (RoMs) during bilateral triple single-leg hop trials were compared for 22 participants with unilateral sport-related knee injuries and 10 uninjured participants. FindingsEstimated angles had root-mean-square and RoM error medians of less than 2.3 and 3.2 degrees for both joints, and correlation coefficients of above 0.92 when compared with the camera-based system, for all hop phases. Injured participants had smaller sagittal ankle RoM (P = .008) on their injured side, during the third hop. Concurrently, they demonstrated smaller knee RoM symmetry indices (P = .017) and injured knee sagittal RoMs (P = .009) compared to uninjured participants. InterpretationThe introduced system had appropriate accuracy to highlight post-injury modifications in hopping kinematics and reveal noteworthy differences in RoM of clinical samples.

Quantification of Triple Single-Leg Hop Test Temporospatial Parameters: A Validated Method using Body-Worn Sensors for Functional Evaluation after Knee Injury.

Lower extremity kinematic alterations associated with sport-related knee injuries may contribute to an unsuccessful return to sport or early-onset post-traumatic osteoarthritis. Also, without access to sophisticated motion-capture systems, temporospatial monitoring of horizontal hop tests during clinical assessments is limited. By applying an alternative measurement system of two inertial measurement units (IMUs) per limb, we obtained and validated flying/landing times and hop distances of triple single-leg hop (TSLH) test against motion-capture cameras, assessed these temporospatial parameters amongst injured and uninjured groups, and investigated their association with the Knee Injury and Osteoarthritis Outcome Score (KOOS). Using kinematic features of IMU recordings, strap-down integration, and velocity correction techniques, temporospatial parameters were validated for 10 able-bodied participants and compared between 22 youth with sport-related knee injuries and 10 uninjured youth. With median (interquartile range) errors less than 10(16) ms for flying/landing times, and less than 4.4(5.6)% and 2.4(3.0)% of reference values for individual hops and total TSLH progression, differences between hopping biomechanics of study groups were highlighted. For injured participants, second flying time and all hop distances demonstrated moderate to strong correlations with KOOS Symptom and Function in Daily Living scores. Detailed temporospatial monitoring of hop tests is feasible using the proposed IMUs system.

Drift-Free Foot Orientation Estimation in Running Using Wearable IMU.

This study aimed to introduce and validate a new method to estimate and correct the orientation drift measured from foot-worn inertial sensors. A modified strap-down integration (MSDI) was proposed to decrease the orientation drift, which, in turn, was further compensated by estimation of the joint center acceleration (JCA) of a two-segment model of the foot. This method was designed to fit the different foot strike patterns observed in running and was validated against an optical motion-tracking system during level treadmill running at 8, 12, and 16 km/h. The sagittal and frontal plane angles obtained from the inertial sensors and the motion tracking system were compared at different moments of the ground contact phase. The results obtained from 26 runners showed that the foot orientation at mean stance was estimated with an accuracy (inter-trial median ± IQR) of 0.4 ± 3.8° and a precision (inter-trial precision median ± IQR) of 3.0 ± 1.8°. The orientation of the foot shortly before initial contact (IC) was estimated with an accuracy of 2.0 ± 5.9° and a precision of 1.6 ± 1.1°; which is more accurate than commonly used zero-velocity update methods derived from gait analysis and not explicitly designed for running. Finally, the study presented the effect initial and terminal contact (TC) detection errors have on the orientation parameters reported.

Effect of Strapdown Integration Order and Sampling Rate on IMU-Based Attitude Estimation Accuracy.

This paper deals with the strapdown integration of attitude estimation Kalman filter (KF) based on inertial measurement unit (IMU) signals. In many low-cost wearable IMU applications, a first-order is selected for strapdown integration, which may degrade attitude estimation performance in high-speed angular motions. The purpose of this research is to provide insights into the effect of the strapdown integration order and sampling rate on the attitude estimation accuracy for low-cost IMU applications. Experimental results showed that the effect of integration order was small when the angular velocity was low and the sampling rate was large. However, as the angular velocity increased and the sampling rate decreased, the effect of integration order increased, i.e., obviously, the third-order KF resulted in better estimations than the first-order KF. When comparing the case where both transient matrix and process noise covariance matrix are applied to the corresponding order and the case where only the transient matrix is applied to the corresponding order but the process noise covariance matrix for the first-order is still used, both cases had almost equivalent estimation accuracy. However, in terms of the calculation cost, the latter case was more economical than the former, particularly for the third-order KF (i.e., the ratio of the former to the latter is 1.22 to 1).

