Time- and computation-efficient calibration of MEMS 3D accelerometers and gyroscopes

A Statistical Approach for Functional Reach-to-Grasp Segmentation Using a Single Inertial Measurement Unit

The aim of this contribution is to present a segmentation method for the identification of voluntary movements from inertial data acquired through a single inertial measurement unit placed on the subject's wrist. Inertial data were recorded from 25 healthy subjects while performing 75 consecutive reach-to-grasp movements. The approach herein presented, called DynAMoS, is based on an adaptive thresholding step on the angular velocity norm, followed by a statistics-based post-processing on the movement duration distribution. Post-processing aims at reducing the number of erroneous transitions in the movement segmentation. We assessed the segmentation quality of this method using a stereophotogrammetric system as the gold standard. Two popular methods already presented in the literature were compared to DynAMoS in terms of the number of movements identified, onset and offset mean absolute errors, and movement duration. Moreover, we analyzed the sub-phase durations of the drinking movement to further characterize the task. The results show that the proposed method performs significantly better than the two state-of-the-art approaches (i.e., percentage of erroneous movements = 3%; onset and offset mean absolute error < 0.08 s), suggesting that DynAMoS could make more effective home monitoring applications for assessing the motion improvements of patients following domicile rehabilitation protocols.

A Method of Precise Auto-Calibration in a Micro-Electro-Mechanical System Accelerometer

A novel design of a MEMS (Micro-Electromechanical System) capacitive accelerometer fabricated by surface micromachining, with a structure enabling precise auto-calibration during operation, is presented. Precise auto-calibration was introduced to ensure more accurate acceleration measurements compared to standard designs. The standard mechanical structure of the accelerometer (seismic mass integrated with elastic suspension and movable plates coupled with fixed plates forming a system of differential sensing capacitors) was equipped with three movable detection electrodes coupled with three fixed electrodes, thus creating three atypical tunneling displacement transducers detecting three specific positions of seismic mass with high precision, enabling the auto-calibration of the accelerometer while it was being operated. Auto-calibration is carried out by recording the accelerometer indication while the seismic mass occupies a specific position, which corresponds to a known value of acting acceleration determined in a pre-calibration process. The diagram and the design of the mechanical structure of the accelerometer, the block diagram of the electronic circuits, and the mathematical relationships used for auto-calibration are presented. The results of the simulation studies related to mechanical and electric phenomena are discussed.

A multi-sensor wearable system for the assessment of diseased gait in real-world conditions

Introduction: Accurately assessing people's gait, especially in real-world conditions and in case of impaired mobility, is still a challenge due to intrinsic and extrinsic factors resulting in gait complexity. To improve the estimation of gait-related digital mobility outcomes (DMOs) in real-world scenarios, this study presents a wearable multi-sensor system (INDIP), integrating complementary sensing approaches (two plantar pressure insoles, three inertial units and two distance sensors). Methods: The INDIP technical validity was assessed against stereophotogrammetry during a laboratory experimental protocol comprising structured tests (including continuous curvilinear and rectilinear walking and steps) and a simulation of daily-life activities (including intermittent gait and short walking bouts). To evaluate its performance on various gait patterns, data were collected on 128 participants from seven cohorts: healthy young and older adults, patients with Parkinson's disease, multiple sclerosis, chronic obstructive pulmonary disease, congestive heart failure, and proximal femur fracture. Moreover, INDIP usability was evaluated by recording 2.5-h of real-world unsupervised activity. Results and discussion: Excellent absolute agreement (ICC >0.95) and very limited mean absolute errors were observed for all cohorts and digital mobility outcomes (cadence ≤0.61 steps/min, stride length ≤0.02 m, walking speed ≤0.02 m/s) in the structured tests. Larger, but limited, errors were observed during the daily-life simulation (cadence 2.72-4.87 steps/min, stride length 0.04-0.06 m, walking speed 0.03-0.05 m/s). Neither major technical nor usability issues were declared during the 2.5-h acquisitions. Therefore, the INDIP system can be considered a valid and feasible solution to collect reference data for analyzing gait in real-world conditions.

