Conversion of Upper-Limb Inertial Measurement Unit Data to Joint Angles: A Systematic Review

Inertial measurement units (IMUs) have become the mainstay in human motion evaluation outside of the laboratory; however, quantification of 3-dimensional upper limb motion using IMUs remains challenging. The objective of this systematic review is twofold. Firstly, to evaluate computational methods used to convert IMU data to joint angles in the upper limb, including for the scapulothoracic, humerothoracic, glenohumeral, and elbow joints; and secondly, to quantify the accuracy of these approaches when compared to optoelectronic motion analysis. Fifty-two studies were included. Maximum joint motion measurement accuracy from IMUs was achieved using Euler angle decomposition and Kalman-based filters. This resulted in differences between IMU and optoelectronic motion analysis of 4° across all degrees of freedom of humerothoracic movement. Higher accuracy has been achieved at the elbow joint with functional joint axis calibration tasks and the use of kinematic constraints on gyroscope data, resulting in RMS errors between IMU and optoelectronic motion for flexion–extension as low as 2°. For the glenohumeral joint, 3D joint motion has been described with RMS errors of 6° and higher. In contrast, scapulothoracic joint motion tracking yielded RMS errors in excess of 10° in the protraction–retraction and anterior-posterior tilt direction. The findings of this study demonstrate high-quality 3D humerothoracic and elbow joint motion measurement capability using IMUs and underscore the challenges of skin motion artifacts in scapulothoracic and glenohumeral joint motion analysis. Future studies ought to implement functional joint axis calibrations, and IMU-based scapula locators to address skin motion artifacts at the scapula, and explore the use of artificial neural networks and data-driven approaches to directly convert IMU data to joint angles.