Novel approach to human walking speed enhancement based on drift estimation

Abstract The speed of human walking is a valuable indicator of individuals’ health status, for example in sports or medicine. Classic methods such as the camera-based approach have serious limitations: (1) they can be used only in the laboratory setting, and (2) the computational complexity of the data processing is remarkably high. The development of small wearable inertial sensing systems and suitable methods of data processing allow the analysis of human motion to be performed outside the laboratory. Moreover, such solutions can work in the real-time regime. Unfortunately, the inertia-based human walking speed estimation systems applying the strap-down integration approach have an unavoidable drawback. The disadvantage is the estimation inaccuracies caused by the accumulation of errors. This paper presents an approach for attenuating these errors by applying a method for estimating drift.

Hand Pose Estimation by Fusion of Inertial and Magnetic Sensing Aided by a Permanent Magnet.

Tracking human body motions using inertial sensors has become a well-accepted method in ambulatory applications since the subject is not confined to a lab-bounded volume. However, a major drawback is the inability to estimate relative body positions over time because inertial sensor information only allows position tracking through strapdown integration, but does not provide any information about relative positions. In addition, strapdown integration inherently results in drift of the estimated position over time. We propose a novel method in which a permanent magnet combined with 3-D magnetometers and 3-D inertial sensors are used to estimate the global trunk orientation and relative pose of the hand with respect to the trunk. An Extended Kalman Filter is presented to fuse estimates obtained from inertial sensors with magnetic updates such that the position and orientation between the human hand and trunk as well as the global trunk orientation can be estimated robustly. This has been demonstrated in multiple experiments in which various hand tasks were performed. The most complex task in which simultaneous movements of both trunk and hand were performed resulted in an average rms position difference with an optical reference system of 19.7±2.2 mm whereas the relative trunk-hand and global trunk orientation error was 2.3±0.9 and 8.6±8.7 deg respectively.

Walking speed estimation using foot-mounted inertial sensors: Comparing machine learning and strap-down integration methods

In this paper we implemented machine learning (ML) and strap-down integration (SDI) methods and analyzed them for their capability of estimating stride-by-stride walking speed. Walking speed was computed by dividing estimated stride length by stride time using data from a foot mounted inertial measurement unit. In SDI methods stride-by-stride walking speed estimation was driven by detecting gait events using a hidden Markov model (HMM) based method (HMM-based SDI); alternatively, a threshold-based gait event detector was investigated (threshold-based SDI). In the ML method a linear regression model was developed for stride length estimation. Whereas the gait event detectors were a priori fixed without training, the regression model was validated with leave-one-subject-out cross-validation. A subject-specific regression model calibration was also implemented to personalize the ML method.Healthy adults performed over-ground walking trials at natural, slower-than-natural and faster-than-natural speeds. The ML method achieved a root mean square estimation error of 2.0% and 4.2%, with and without personalization, against 2.0% and 3.1% by HMM-based SDI and threshold-based SDI. In spite that the results achieved by the two approaches were similar, the ML method, as compared with SDI methods, presented lower intra-subject variability and higher inter-subject variability, which was reduced by personalization.

Measurement of Multi-segment Foot Joint Angles During Gait Using a Wearable System