Base of Support, Step Length and Stride Width Estimation during Walking Using an Inertial and Infrared Wearable System

The analysis of the stability of human gait may be effectively performed when estimates of the base of support are available. The base of support area is defined by the relative position of the feet when they are in contact with the ground and it is closely related to additional parameters such as step length and stride width. These parameters may be determined in the laboratory using either a stereophotogrammetric system or an instrumented mat. Unfortunately, their estimation in the real world is still an unaccomplished goal. This study aims at proposing a novel, compact wearable system, including a magneto-inertial measurement unit and two time-of-flight proximity sensors, suitable for the estimation of the base of support parameters. The wearable system was tested and validated on thirteen healthy adults walking at three self-selected speeds (slow, comfortable, and fast). Results were compared with the concurrent stereophotogrammetric data, used as the gold standard. The root mean square errors for the step length, stride width and base of support area varied from slow to high speed between 10-46 mm, 14-18 mm, and 39-52 cm², respectively. The mean overlap of the base of support area as obtained with the wearable system and with the stereophotogrammetric system ranged between 70% and 89%. Thus, this study suggested that the proposed wearable solution is a valid tool for the estimation of the base of support parameters out of the laboratory.

A novel motion-reconstruction method for inertial sensors with constraints

Motion reconstruction for rigid bodies and rigid-body frames using data from inertial measurement units (IMUs) is a challenging task. Position and orientation determination by means of IMUs is erroneous, as deterministic and stochastic errors accumulate over time. The former of which errors can be minimized by standard calibration approaches, however, sensor calibration with respect to a common reference coordinate system to correct misalignment, has not been fully addressed yet. The latter stochastic errors are mostly reduced using sensor fusion. In this paper, we present a novel motion-reconstruction method utilizing optimization to correct measured IMU data by means of correction polynomials to minimize the deviation of motion constraints. In addition, we perform gyrometer and accelerometer calibration with an industrial manipulator to address deterministic IMU errors, especially misalignment. To evaluate the performance of the novel methods, two types of experiments, one at constant orientation and another with simultaneous translation and rotation, were conducted utilizing the manipulator. The experiments were repeated for five individual IMUs successively. Application of the calibration and optimization methods yielded an average decrease of 95% in the maximum position error compared to the results of common motion reconstruction. Moreover, the average position error over the measurement duration decreased by nearly 90%. The proposed method is applicable to velocity, position, and orientation constraints for every experiment that starts and ends at standstill.

MEMS Inertial Sensor Calibration Technology: Current Status and Future Trends

A review of various calibration techniques of MEMS inertial sensors is presented in this paper. MEMS inertial sensors are subject to various sources of error, so it is essential to correct these errors through calibration techniques to improve the accuracy and reliability of these sensors. In this paper, we first briefly describe the main characteristics of MEMS inertial sensors and then discuss some common error sources and the establishment of error models. A systematic review of calibration methods for inertial sensors, including gyroscopes and accelerometers, is conducted. We summarize the calibration schemes into two general categories: autonomous and nonautonomous calibration. A comprehensive overview of the latest progress made in MEMS inertial sensor calibration technology is presented, and the current state of the art and development prospects of MEMS inertial sensor calibration are analyzed with the aim of providing a reference for the future development of calibration technology.

Recognizing Solo Jazz Dance Moves Using a Single Leg-Attached Inertial Wearable Device

We present here a method for recognising dance moves in sequences using 3D accelerometer and gyroscope signals, acquired by a single wearable device, attached to the dancer's leg. The recognition entails dance tempo estimation, temporal scaling, a wearable device orientation-invariant coordinate system transformation, and, finally, sliding correlation-based template matching. The recognition is independent of the orientation of the wearable device and the tempo of dancing, which promotes the usability of the method in a wide range of everyday application scenarios. For experimental validation, we considered the versatile repertoire of solo jazz dance moves. We created a database of 15 authentic solo jazz template moves using the performances of a professional dancer dancing at 120 bpm. We analysed 36 new dance sequences, performed by the professional and five recreational dancers, following six dance tempos, ranging from 120 bpm to 220 bpm with 20 bpm increment steps. The recognition F1 scores, obtained cumulatively for all moves for different tempos, ranged from 0.87 to 0.98. The results indicate that the presented method can be used to recognise repeated dance moves and to assess the dancer's consistency in performance. In addition, the results confirm the potential of using the presented method to recognise imitated dance moves, supporting the learning process.

Tilt Sensor with Recalibration Feature Based on MEMS Accelerometer

The main errors of MEMS accelerometers are misalignments of their sensitivity axes, thermal and long-term drifts, imprecise factory calibration, and aging phenomena. In order to reduce these errors, a two-axial tilt sensor comprising a triaxial MEMS accelerometer, an aligning unit, and solid cubic housing was built. By means of the aligning unit it was possible to align the orientation of the accelerometer sensitive axes with respect to the housing with an accuracy of 0.03°. Owing to the housing, the sensor could be easily and quickly recalibrated, and thus errors such as thermal and long-term drifts as well as effects of aging were eliminated. Moreover, errors due to local and temporal variations of the gravitational acceleration can be compensated for. Procedures for calibrating and aligning the accelerometer are described. Values of thermal and long-term drifts of the tested sensor, resulting in tilt errors of even 0.4°, are presented. Application of the sensor for monitoring elevated loads is discussed.