Introduction
Quantification of joint motion has played a key role in our understanding of upper-limb function, from rehabilitation [1][2][3][4], sports science [5][6][7], and ergonomics [8][9][10], to robotics [11][12][13][14]. Joint angles remain the standardized, clinically relevant measure to quantify inter-segment angles at a joint and are critically important for interpreting upper-limb joint function and consolidating data, e.g., across different subjects, laboratories, or motion measurement modalities [15][16][17][18]. Several types of instrumentation have been employed to measure human motion data, including optoelectronic motion analysis [19][20][21], RGB and RGB-D cameras [22][23][24][25], radar [26,27], and ultrasonic measurement devices [28,29]. Optoelectronic motion analysis systems such as Vicon (Oxford Metrics, Oxford, UK) and Optotrak (Northern Digital Inc.,Waterloo, Canada) are considered the gold standard in non-invasive joint-angle measurement, and are used extensively in the evaluation of scapulothoracic, glenohumeral, and elbow joint function [19,30,31]. During movement, video motion analysis systems directly measure 3D trajectories of markers placed on body landmarks at high speed and accuracy, and these data are then used to reconstruct anatomical coordinate systems for the calculation of joint angles between adjacent bones. Unfortunately, these systems are costly, require a dedicated capture space that is typically indoors, are restricted in terms of the available marker capture volume, and are associated with significant setup time before data acquisition. RGB cameras, radar, and ultrasound are susceptible to occlusion between the subject and receiver, and are thus less desirable in a data collection environment with complex or unanticipated object layouts [22,32,33].
We are currently at the frontier of new technological developments in human motion measurement, with commercially available inertial measurement units (IMUs) now inexpensive, lightweight, portable, wireless, and thus highly amenable to "wearable" human motion measurement in and outside of the laboratory environment without limitation on capture volume [34,35]. Modern IMUs can provide orientation data with respect to a local reference system via micro-electromechanical systems (MEMS) comprising tri-axial accelerometers, gyroscopes, and magnetometers. Accelerometers are used to measure the linear acceleration relative to gravity [36][37][38], gyroscopes measure the angular velocity of rotation, and magnetometers provide heading or yaw axis information by measuring the Earth's magnetic field. Unfortunately, MEMS have hardware limitations that can substantially affect human movement data and sensor usage. For example, accelerometers are sensitive to impact; gyroscopic output, which can be integrated to obtain angular position, is prone to instrumentation noise accumulation resulting in sensor drift; while magnetometers can be sensitive to magnetic disturbances from surrounds [36,[39][40][41]. To improve measurement accuracy and reduce orientation estimation errors using IMUs, sensor-fusion algorithms have been developed and are frequently employed, including Kalman-based filters [42][43][44], complementary filters [45][46][47], and gradient descent algorithms [48][49][50]. A recent systematic review by Longo et al. (2022) compared the performance of different sensor-fusion algorithms in the measurement of shoulder joint angles [51]. However, the accuracy of upper-limb joint angles computed using IMUs, which are dependent on the use of sensor-fusion algorithms and the alignment of sensors to anatomical segments, remains poorly understood.
Calculation of joint angles using IMUs is fundamentally different from that using optical motion analysis methods since IMUs cannot be explicitly used to define anatomical landmarks and bony coordinate systems. Instead, a sensor-to-segment calibration is required to establish the angular position relationship between the sensor and the body [36,41,52]. Specifically, IMUs are positioned on the body so that their sensing axes are aligned with anatomical references, such as the longitudinal axis of a bone [30,53]. Static poses and dynamic calibration tasks can also be used to define joint axes of rotation [36,54,55]. However, this requires a well-planned experimental protocol and user experience, and out-of-plane joint motion axes remain challenging to quantify. Another major challenge in the calculation of joint angles using IMUs is skin motion artifacts, which describe the motion of the surface of the skin, in which IMUs are affixed, relative to the underlying bony segments. The scapula, for example, can glide over 10 cm beneath the skin during abduction [20,56].
Several systematic reviews on human upper-limb motion analysis using IMUs have been carried out to date. De Baets et al. (2017) conducted a review of shoulder kinematics measurement using IMUs and showed that protocols for scapulothoracic joint motion quantification demonstrated high reliability and repeatability, while limited consistency was found in humerothoracic joint-angle evaluation. However, these approaches did not perform comparisons relative to a reference motion measurement modality [57]. Other reviews have demonstrated that the accuracy of IMU-based joint-angle measurement is dependent on the specific joint under investigation, the motion task [31,58,59], and is largely driven by the IMU data processing technique employed [34,60,61]. For instance, Walmsley et al. (2018) showed that shoulder joint motion tracking errors using IMUs were lower for single plane movements such as flexion-extension than for multiple degree-of-freedom joint motions. Poitras et al. (2019) investigated the validity and reliability of whole-body movements using IMUs on a joint-by-joint basis, showing that task complexity can increase the variability of out-of-plane shoulder joint angles, including abductionadduction. Furthermore, five algorithms employed in reconstructing joint motion from IMU data were compared by Filippeschi et al. (2017), with the Kalman filter and QUEST (QUaternion ESTimator) algorithm shown to be the most accurate [34,62]. However, despite numerous studies exploring different sensor processing algorithms across various joints, a consistent approach to the conversion of IMU data to joint angles has not been adopted. The considerable variability and inconsistencies in IMU-derived motion data underscores the need for a standardized modeling approach for IMU to joint-angle conversion.
The aims of this study were two-fold. The first was to evaluate computational methods used to convert IMU data to joint angles in the upper limb, which included the scapulothoracic, humerothoracic, glenohumeral, and elbow joints; the second was to quantify the accuracy of these approaches when compared to optoelectronic motion analysis. The findings will help guide the use of IMUs for upper-limb joint motion measurement in both the research and clinical settings.

