Accuracy of the Orientation Estimate Obtained Using Four Sensor Fusion Filters Applied to Recordings of Magneto-Inertial Sensors Moving at Three Rotation Rates

6Magneto-Inertial technology is a well-established alternative to optical motion capture for human motion analysis applications since it allows prolonged monitoring in free-living conditions. Magneto and Inertial Measurement Units (MIMUs) integrate a triaxial accelerometer, a triaxial gyroscope and a triaxial magnetometer in a single and lightweight device. The orientation of the body to which a MIMU is attached can be obtained by combining its sensor readings within a sensor fusion framework. Despite several sensor fusion implementations have been proposed, no well-established conclusion about the accuracy level achievable with MIMUs has been reached yet. The aim of this preliminary study was to perform a direct comparison among four popular sensor fusion algorithms applied to the recordings of MIMUs rotating at three different rotation rates, with the orientation provided by a stereophotogrammetric system used as a reference. A procedure for suboptimal determination of the parameter filter values was also proposed. The findings highlighted that all filters exhibited reasonable accuracy (rms errors < 6.4°). Moreover, in accordance with previous studies, every algorithm's accuracy worsened as the rotation rate increased. At the highest rotation rate, the algorithm from Sabatini (2011) showed the best performance with errors smaller than 4.1° rms.partially_openopenCaruso M.; Sabatini A.M.; Knaflitz M.; Gazzoni M.; Della Croce U.; Cereatti A.Caruso, M.; Sabatini, A. M.; Knaflitz, M.; Gazzoni, M.; Della Croce, U.; Cereatti, A

Orientation Estimation Through Magneto-Inertial Sensor Fusion: A Heuristic Approach for Suboptimal Parameters Tuning

Magneto-Inertial Measurement Units (MIMUs) are a valid alternative tool to optical stereophotogrammetry in human motion analysis. The orientation of a MIMU may be estimated by using sensor fusion algorithms. Such algorithms require input parameters that are usually set using a trial-and-error (or grid-search ) approach to find the optimal values. However, using trial-and-error requires a known reference orientation, a circumstance rarely occurring in real-life applications. In this article, we present a way to suboptimally set input parameters, by exploiting the assumption that two MIMUs rigidly connected are expected to show no orientation difference during motion. This approach was validated by applying it to the popular complementary filter by Madgwick et al. and tested on 18 experimental conditions including three commercial products, three angular rates, and two dimensionality motion conditions. Two main findings were observed: i) the selection of the optimal parameter value strongly depends on the specific experimental conditions considered, ii) in 15 out of 18 conditions the errors obtained using the proposed approach and the trial-and-error were coincident, while in the other cases the maximum discrepancy amounted to 2.5 deg and less than 1.5 deg on average

Extension of the rigid‐constraint method for the heuristic suboptimal parameter tuning to ten sensor fusion algorithms using inertial and magnetic sensing

The orientation of a magneto‐inertial measurement unit can be estimated using a sensor fusion algorithm (SFA). However, orientation accuracy is greatly affected by the choice of the SFA parameter values which represents one of the most critical steps. A commonly adopted approach is to fine‐tune parameter values to minimize the difference between estimated and true orientation. However, this can only be implemented within the laboratory setting by requiring the use of a concurrent gold‐standard technology. To overcome this limitation, a Rigid‐Constraint Method (RCM) was proposed to estimate suboptimal parameter values without relying on any orientation reference. The RCM method effectiveness was successfully tested on a single‐parameter SFA, with an average error increase with respect to the optimal of 1.5 deg. In this work, the applicability of the RCM was evaluated on 10 popular SFAs with multiple parameters under different experimental scenarios. The average residual between the optimal and suboptimal errors amounted to 0.6 deg with a maximum of 3.7 deg. These encouraging results suggest the possibility to properly tune a generic SFA on different scenarios without using any reference. The synchronized dataset also including the optical data and the SFA codes are available online

Analysis of the accuracy of ten algorithms for orientation estimation using inertial and magnetic sensing under optimal conditions: One size does not fit all

The orientation of a magneto and inertial measurement unit (MIMU) is estimated by means of sensor fusion algorithms (SFAs) thus enabling human motion tracking. However, despite several SFAs implementations proposed over the last decades, there is still a lack of consensus about the best performing SFAs and their accuracy. As suggested by recent literature, the filter parameters play a central role in determining the orientation errors. The aim of this work is to analyze the accuracy of ten SFAs while running under the best possible conditions (i.e., their parameter values are set using the orientation reference) in nine experimental scenarios including three rotation rates and three commercial products. The main finding is that parameter values must be specific for each SFA according to the experimental scenario to avoid errors comparable to those obtained when the de-fault parameter values are used. Overall, when optimally tuned, no statistically significant differ-ences are observed among the different SFAs in all tested experimental scenarios and the absolute errors are included between 3.8 deg and 7.1 deg. Increasing the rotation rate generally leads to a significant performance worsening. Errors are also influenced by the MIMU commercial model. SFA MATLAB implementations have been made available online