Technical validation of real-world monitoring of gait: a multicentric observational study

INTRODUCTION

Existing mobility endpoints based on functional performance, physical assessments and patient self-reporting are often affected by lack of sensitivity, limiting their utility in clinical practice. Wearable devices including inertial measurement units (IMUs) can overcome these limitations by quantifying digital mobility outcomes (DMOs) both during supervised structured assessments and in real-world conditions. The validity of IMU-based methods in the real-world, however, is still limited in patient populations. Rigorous validation procedures should cover the device metrological verification, the validation of the algorithms for the DMOs computation specifically for the population of interest and in daily life situations, and the users' perspective on the device.

METHODS AND ANALYSIS

This protocol was designed to establish the technical validity and patient acceptability of the approach used to quantify digital mobility in the real world by Mobilise-D, a consortium funded by the European Union (EU) as part of the Innovative Medicine Initiative, aiming at fostering regulatory approval and clinical adoption of DMOs.After defining the procedures for the metrological verification of an IMU-based device, the experimental procedures for the validation of algorithms used to calculate the DMOs are presented. These include laboratory and real-world assessment in 120 participants from five groups: healthy older adults; chronic obstructive pulmonary disease, Parkinson's disease, multiple sclerosis, proximal femoral fracture and congestive heart failure. DMOs extracted from the monitoring device will be compared with those from different reference systems, chosen according to the contexts of observation. Questionnaires and interviews will evaluate the users' perspective on the deployed technology and relevance of the mobility assessment.

ETHICS AND DISSEMINATION

The study has been granted ethics approval by the centre's committees (London-Bloomsbury Research Ethics committee; Helsinki Committee, Tel Aviv Sourasky Medical Centre; Medical Faculties of The University of Tübingen and of the University of Kiel). Data and algorithms will be made publicly available.

TRIAL REGISTRATION NUMBER

ISRCTN (12246987).

Dance Tempo Estimation Using a Single Leg-Attached 3D Accelerometer

We present a methodology that enables dance tempo estimation through the acquisition of 3D accelerometer signals using a single wearable inertial device positioned on the dancer’s leg. Our tempo estimation method is based on enhanced multiple resonators, implemented with comb feedback filters. To validate the methodology, we focus on the versatile solo jazz dance style. Including a variety of dance moves, with different leg activation patterns and rhythmical variations, solo jazz provides for a highly critical validation environment. We consider 15 different solo jazz dance moves, with different leg activation patterns, assembled in a sequence of 5 repetitions of each, giving 65 moves altogether. A professional and a recreational dancer performed this assembly in a controlled environment, following eight dancing tempos, dictated by a metronome, and ranging from 80 bpm to 220 bpm with 20 bpm increment steps. We show that with appropriate enhancements and using single leg signals, the comb filter bank provides for accurate dance tempo estimates for all moves and rhythmical variations considered. Dance tempo estimates for the overall assembles match strongly the dictated tempo—the difference being at most 1 bpm for all measurement instances is within the limits of the established beat onset stability of the used metronome. Results further show that this accuracy is achievable for shorter dancing excerpts, comprising four dance moves, corresponding to one music phrase, and as such enables real-time feedback. By providing for a dancer’s tempo quality and consistency assessment, the presented methodology has the potential of supporting the learning process, classifying individual level of experience, and assessing overall performance. It is extendable to other dance styles and sport motion in general where cyclical patterns occur.

Efficacy of Inertial Measurement Units in the Evaluation of Trunk and Hand Kinematics in Baseball Hitting

Baseball hitting is a highly dynamic activity, and advanced methods are required to accurately obtain biomechanical data. Inertial measurement units (IMUs) can capture the motion of body segments at high sampling rates both indoor and outdoor. The bat rotates around the longitudinal axis of the body; thus, trunk motion plays a key role in baseball hitting. Segmental coordination is important in transferring power to a moving ball and, therefore, useful in evaluating swing kinematics. The current study aimed to investigate the validity and reliability of IMUs with a sampling rate of 1000 Hz attached on the pelvis, thorax, and hand in assessing trunk and hand motion during baseball hitting. Results obtained using the IMU and optical motion capture system (OMCS) were compared. Angular displacements of the trunk segments and spine joint had a root mean square error of <5°. The mean absolute error of the angular velocities was ≤5%. The intra-class correlation coefficient (>0.950) had excellent reliability for trunk kinematics along the longitudinal-axis. Hand velocities at peak and impact corresponded to the values determined using the OMCS. In conclusion, IMUs with high sampling rates are effective in evaluating trunk and hand movement coordination during hitting motion.