Database Search Strategy
A literature search was conducted to identify previously published articles that describe the measurement of upper-limb joint angles using IMUs following the PRISMA 2020 protocol for systematic reviews [63]. Articles were identified through a systematic search of the following five databases: Scopus, Web of Science, EMBASE (via Ovid), Medline (via Ovid), and CENTRAL. These databases were searched for English publications before 14 June 2023. To maximize capture of all relevant articles, a broad search strategy was used with the following terms: IMU* OR inertial measurement unit* OR inertial sensor* OR wearable sensor* OR accelerometer* OR gyroscope* OR magnetometer* AND joint angle* OR kinematic* OR range of motion AND Upper limb* OR upper extremit* OR shoulder* OR elbow* OR arm* OR humer* OR scapul* AND optoelectronic* OR optical OR gold standard OR video* OR camera*

Selection Criteria
After the removal of duplicates from search results, all titles and abstracts were screened using the following inclusion and exclusion criteria ( Figure 1).
Motion analysis experiments conducted on human subjects ii.
Studies evaluating joint angles in the upper limb, including those associated with one or more of the shoulder, elbow, and scapula segments iii.
Use of IMUs that operate with an accelerometer, gyroscope, magnetometer, or a combination iv.
Comparison of IMU-based joint angles with those derived from optoelectronic motion analysis.
Exclusion criteria: i. Non-English studies ii.
Thesis, conference papers, or review articles iii.
Non-human studies iv.
Studies that employ sensors other than IMUs  Inclusion criteria: i.
Motion analysis experiments conducted on human subjects ii. Studies evaluating joint angles in the upper limb, including those associated with one or more of the shoulder, elbow, and scapula segments iii. Use of IMUs that operate with an accelerometer, gyroscope, magnetometer, or a combination iv. Comparison of IMU-based joint angles with those derived from optoelectronic motion analysis.
Exclusion criteria: i. Non-English studies ii. Thesis, conference papers, or review articles iii. Non-human studies iv. Studies that employ sensors other than IMUs

Quality Assessment
The quality of all included studies was evaluated using a customized quality assessment based on the Downs & Black and STROBE checklist [64,65]. The quality assessment questions covered key characteristics of the studies including aim(s), measurement protocols, findings, and error analyses. There were 11 questions in total, and each was scored 0, 1, or 2 which corresponded to not addressed, partially addressed, or fully addressed, respectively. Quality scores were collated, and their mean and range were calculated. High methodological quality was defined as a score of ≥20 (to a maximum of 22), moderate quality was defined as a score of <20 and ≥15, and low quality was defined as a score of

Quality Assessment
The quality of all included studies was evaluated using a customized quality assessment based on the Downs & Black and STROBE checklist [64,65]. The quality assessment questions covered key characteristics of the studies including aim(s), measurement protocols, findings, and error analyses. There were 11 questions in total, and each was scored 0, 1, or 2 which corresponded to not addressed, partially addressed, or fully addressed, respectively. Quality scores were collated, and their mean and range were calculated. High methodological quality was defined as a score of ≥20 (to a maximum of 22), moderate quality was defined as a score of <20 and ≥15, and low quality was defined as a score of <15. Two reviewers participated in the quality assessment independently, and any disagreement in the scores was resolved by discussion. The quality assessment questions included:

Data Extraction
For the scapulothoracic, humerothoracic, glenohumeral, and elbow joints, data extracted were summarized by study sample size, sensor-to-segment calibration approach (if any), sensor-fusion algorithm, joint-angle calculation method, motion tasks, and error metrics describing differences between IMU and optoelectronic motion data.