Methods and good practice guidelines for human joint kinematics estimation through magnetic and inertial wearable sensors

According to the World Health Organization, the ability to move is recognized as a key factor for the human well-being. From the wearable Magnetic and Inertial Measurement Units (MIMUs) signals it is possible to extract several digital mobility outcomes including the joint kinematics. To this end, it is first required to estimate the orientation of the MIMUs by means of a sensor fusion algorithm (SFA). After that, the relative orientation is computed and then decomposed to obtain the joint angles. However, the MIMUs do not provide a direct output of the physical quantity of interest which can be only determined after an ad hoc processing of their signals. It follows that the joint angle accuracy mostly depends on multiple factors. The first one is the magnitude of the MIMU measurements errors and up to date there is still a lack of methods for their characterization. A second crucial factor is the choice of the SFA to use. Despite the abundance of formulations in the literature, no-well established conclusions about their accuracy have been reached yet. The last factor is the biomechanical model used to compute the joint angles. In this context, unconstrained methods offer a simple way to decompose the relative orientation using the Euler angles but suffer from the inherent issues related to the SFA. In contrast, constrained approaches aim at increasing the robustness of the estimates by adopting models in which an objective function is minimized through the definition of physiological constraints. This thesis proposed the methods to accurately estimate the human joint kinematics starting from the MIMU signals. Three main contributions were provided. The first consisted in the design of a comprehensive battery of tests to completely characterize the sources of errors affecting the quality of the measurements. These tests rely on simple hypotheses based on the sensor working principles and do not require expensive equipment. Nine parameters were defined to quantify the signal accuracy improvements (if any) of 24 MIMUs before and after the refinement of their calibration coefficients. The second contribution was focused on the SFAs. Ten among the most popular SFAs were compared under different experimental conditions including different MIMU models and rotation rate magnitudes. To perform a “fair” comparison it was necessary to set the optimal parameter values for each SFA. The most important finding was that all the errors fall within a range from 3.8 deg to 7.1 deg thus making it impossible to draw any conclusions about the best performing SFA since no statistically significant differences were found. In addition, the orientation accuracy was heavily influenced by the experimental variables. After that, a novel method was designed to estimate the suboptimal parameter values of a given SFA without relying on any orientation reference. The maximum difference between the errors obtained using optimal and suboptimal parameter values amounted to 3.7 deg and to 0.6 deg on average. The last contribution consisted in the design of an unconstrained and a constrained methods for estimating the joint kinematics without considering the magnetometer to avoid the ferromagnetic disturbances. The unconstrained method was employed in a telerehabilitation platform in which the joint angles were estimated in real time. Errors collected during the execution of a full-body protocol were lower than 5 deg (considered the acceptability threshold). However, this method may be inaccurate after few minutes since no solutions can be taken to mitigate the drift error. To overcome this limitation a constrained method was developed based on a robotic model of the upper limb to set appropriate constraints. Errors relative to a continuous robot motion for twenty minutes were lower than 3 deg at most suggesting the feasibility of employing these solutions in the rehabilitation programs to properly plan the treatment and to accurately evaluate the outcomes

An optimal procedure for stride length estimation using foot-mounted magneto-inertial measurement units

Stride length is often used to quantitatively evaluate human locomotion performance. Stride by stride estimation can be conveniently obtained from the signals recorded using miniaturized inertial sensors attached to the feet and appropriate algorithms for data fusion and integration. To reduce the detrimental drift effect, different algorithmic solutions can be implemented. However, the overall method accuracy is supposed to depend on the optimal selection of the parameters which are required to be set. This study aimed at evaluating the influence of the main parameters involved in well-established methods for stride length estimation. An optimization process was conducted to improve methods' performance and preferable values for the considered parameters according to different walking speed ranges are suggested. A parametric solution is also proposed to target the methods on specific subjects' gait characteristics. The stride length estimates were obtained from straight walking trials of five healthy volunteers and were compared with those obtained from a stereo-photogrammetric system. After parameters tuning, percentage errors for stride length were 1.9%, 2.5% and 2.6% for comfortable, slow, and fast walking conditions, respectively