Usually the measurement of multi-segment foot and ankle complex kinematics is done with stationary motion capture devices which are limited to use in a gait laboratory. This study aimed to propose and validate a wearable system to measure the foot and ankle complex joint angles during gait in daily conditions, and then to investigate its suitability for clinical evaluations. The foot and ankle complex consisted of four segments (shank, hindfoot, forefoot, and toes), with an inertial measurement unit (3D gyroscopes and 3D accelerometers) attached to each segment. The angles between the four segments were calculated in the sagittal, coronal, and transverse planes using a new algorithm combining strap-down integration and detection of low-acceleration instants. To validate the joint angles measured by the wearable system, three subjects walked on a treadmill for five minutes at three different speeds. A camera-based stationary system that used a cluster of markers on each segment was used as a reference. To test the suitability of the system for clinical evaluation, the joint angle ranges were compared between a group of 10 healthy subjects and a group of 12 patients with ankle osteoarthritis, during two 50-m walking trials where the wearable system was attached to each subject. On average, over all joints and walking speeds, the RMS differences and correlation coefficients between the angular curves obtained using the wearable system and the stationary system were 1 deg and 0.93, respectively. Moreover, this system was able to detect significant alteration of foot and ankle function between the group of patients with ankle osteoarthritis and the group of healthy subjects. In conclusion, this wearable system was accurate and suitable for clinical evaluation when used to measure the multi-segment foot and ankle complex kinematics during long-distance walks in daily life conditions.

A Unified Mathematical Framework for Strapdown Algorithm Design

A Unified Mathematical Framework for Strapdown Algorithm Design

In-use calibration of body-mounted gyroscopes for applications in gait analysis

In this paper, we propose an in-use calibration procedure for gyroscopes. The case report is a simple inertial measurement unit (IMU), which is used in our current research on inertial motion-sensing for advanced footware. The IMU contains two biaxial accelerometers and one gyroscope; it is developed for being mounted on one subject's foot instep, with the aim to reconstruct the trajectory in the sagittal plane of the sensed anatomical point. Since the IMU sagittal displacements can be estimated by performing strapdown integration, they can also be compared with their true values. One movement, which corresponds to known (vertical) displacements, consists of foot placements from the ground level on to top of steps of known height (step climbing). Provided that the IMU accelerometers are calibrated separately by any standard calibration procedure, motion tracking during the stepping movement allows to estimate the gyroscope sensitivity. The experimental results we present in this paper demonstrate the proposed in-use calibration procedure.

Assessment of Walking Features From Foot Inertial Sensing

An ambulatory monitoring system is developed for the estimation of spatio-temporal gait parameters. The inertial measurement unit embedded in the system is composed of one biaxial accelerometer and one rate gyroscope, and it reconstructs the sagittal trajectory of a sensed point on the instep of the foot. A gait phase segmentation procedure is devised to determine temporal gait parameters, including stride time and relative stance; the procedure allows to define the time intervals needed for carrying an efficient implementation of the strapdown integration, which allows to estimate stride length, walking speed, and incline. The measurement accuracy of walking speed and inclines assessments is evaluated by experiments carried on adult healthy subjects walking on a motorized treadmill. Root-mean-square errors less than 0.18 km/h (speed) and 1.52% (incline) are obtained for tested speeds and inclines varying in the intervals [3, 6] km/h and [-5, + 15]%, respectively. Based on the results of these experiments, it is concluded that foot inertial sensing is a promising tool for the reliable identification of subsequent gait cycles and the accurate assessment of walking speed and incline.

Quaternion-based strap-down integration method for applications of inertial sensing to gait analysis

The proposed strap-down integration method exploits the cyclical nature of human gait: during the gait swing phase, the quaternion-based attitude representation is integrated using a gyroscope from initial conditions that are determined during stance by an accelerometer. Positioning requires double time integration of the gravity-compensated accelerometer signals during swing. An interpolation technique applied to attitude quaternions was developed to improve the accuracy of orientation and positioning estimates by accounting for the effect of sensor bias and scale factor drifts. A simulation environment was developed for the analysis and testing of the proposed algorithm on a synthetic movement trajectory. The aim was to define the true attitude and positioning used in the computation of estimation errors. By thermal modelling, the changes of bias and scale factor of the inertial sensors, calibrated at a single reference temperature, were analysed over a range of +/- 10 degrees C, for measurement noise standard deviations up to sigma(g) = 2.5 degrees s(-1) (gyroscope) and sigma(a) = 0.05 m s(-2) (accelerometer). The compensation technique reduced the maximum root mean square errors (RMSEs) to: RMSE(theta) = 14.6 degrees (orientation) and RMSE(d) = 17.7cm (positioning) for an integration interval of one gait cycle (an improvement of 3 degrees and 7 cm); RMSE(theta) = 14.8 degrees and RMSE(d) = 30.0 cm for an integration interval of two gait cycles (an improvement of 11 degrees and 262 cm).