Search Outcome and Quality
A total of 989 studies were identified from the initial search in the 5 databases, of which 262 duplicates were removed. After title and abstract screening, 136 eligible studies were retrieved for the full-text screening based on the selection criteria. During the full-text screening, two additional studies were included by manually checking the bibliography. Fifty-two studies were included for data extraction (Figure 1). The methodological quality scores of these studies ranged from 9 to 22, with an average score of 17.6. Fourteen studies were of high quality, 32 studies were of moderate quality and 6 studies were of low quality. Studies scored highest on questions related to objectives and outcomes, achieving an average quality score of 2.0. However, quality assessment questions concerning validity and reliability, as well as limitations and bias, received average scores below the 25th percentile (1.3) of the average scores of all studies ( Figure 2). Although all included studies validated their methodology against an optoelectronic measurement system, 30 studies did not assess the reliability of their methodology by repeating testing on the same subject or with different operators, leading to a low average score in validity and reliability.
To establish a relationship between IMU orientation and that of an underlying anatomical coordinate system, a sensor-to-segment calibration process is typically employed. Common calibration methods include predefined sensor alignment with a segment [66,94,103,104], static pose alignment [67,[69][70][71][72][73][74]83,84,88,[98][99][100]102,105,109], functional joint movements [92,107], or their combinations [30,36,41,61,68,79,81,91,96,97,106,108,110,[112][113][114], as well as use of IMU palpation calipers [90,93] (Figure 4). Predefined sensor alignment involves the placement of an IMU on the body to align with a bone-fixed reference frame. For static pose calibration, a subject may perform one or more pre-determined static postures, for example, standing with the palms facing to the front [107,112], an N-pose with arms neutrally placed alongside the body [41,83,100,106,111], or a T-pose with arms abducted to 90 • [69,86,97]. Static calibration then aims to define the sensor coordinate system using gravity as a reference by averaging resultant accelerometer data for a given pose while also establishing a neutral or reference alignment of a joint. In contrast, functional joint movements are performed by repetitively moving a joint through a specific degree of freedom, and anatomical joint axis calculation can be performed using averaged gyroscope data [41,101,106,107,111], or by solving a kinematic constraint function on gyroscope data using optimization [41,75,77]. IMU palpation calipers can be used to identify bony landmark positions for IMU registration [90,93]. joint movements [92,107], or their combinations [30,36,41,61,68,79,81,91,96,97,106,108,110,[112][113][114], as well as use of IMU palpation calipers [90,93] (Figure 4). Predefined sensor alignment involves the placement of an IMU on the body to align with a bone-fixed reference frame. For static pose calibration, a subject may perform one or more pre-determined static postures, for example, standing with the palms facing to the front [107,112], an N-pose with arms neutrally placed alongside the body [41,83,100,106,111], or a T-pose with arms abducted to 90 [69,86,97]. Static calibration then aims to define the sensor coordinate system using gravity as a reference by averaging resultant accelerometer data for a given pose while also establishing the neutral or reference alignment of a joint. In contrast, functional joint movements are performed by repetitively moving a joint through a specific degree of freedom, and anatomical joint axis calculation can be performed using averaged gyroscope data [41,101,106,107,111], or by solving a kinematic constraint function on gyroscope data using optimization [41,75,77]. IMU palpation calipers can be used to identify bony landmark positions for IMU registration [90,93].  [81] with permission from IEEE, Subfigure C was adapted from [92] with permission from Elsevier, and Subfigure D was adapted from [93] with permission from Nature Portfolio. Subfigure A adapted from [81] with permission from IEEE, Subfigure C adapted from [92] with permission from Elsevier, and Subfigure D adapted from [93] with permission from Nature Portfolio.

Inertial Measurement Unit (IMU) Data to Joint-Angle Conversion
Strategies to reduce gyroscopic drift and magnetic disturbance have been employed on raw IMU data to improve sensor orientation estimates. Slade et al. (2022) corrected gyroscopic drift by keeping IMUs stationary for a period of time, calculating the gyroscopic bias by averaging the angular velocity in each sensing axis, and then eliminating this bias from the raw gyroscopic data [81]. Similar approaches to eliminate gyroscopic drift were applied by Ligorio et al. (2020) with IMUs placed stationary on the floor [41], and Bessone et al. (2019) during a "T-pose" performed by the subject using "aktos-t" software [69]. Truppa et al. (2021) evaluated gyroscopic bias as a variable that was updated during static IMUs data collection. To achieve this, accelerometer data were restricted within a spherical neighborhood of a specific value. At each static frame, the corresponding gyroscopic bias was calculated using sensor coordinate system orthogonalization and then eliminated in subsequent dynamic motions. Magnetic disturbance has also been minimized by sensor calibration in the surrounding magnetic field using spherical [73,95] or ellipsoidal fitting of raw magnetometer data [70]. Additionally, Laidig et al. (2017) proposed a linear model to evaluate heading angle errors in IMU orientation due to magnetic field disturbance, which was solved using optimization and subsequently eliminated [77].