Contributions to physical exercises monitoring with inertial measurement units

Resumen: La monitorización de movimientos trata de obtener información sobre su ejecución, siendo esencial en múltiples aplicaciones, como el seguimiento de terapias físicas. La monitorización tiene un doble objetivo esencial para lograr los beneficios de dichas terapias: asegurar la corrección en la ejecución de movimientos y mejorar la adherencia a los programas prescritos. Para lograr esta monitorización de forma remota y poco intrusiva, se necesitan recursos tecnológicos. Este trabajo se centra en las soluciones basadas en sensores inerciales. Esta tesis estudia los algoritmos de la literatura para el análisis de movimientos con sensores inerciales, determinando un parámetro anatómico requerido en diversas propuestas: la posición de las articulaciones respecto de los sensores, así como longitud de los segmentos anatómicos. En este trabajo se introducen dos algoritmos de calibración anatómica. El primero, basado en mínimos cuadrados, determina el punto o el eje medios de aceleración nula presente en las articulaciones fijas. El algoritmo está adaptado a los movimientos lentos dados en los miembros inferiores para estabilizar las articulaciones. El segundo, adaptado a la variación de la posición relativa del punto de aceleración nula respecto de los sensores a causa del característico tejido blando asociado al cuerpo humano, emplea las medidas inerciales como entradas en un filtro de Kalman extendido. Por otro lado, esta tesis aborda la falta de datos comunes para la evaluación y comparación de los algoritmos. Para ello, se diseña y crea una base de datos centrada en movimientos habituales en rutinas físicas, que se encuentra publicada en Zenodo. Esta base de datos contiene movimientos de calibración articular y de ejercicios de miembros inferiores y superiores ejecutados de forma correcta e incorrecta por 30 voluntarios de ambos sexos con un amplio rango de edades, grabados con cuatro sensores inerciales y un sistema de referencia óptico de alta precisión. Además, las grabaciones se encuentran etiquetadas acorde al tipo de ejercicio realizado y su evaluación. Finalmente, se estudia un segundo enfoque de monitorización de rutinas físicas, cuyo objetivo es reconocer y evaluar simultáneamente los ejercicios ejecutados, retos comúnmente estudiados individualmente. Se proponen tres sistemas que emplean las medidas de cuatro sensores inerciales y difieren en el nivel de detalle en las salidas del sistema. Para realizar las clasificaciones propuestas, se evalúan seis algoritmos de machine learning determinando el más adecuado.This thesis is framed in the field of remote motion monitoring, which aims to obtain information about the execution of movements. This information is essential in many applications, including the clinical ones, to measure the evolution of patients, to assess possible pathologies, such as motor or cognitive ones, and to follow up physical therapies. The monitoring of physical therapies has twofold purpose: to ensure the correct execution of movements and to improve adherence to the programs. Both purposes are essential to achieve the benefits associated with physical therapies. To accomplish this monitoring in a remote and non-intrusive way, technological resources such as the well-known inertial sensors are needed, which are commonly integrated into the so-called wearables. This work focuses on inertial-based solutions for monitoring physical therapy routines. However, the results of this work are not exclusive of this field, being able to be applied in other fields that require a motion monitoring. This work is intended to meet the needs of the monitoring systems found in the literature. In the review of previous proposals for remote monitoring of rehabilitation routines, we found two different main approaches. The first one is based on the analysis of movements, which estimates kinematic parameters, and the second one focuses on the qualitative characterization of the movements. From this differentiation, we identify and contribute to the limitations of each approach. With regard to the motion analysis for the estimation of kinematic parameters, we found an anatomical parameter required in various methods proposed in the literature. This parameter consists in the position of the joints with respect to the sensors, and sometimes these methods also require the length of the anatomical segments. The determination of these internal parameters is complex and is usually performed in controlled environments with optical systems or through palpation of anatomical landmarks by trained personnel. There is a lack of algorithms that determine these anatomical parameters using inertial sensors. This work introduces an algorithm for this anatomical calibration, which is based on the determination of the point of zero acceleration present in fixed joints. We use one inertial sensor per joint in order to simplify the complexity of algorithms versus using xv xvi ABSTRACT more than one. Since the relative position of this point may vary due to soft tissue movements or joint motion, the mean null acceleration point for the calibration motion is estimated by least squares. This algorithm is adapted to slow movements occurring in the lower-limbs to meet the required joint stabilization. Moreover, it can be applied to both joint centers and axes, although the latter is more complex to determine. Since we are dealing with the calibration of a system as complex as the human body, we evaluate different movements and their relation to the accuracy of the proposed system. This thesis also proposes a second, more versatile calibration method, which is adapted to the characteristic soft tissue associated with the human body. This method is based on the measurements of one inertial sensors used as inputs of an extended Kalman filter. We test the proposal both in synthetic data and in the real scenario of hip center of rotation determination. In simulations it provides an accuracy of 3% and in the real scenario, where the reference is obtained with a high precision optical system, the accuracy is 10 %. In this way, we propose a novel algorithm that localizes the joints adaptively to the motion of the tissues. In addition, this work addresses another limitation of motion analysis which is the lack of common datasets for the evaluation of algorithms and for the development of new proposals of motion monitoring methods. For this purpose, we design and create a public database focused on common movements in rehabilitation routines. Its design takes into account the joint calibration that is usually considered for the monitoring of joint parameters, performing functional movements for it. We monitor lower and upper limb exercises correctly and incorrectly performed by 30 volunteers of both sexes and a wide range of ages. One of the main objectives to be fulfilled by this database is the validation of algorithms based on inertial systems. Thus, it is recorded by using four inertial systems placed on different body limbs and including a highly accurate reference system based on infrared cameras. In addition, the recorded movements are labeled according to their characterization, which is based on the type of exercise performed and their quality. We provide a total of 7 076 files of inertial kinematic data with a high-precision reference, characterized with respect to the kind of performed motion and their correctness in performance, together with a function for automatic processing. Finally, we focus on the analysis of the second approach of monitoring physical routines, whose objective is to obtain qualitative information of their execution. This work contributes to the characterization of movements including their recognition and evaluation, which are usually studied separately. We propose three classification systems which use four inertial sensors. The proposals differ in the distribution of data and, therefore, the level of detail in the system outputs. We evaluate six machine learning techniques for the proposed classification systems in order to determine the most suitable for each of them: Support Vector Machines, Decision Trees, Random Forest, xvii K Nearest Neighbors, Extreme Learning Machines and Multi-Layer Perceptron. The proposals result in accuracy, F1-value, precision and sensitivity above the 88 %. Furthermore, we achieve a system with an accuracy of 95% in the complete qualitative characterization of the motions, which recognizes the performed motion and evaluates the correctness of its performance. It is worth highlighting that the highest metrics are always obtained with Support Vector Machines, among all the methods evaluated. The proposed classifier that provides the highest metrics is the one divided into two stages, that first recognizes the exercises and then evaluates them, compared with the other proposals that perform both tasks in one single-stage classification. From our work, it can be concluded that inertial systems are appropriate for remote physical exercise monitoring. On the one hand, they are suitable for the calibration of human joints necessary for various methods of motion analysis using one inertial sensor per joint. These sensors allow to obtain the estimation of an average joint location as well as the average length of anatomical segments. Also, joint centers can be located in scenarios where joint-related sensor movements occur, associated with soft tissue movement. On the other hand, a complete characterization of the physical exercises performed can be achieved with four inertial sensors and the appropriate algorithms. In this way, anatomical information can be obtained, as well as quantitative and qualitative information on the execution of physical therapies through the use of inertial sensors