Computationally Efficient 3D Orientation Tracking Using Gyroscope Measurements

Computationally efficient 3D orientation (3DO) tracking using gyroscope angular velocity measurements enables a short execution time and low energy consumption for the computing device. These are essential requirements in today's wearable device environments, which are characterized by limited resources and demands for high energy autonomy. We show that the computational efficiency of 3DO tracking is significantly improved by correctly interpreting each triplet of gyroscope measurements as simultaneous (using the rotation vector called the Simultaneous Orthogonal Rotation Angle, or SORA) rather than as sequential (using Euler angles) rotation. For an example rotation of 90°, depending on the change in the rotation axis, using Euler angles requires 35 to 78 times more measurement steps for comparable levels of accuracy, implying a higher sampling frequency and computational complexity. In general, the higher the demanded 3DO accuracy, the higher the computational advantage of using the SORA. Furthermore, we demonstrate that 12 to 14 times faster execution is achieved by adapting the SORA-based 3DO tracking to the architecture of the executing low-power ARM Cortex^® M0+ microcontroller using only integer arithmetic, lookup tables, and the small-angle approximation. Finally, we show that the computational efficiency is further improved by choosing the appropriate 3DO computational method. Using rotation matrices is 1.85 times faster than using rotation quaternions when 3DO calculations are performed for each measurement step. On the other hand, using rotation quaternions is 1.75 times faster when only the final 3DO result of several consecutive rotations is needed. We conclude that by adopting the presented practices, the clock frequency of a processor computing the 3DO can be significantly reduced. This substantially prolongs the energy autonomy of the device and enhances its usability in day-to-day measurement scenarios.

Gravity-Based Characterization of Three-Axis Accelerometers in Terms of Intrinsic Accelerometer Parameters

Cross-sensitivity matrices are used to translate the response of three-axis accelerometers into components of acceleration along the axes of a specified coordinate system. For inertial three-axis accelerometers, this coordinate system is often defined by the axes of a gimbal-based instrument that exposes the device to different acceleration inputs as the gimbal is rotated in the local gravitational field. Therefore, the cross-sensitivity matrix for a given three-axis accelerometer is not unique. Instead, it depends upon the orientation of the device when mounted on the gimbal. We define nine intrinsic parameters of three-axis accelerometers and describe how to measure them directly and how to calculate them from independently determined cross-sensitivity matrices. We propose that comparisons of the intrinsic parameters of three axis accelerometers that were calculated from independently determined cross-sensitivity matrices can be useful for comparisons of the cross-sensitivity-matrix measurement capability of different institutions because the intrinsic parameters will separate the accelerator-gimbal alignment differences among the participating institutions from the purely gimbal-related differences, such as gimbal-axis orthogonality errors, z-axis gravitational-field alignment errors, and angle-setting or angle-measurement errors.

An Acceleration-Based Gait Assessment Method for Children with Cerebral Palsy

With the aim of providing an objective tool for motion disability assessment in clinical diagnosis and rehabilitation therapy of cerebral palsy (CP) patients, an acceleration-based gait assessment method was proposed in this paper. To capture gait information, three inertial measurement units (IMUs) were placed on the lower trunk and thigh, respectively. By comparing differences in the gait acceleration modes between children with CP and healthy subjects, an assessment method based on grey relational analysis and five gait parameters, including Pearson coefficient, variance ratio, the number of extreme points, harmonic ratio and symmetry was established. Twenty-two children with cerebral palsy (7.49 ± 2.86 years old), fourteen healthy adults (24.2 ± 1.55 years old) and ten healthy children (7.03 ± 1.49 years old) participated in the gait data acquisition experiment. The results demonstrated that, compared to healthy subjects, the symptoms and severity of motor dysfunction of CP children could result in abnormality of the gait acceleration modes, and the proposed assessment method was able to effectively evaluate the degree gait abnormality in CP children.