Scapulothoracic Joint Motion Measurement
Three studies, two of high-quality [79,90] and one of moderate quality [30], measured scapular kinematics with respect to the thorax using IMUs [30,79] (Table 2). Cutti et al. (2008) reported RMS errors of between 0.2 and 3.2 for humerothoracic flexion-extension, abduction-adduction, hand-to-nape, hand-to-top-of-head, shoulder girdle eleva- Figure 5. Strategies to define anatomical coordinate systems using IMUs including (A) Denavit-Hartenberg joint representation (B) orthonormal segment coordinate system (C) non-orthonormal segment coordinate system. Subfigure A was adapted from [61] with permission from IEEE, Subfigure B adapted from [92] with permission from Elsevier, and Subfigure C adapted from [36] with permission from MPDI.

Scapulothoracic Joint Motion Measurement
Three studies, two of high-quality [79,90] and one of moderate quality [30], measured scapular kinematics with respect to the thorax using IMUs [30,79] (Table 2). Cutti et al. (2008) reported RMS errors of between 0.2 • and 3.2 • for humerothoracic flexion-extension, abductionadduction, hand-to-nape, hand-to-top-of-head, shoulder girdle elevation-depression and protraction-retraction, when comparing IMU data with optoelectronic motion data via markers placed on IMUs. They defined a set of sensor orientations and positions on the body and adopted static pose calibration. They employed Xsens' proprietary Kalman filter, followed by Euler angle decomposition, to calculate the 3D scapulothoracic joint angles. This method was also adopted by Parel [69,74,87], and 1 study employed axis-angle-based inverse kinematics [81].
Six studies of moderate quality achieved RMS errors or mean absolute errors that were less than 5 • in all three degrees of freedom of humerothoracic joint motion, which were of the highest accuracy among the studies on this joint [30,61,91,95,102,105]. Truppa and colleagues (2021) exploited a sensor-fusion algorithm that automatically eliminated gyroscopic bias during a series of yoga poses (mean absolute error < 4 • ) [91]. They mitigated sensor-fusion drift by first defining an orthogonal coordinate system for the thorax and upper arm based on a gravity vector and humeral flexion-extension axis derived from a functional movement calibration. Once static IMU motion was detected with IMUs, the sensor's local frame was then re-orthogonalized using the gravity vector, and the gyroscope bias was subsequently evaluated and eliminated. Cutti et al. (2008) obtained RMS errors in the range of 0.2 • to 3.2 • for humerothoracic flexion-extension, abduction-adduction, internal-external rotation, hand-to-nape, and head-touching using a predefined sensor alignment with a static pose calibration, Xsens Kalman filter and Euler angle decomposition [30]. Zhang et al. (2011) reported RMS errors during arbitrary upper-limb movements of 2.36 • , 0.88 • , and 2.9 • in flexion-extension, abduction-adduction, and internal-external rotation angles, respectively [61]. They defined upper-limb joints as mechanical linkages and modeled angular joint motion as state-space vectors. A neutral pose was performed for sensor-to-segment calibration, and measurement noise at the accelerometer, gyroscope, and magnetometer was modeled as Gaussian white noise with zero mean and finite covariances. An unscented Kalman filter was used to solve forward kinematics equations that related the sensor measurement data to joint angles [116].
Lambrecht et al. (2014) applied a magnetic heading compensation to the InvenSense proprietary sensor-fusion algorithm, which utilized accelerometer and gyroscope data [115]. The raw magnetometer data about the sensor was calibrated by spherical fitting followed by a tilt angle compensation using quaternion output from the sensor fusion. Then, magnetic compensation was used to correct heading angles caused by gyroscopic drift, improving the orientation estimation for long-term data collection. During reaching, RMS errors of 4.9 • , 1.2 • , and 2.9 • were reported for humerothoracic plane, elevation, and axial rotation, respectively. Table 3. Studies that measured humerothoracic joint angles using IMUs, including their sample size, study quality, sensor-to-segment calibration method, sensor-fusion approach, joint-angle calculation method, tasks performed, kinematic errors, and associated error metric when comparing joint angles with those calculated using an optoelectronic motion analysis system. Errors during flexion-extension, abduction-adduction, and internal-external rotation are given in plain text, while errors in the Euler angle plane of elevation, elevation angle, and axial rotation are given in parentheses. Kinematic errors and error ranges [square brackets] are given. Error metrics with "r" represent the right side of the body only. Acronyms used include PSA, predefined sensor alignment; PA, proprietary algorithm; KF, Kalman filter; F/E, flexion/extension; AB/AD, abduction/adduction; IN/EX, internal/external rotation; EAD, Euler angle decomposition; FJM, functional joint movement; MFC, Magnetic field calibration; ABV, angle between vectors.