A wearable multi-sensor system for real world gait analysis

Gait analysis is commonly performed in standardized environments, but there is a growing interest in assessing gait also in ecological conditions. In this regard, an important limitation is the lack of an accurate mobile gold standard for validating any wearable system, such as continuous monitoring devices mounted on the trunk or wrist. This study therefore deals with the development and validation of a new wearable multi-sensor-based system for digital gait assessment in free-living conditions. In particular, results obtained from five healthy subjects during lab-based and real-world experiments were presented and discussed. The in-lab validation, which assessed the accuracy and reliability of the proposed system, shows median percentage errors smaller than 2% in the estimation of spatio-temporal parameters. The system also proved to be easy to use, comfortable to wear and robust during the out-of-lab acquisitions, showing its feasibility for free-living applications

Validation of Spatiotemporal and Kinematic Measures in Functional Exercises Using a Minimal Modeling Inertial Sensor Methodology

This study proposes a minimal modeling magnetic, angular rate and gravity (MARG) methodology for assessing spatiotemporal and kinematic measures of functional fitness exercises. Thirteen healthy persons performed repetitions of the squat, box squat, sandbag pickup, shuffle-walk, and bear crawl. Sagittal plane hip, knee, and ankle range of motion (ROM) and stride length, stride time, and stance time measures were compared for the MARG method and an optical motion capture (OMC) system. The root mean square error (RMSE), mean absolute percentage error (MAPE), and Bland&ndash;Altman plots and limits of agreement were used to assess agreement between methods. Hip and knee ROM showed good to excellent agreement with the OMC system during the squat, box squat, and sandbag pickup (RMSE: 4.4&ndash;9.8&deg;), while ankle ROM agreement ranged from good to unacceptable (RMSE: 2.7&ndash;7.2&deg;). Unacceptable hip and knee ROM agreement was observed for the shuffle-walk and bear crawl (RMSE: 3.3&ndash;8.6&deg;). The stride length, stride time, and stance time showed good to excellent agreement between methods (MAPE: (3.2 &plusmn; 2.8)%&ndash;(8.2 &plusmn; 7.9)%). Although the proposed MARG-based method is a valid means of assessing spatiotemporal and kinematic measures during various exercises, further development is required to assess the joint kinematics of small ROM, high velocity movements