Motor Function Evaluation of Hemiplegic Upper-Extremities Using Data Fusion from Wearable Inertial and Surface EMG Sensors

Quantitative evaluation of motor function is of great demand for monitoring clinical outcome of applied interventions and further guiding the establishment of therapeutic protocol. This study proposes a novel framework for evaluating upper limb motor function based on data fusion from inertial measurement units (IMUs) and surface electromyography (EMG) sensors. With wearable sensors worn on the tested upper limbs, subjects were asked to perform eleven straightforward, specifically designed canonical upper-limb functional tasks. A series of machine learning algorithms were applied to the recorded motion data to produce evaluation indicators, which is able to reflect the level of upper-limb motor function abnormality. Sixteen healthy subjects and eighteen stroke subjects with substantial hemiparesis were recruited in the experiment. The combined IMU and EMG data yielded superior performance over the IMU data alone and the EMG data alone, in terms of decreased normal data variation rate (NDVR) and improved determination coefficient (DC) from a regression analysis between the derived indicator and routine clinical assessment score. Three common unsupervised learning algorithms achieved comparable performance with NDVR around 10% and strong DC around 0.85. By contrast, the use of a supervised algorithm was able to dramatically decrease the NDVR to 6.55%. With the proposed framework, all the produced indicators demonstrated high agreement with the routine clinical assessment scale, indicating their capability of assessing upper-limb motor functions. This study offers a feasible solution to motor function assessment in an objective and quantitative manner, especially suitable for home and community use.

Evaluation of Smartphone Inertial Sensor Performance for Cross-Platform Mobile Applications

Smartphone sensors are being increasingly used in mobile applications. The performance of sensors varies considerably among different smartphone models and the development of a cross-platform mobile application might be a very complex and demanding task. A publicly accessible resource containing real-life-situation smartphone sensor parameters could be of great help for cross-platform developers. To address this issue we have designed and implemented a pilot participatory sensing application for measuring, gathering, and analyzing smartphone sensor parameters. We start with smartphone accelerometer and gyroscope bias and noise parameters. The application database presently includes sensor parameters of more than 60 different smartphone models of different platforms. It is a modest, but important start, offering information on several statistical parameters of the measured smartphone sensors and insights into their performance. The next step, a large-scale cloud-based version of the application, is already planned. The large database of smartphone sensor parameters may prove particularly useful for cross-platform developers. It may also be interesting for individual participants who would be able to check-up and compare their smartphone sensors against a large number of similar or identical models.

Suitability of Smartphone Inertial Sensors for Real-Time Biofeedback Applications

This article studies the suitability of smartphones with built-in inertial sensors for biofeedback applications. Biofeedback systems use various sensors to measure body functions and parameters. These sensor data are analyzed, and the results are communicated back to the user, who then tries to act on the feedback signals. Smartphone inertial sensors can be used to capture body movements in biomechanical biofeedback systems. These sensors exhibit various inaccuracies that induce significant angular and positional errors. We studied deterministic and random errors of smartphone accelerometers and gyroscopes, primarily focusing on their biases. Based on extensive measurements, we determined accelerometer and gyroscope noise models and bias variation ranges. Then, we compiled a table of predicted positional and angular errors under various biofeedback system operation conditions. We suggest several bias compensation options that are suitable for various examples of use in real-time biofeedback applications. Measurements within the developed experimental biofeedback application show that under certain conditions, even uncompensated sensors can be used for real-time biofeedback. For general use, especially for more demanding biofeedback applications, sensor biases should be compensated. We are convinced that real-time biofeedback systems based on smartphone inertial sensors are applicable to many similar examples in sports, healthcare, and other areas.

Improving the precision and speed of Euler angles computation from low-cost rotation sensor data

This article compares three different algorithms used to compute Euler angles from data obtained by the angular rate sensor (e.g., MEMS gyroscope)—the algorithms based on a rotational matrix, on transforming angular velocity to time derivations of the Euler angles and on unit quaternion expressing rotation. Algorithms are compared by their computational efficiency and accuracy of Euler angles estimation. If attitude of the object is computed only from data obtained by the gyroscope, the quaternion-based algorithm seems to be most suitable (having similar accuracy as the matrix-based algorithm, but taking approx. 30% less clock cycles on the 8-bit microcomputer). Integration of the Euler angles’ time derivations has a singularity, therefore is not accurate at full range of object’s attitude. Since the error in every real gyroscope system tends to increase with time due to its offset and thermal drift, we also propose some measures based on compensation by additional sensors (a magnetic compass and accelerometer). Vector data of mentioned secondary sensors has to be transformed into the inertial frame of reference. While transformation of the vector by the matrix is slightly faster than doing the same by quaternion, the compensated sensor system utilizing a matrix-based algorithm can be approximately 10% faster than the system utilizing quaternions (depending on implementation and hardware).