Glenohumeral Joint Motion Measurement
Six studies that included 1 of high quality [97] and 5 of moderate quality [71,98,99,108,110], measured glenohumeral joint angles using IMUs. Five of these studies used an Xsens IMU system and the Xsens-defined biomechanical model known as the MVN model, which consists of 23 segments and 22 joints, for kinematic analysis [71,97,98,108,110] (Table 4). All studies used proprietary sensor-fusion algorithms, while 4 studies relied on proprietary software to compute the joint angles. Table 4. Studies that measured glenohumeral joint angles using IMUs, including their sample size, study quality, sensor-to-segment calibration method, sensor-fusion approach, joint-angle calculation method, tasks performed, kinematic errors, and associated error metric when comparing joint angles with those calculated using an optoelectronic motion analysis system. Error metrics with "r" representing the right side of the body only. Acronyms used include PSA, predefined sensor alignment; PA, proprietary algorithm; KF, Kalman filter; F/E, flexion/extension; AB/AD, abduction/adduction; IN/EX, internal/external rotation; EAD, Euler angle decomposition; FJM, functional joint movement. . ISB definitions of joint coordinate systems were employed for both IMU and optoelectronic systems by calculating rotation matrices that transferred marker clusters fixed with IMUs to bony landmarks using the optoelectronic measurement system. Euler angle decomposition was subsequently used to calculate glenohumeral joint angles during a box-moving task [97]. Pedro et al. (2021) also obtained good accuracy in glenohumeral joint-angle measurement during tennis forehand drives using Xsens software (RMS error ≤ 6.1 • ). This was achieved using an MVN model for both IMU and optoelectronic systems [110].

Study Sample
Muller et al. (2016) applied a similar kinematic constraint to gyroscope data for the evaluation of the joint axis, which was solved using the Moore-Penrose pseudoinverse. In door-opening tasks, RMS errors were 2.7 • and 3.8 • in flexion-extension and pronationsupination, respectively [80]. Ligorio et al. (2017) proposed a four-step functional calibration method that involved planar forearm and upper-arm movements, achieving RMS errors that were less than 4 • during both elbow flexion-extension and pronation-supination tasks [111]. For the same movement tasks, Picerno et al. (2019) obtained comparable accuracy with a novel sensor-calibration method that employed a customized IMU caliper device to identify bony landmarks, thus allowing the definition of an anatomical coordinate system [93]. Mavor et al. (2020) obtained mean RMS errors of approximately 40 • for the pronationsupination angle of the left and right elbow during 8 military movements [98]. They used the Xsens MVN model in the calculation of IMU angles, while a biomechanical model based on anatomical landmarks was used in optoelectronic motion analysis (Visual 3D). Humadi (2021) measured elbow flexion-extension angles during box-moving, box-elevation, and reaching tasks using the MVN model for IMUs and ISB coordinates systems for optoelectronic motion analysis [71]. An offset error of up to 26 • was found in the IMU-based joint angles which predominantly contributed to a total RMS error of approximately 30 • .

Discussion
The purpose of this systematic review was to assess strategies for upper-limb jointangle calculation using IMUs and their accuracy when compared to optoelectronic motion analysis. Due to skin motion artifacts and challenges associated with tracking dynamic scapula motion, the accuracy of IMU-based joint-angle calculations is generally highest at the humerothoracic and elbow joints and lowest at the scapulothoracic joint and glenohumeral joints. Although scapular landmarks can be digitized using an optoelectronic system, this cannot be achieved using IMUs, and consequently, most upper-limb motion studies using inertial sensors focus on the measurement of humerothoracic motion. The use of Euler angle decomposition resulted in the highest accuracy of humerothoracic, glenohumeral, and elbow joint-angle measurements using IMUs; however, joint-angle calculations are strongly dependent on the sensor-fusion approach employed.
Humerothoracic motion measurement using IMUs is a convenient approach to quantifying upper-limb motion since it does not require measurement and modeling of scapular motion. This has included assessment of upper-limb range of motion and mobility, and sports performance, including real-time applications [60,96,121,122]. Alignment of IMUs with respect to the thorax and humeral segments can be achieved using calibration approaches such as static poses and dynamic functional tasks, which facilitate the establishment of anatomical coordinate systems. For example, Truppa et al. (2021) used accelerometer data during a static standing task to determine a vertical axis, and orthogonal projections of gyroscope data during upper-arm flexion-extension to define a lateral axis, resulted in high joint motion accuracy [91]. Such calibration approaches ensure greater consistency in joint axis definitions with anatomical landmark-based optoelectronic motion analysis and avoid alignment errors that can be introduced from manual sensor placement. High humerothoracic motion analysis accuracy was also achieved by computing orientations of anatomical segments using a sensor-fusion algorithm such as a Kalman-based filter [30,61,105]. This approach is capable of predicting and updating sensor orientation on a recursive basis, taking sensor noise into account, and enabling noise reduction and robust sensor orientation estimation [51]. However, the accuracy of MEMS data fusion is generally dependent on an undistorted surrounding magnetic field. Magnetic field calibration can account for potential magnetic field disturbances, or magnetometer data can simply be omitted from the sensor fusion. This may reduce the sensor's ability to accurately evaluate the heading angle [52,81,120].
Measurement of scapulothoracic angles using IMUs can be challenging since the scapula slides considerably under the skin during upper-limb elevation, and fixing sen-sors to the scapula is difficult to achieve [123]. Conventional methods for measuring dynamic scapular motion using an optoelectronic system have involved the use of a scapular tracker [124] or an acromial marker cluster [123,125,126]. These approaches enable anatomical landmarks on the scapula to be digitized across a small number of postures and mapped to a scapular-fixed marker cluster using a regression model. This ultimately facilitates the estimation of scapula movement during continuous dynamic upper-limb motions. Van den Noort et al. (2015) developed an IMU scapula locator to register the alignment of the scapula at different humeral elevations, thus allowing the measurement of scapular motion during upper-limb tasks [127]. Friesen et al. (2023) adopted this approach and employed a regression model to facilitate the interpolation of scapular angles between bone positions registered with the IMU scapula locator [90].
At the glenohumeral joint, the highest accuracy in joint motion measurement using IMUs was achieved by Pedro et al. (2021) using Xsens' proprietary software [110], which involved the use of an MVN model to establish segment coordinate systems [128]. The tracking of the scapula used a skin-placed IMU, static poses, and functional joint movements to align sensor coordinate systems with the scapula. Joint angles were subsequently computed using Euler angle decomposition between the scapula and humerus. Motion measurement at the glenohumeral joint is substantially affected by skin motion artifacts at the scapula, and segment orientation accuracy is dependent on sensor-fusion algorithm performance. Future development of fast and efficient scapular location methods, including the use of IMU-based scapula locator, will improve glenohumeral joint-angle measurement accuracy.
Elbow joint motion measurement using IMUs has been shown to produce more accurate joint angles than those associated with humerothoracic or glenohumeral joint motion since this motion is more constrained and less influenced by skin motion artifacts than other upper-limb joints. The highest elbow joint motion accuracy was achieved with the use of functional joint movements [41,111] and by applying kinematic constraints to elbow joint axes using optimization [41,52,75]. Once elbow joint axes were established, flexion-extension was typically selected as the first axis of the Euler angle decomposition, which minimized propagation of IMU signal error through the Euler sequence and resulted in optimal flexion-extension motion accuracy [129]. The limited range of elbow carrying angle motion was associated with reduced variability in out-of-plane movements measured during uniaxial elbow flexion-extension motion, as well as reduced joint-angle crosstalk relative to multi-degree-of-freedom joints such as the shoulder [31,59].
Several limitations of this study ought to be considered. First, there was variability in the way joint angles were computed using optoelectronic motion analysis, including retroreflective marker placement i.e., on landmarks, over body suits, or directly to IMUs, as well as the joint coordinate system definitions, which may ultimately make direct comparisons between studies more subjective. Second, the IMU accuracy metrics were not consistent across studies, with some adopting RMS error, peak error and mean absolute error, which can make interpreting accuracy across studies challenging. Third, a variety of IMU models were employed, each with different sample rates, sensitivity, and fidelity, which may affect joint-angle predictions. Finally, this study focused on activities of daily living, and the results may be different for high-speed joint motions, which were generally not considered in the studies considered, including those during throwing, swimming, and impact sports.
As machine-learning and artificial-intelligence (AI) approaches to data analytics evolve, these techniques are likely to have a greater role in advancing human motion analysis using IMUs. Artificial neural networks have been used to analyze large datasets of IMU sensor data, identify human movement patterns and generate joint angles in an automated manner [130][131][132]. For example, Senanayake et al. (2021) developed a generative adversarial network (GAN) that predicted 3D ankle joint angles using raw IMU data, achieving an accuracy of 3.8 • , 2.1 • and 3.5 • in dorsiflexion, inversion, and axial rotation, respectively [133]. Mundt et al. (2020) estimated 3D lower limb joint angles during gait using a feedforward neural network and achieved RMS errors lower than 4.8 • , with the best results in the sagittal motion plane [134]. These findings indicate the feasibility of accurate and reliable computation of joint angles using data-driven approaches without dependence on conventional sensor-fusion algorithms such as Kalman filters. Such models, once trained, can also operate in real time, and provide robust motion analysis that is not dependent on accurate sensor placement. However, the performance of these approaches depends on sufficient quantity and diversity of training data, which may not always be practical to obtain. An inadequate training dataset may result in limited generalizability and model robustness to new subjects and different onboard MEMS hardware configurations, and an inability to predict new pathological movements [134][135][136][137]. Furthermore, the generation of artificial neural networks such as GANs can be challenging due to the large number of hyperparameters that require tuning, which has limited their uptake to date. Thus, the usability and accessibility of these models is also a challenge that must be addressed.
With the increasing availability of low-cost wearable technology, and the establishment of robust joint-angle calculation methods, greater applications of IMUs will be realized, including remote real-time monitoring and telemedicine, particularly in the elderly and motor-compromised [138][139][140], sports training, and human performance optimization [141][142][143], defense applications such as measurement and monitoring of front-line soldiers [98,144], habitual motion evaluation over extended periods including in submarines and spaceflight, and film and animation applications [145,146].

Conclusions
This systematic review evaluated the accuracy of IMU to joint-angle conversion methods in the upper limb. Due to challenges associated with tracking dynamic scapula motion, motion measurement accuracy using IMUs is generally higher at the humerothoracic and elbow joints, and lowest at the scapulothoracic joint and glenohumeral joints. For humerothoracic and elbow joint motion measurement, maximum measurement accuracy was achieved using sensor-fusion algorithms that include Kalman-based filters to integrate accelerometer, gyroscope, and magnetometer data, and Euler angle decomposition of adjacent IMU-based segment orientations. Optimization-based kinematic constraints on gyroscope data, together with functional joint movement calibration, were also employed for the estimation of elbow joint axes, leading to high-accuracy elbow joint-angle calculation. Future approaches to calculating upper-limb joint angles using IMUs ought to leverage static or functional calibration tasks to establish joint axes of rotation for Euler angle decomposition, implement fast and user-friendly scapula locator jigs to aid in scapulothoracic and glenohumeral joint motion measurement, and draw on robust AI-based algorithms for robust, real-time IMU to joint-angle conversion.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.