# Inertial Sensors for Human Motion Analysis: A Comprehensive Review

Sara García-de-Villa, David Casillas-Pérez, Ana Jiménez-Martín , and Juan
Jesús García-Domínguez November 2nd, 2022. Financial support acknowledgment.
This work was supported in part by Junta de Comunidades de Castilla La Mancha
(FrailAlert project, SBPLY/21/180501/000216), the Spanish Ministry of Science
and Innovation (INDRI project, PID2021-122642OB-C41) , Comunidad de Madrid
(RACC project, CM/JIN/2021-016) and NEXTPERCEPTION European Union project
funded by ECSEL Joint Undertaking (JU), under grant agreement No.876487
(ECSEL-2019-2-RIA). S. G. V. was with the Department of Electronics,
University of Alcala, Alcalá de Henares, 28805, Spain and in the Center of
Automation and Robotics (CSIC-UPM), Arganda del Rey, 28500, Spain (e-mail:
sara.garciavilla@uah.es). She is now with the Department of Signal Theory and
Communications, Rey Juan Carlos University, Fuenlabrada, 28942, Spain.
(e-mail: sara.garcia.devilla@urjc.es). A. J. M. and J. J. G. D. are with the
Department of Electronics, University of Alcala, Alcalá de Henares, 28805,
Spain. (A. J. M. e-mail<EMAIL_ADDRESS>J. J. G. D. e-mail:
jjesus.garcia@uah.es).D. C. P. is with the Department of Signal Theory and
Communications, Rey Juan Carlos University, Fuenlabrada, 28942, Spain.
(e-mail: david.casillas@urjc.es).

###### Abstract

Inertial motion analysis is having a growing interest during the last decades
due to its advantages over classical optical systems. The technological
solution based on inertial measurement units allows the measurement of
movements in daily living environments, such as in everyday life, which is key
for a realistic assessment and understanding of movements. This is why
research in this field is still developing and different approaches are
proposed. This presents a systematic review of the different proposals for
inertial motion analysis found in the literature. The search strategy has been
carried out in eight different platforms, including journal articles and
conference proceedings, which are written in English and published until
August 2022. The results are analyzed in terms of the publishers, the sensors
used, the applications, the monitored units, the algorithms of use, the
participants of the studies and the validation systems employed. In addition,
we delve deeply into the machine learning techniques proposed in recent years
and in the approaches to reduce the estimation error. In this way, we show an
overview of the research carried out in this field, going into more detail in
recent years, and providing some research directions for future work.

###### Index Terms:

Human motion, motion analysis, kinematic analysis, inertial measurement units,
IMU, inertial sensors.

##  I Introduction

Human motion analysis is an essential support tool for the assessment of the
parameters of movements, which is specially important in the evaluation of
workout routines, clinical rehabilitation and preventive treatments [1]. It is
also becoming very popular for the physical activity monitoring in the
elderly. Indeed, as the population of developed countries ages, the demand for
home-based rehabilitation and the need to obtain quantitative exercise data
remotely will increase [2].

Optical methods are considered the _gold standard_ in the motion analysis
field because of their accurate measurements of kinematic and spatio-temporal
parameters [3]. However, these systems entail several disadvantages, such as
the high cost of equipment, the need for trained personnel to use the
equipment, the required large spaces for installation and their restricted
margin of maneuverability, that limits their use to controlled indoor
environments.

The inertial motion analysis has emerged as a promising alternative to optical
methods attracting a great scientific interest. Inertial systems are portable
and can be used everywhere, what means an advantage to the optical systems,
which are commonly constraint to a limited space. That makes the Inertial
Measurement Units (IMUs) an affordable and friendly use alternative for the
estimation of human kinematics. These devices allow continuous monitoring of
human motions in daily environments, which is crucial in order to obtain more
reliable information than the obtained in sporadic laboratory tests. For these
reasons, the use of IMUs has increased in the last few decades for continuous
monitoring of human motions, as reported in [4].

Previous works extensively review the use of portable sensors. A recent review
analyzes the integration of portable sensors in clothes to obtain
physiological and motion information [5]. However, inertial sensors are not
considered in the analysis, in spite of their frequent use in this field.
Reviews that take into account the use of inertial sensors are focused on
applications, such as sign languages or motion analysis [6, 3]. Works about
the inertial motion analysis, as [3], address the motion monitoring and
kinematic feature extraction, but only considering the specific area of sport-
related exercises evaluation and their analysis is up to April $2017$. A
lower-limb focused study is carried out in [7], but it does not provide a
complete overview of the literature on inertial motion analysis. For the best
of our knowledge, the last in-depth and generic systematic review on inertial
sensors for human motion analysis is reported in [4], published in $2016$.
Since the number of publications about human motion analysis increases over
time, as shown in Fig. 1, we consider there is a need to update the literature
review on this topic. According to Fig. 1, the number of existing publications
on the inertial motion analysis field has considerably increased since the
previous review was published [4].

Figure 1: Number of publications focused on the inertial motion analysis,
referred to obtaining kinematic parameters by using portable inertial sensors,
found in the literature.

Furthermore, during the last years, Machine Learning (ML) methods have arisen
and they have been applied to the inertial motion analysis. Consequently, it
is required an update to provide an overview of the algorithms analyzed in
[4], as the Kalman filters, complementary filters, integration, vector
observation and others, but in combination with the novel ML-based approaches.

For these reasons, the main aim of this work is to review the current state of
inertial sensors for human monitoring, especially considering the occurrence
and evolution of ML methods for this research field. Another objective of this
work is to analyze the current trends and provide insights into inertial
motion analysis. To do so, we review the published works on human motion
analysis using IMUs and analyze the selected ones in terms of: _1)_ publisher
and years, _2)_ sensors used, _3)_ type of estimations referred to the
dimensions of the estimated magnitudes, _4)_ the aimed applications of the
proposals, _5)_ the monitored motion units, _6)_ the algorithmic approaches,
with an in-depth analysis of sensor fusion filters, data science algorithms
and the approaches for error reduction, _7)_ the study participants and _8)_
the validation systems and metrics. Finally, on the basis of the findings, we
suggest future research directions.

The rest of this document is structured as follows: Section II describes the
search strategy and the eligibility criteria applied in this work; Section III
details and analyzes the findings according to the terms explained above;
Section IV discusses the general trends of the studied works and analyzes the
future directions; and finally, Section V summarizes the main contributions of
this work.

##  II Materials and Methods

In this section, we describe the workflow to search and select the works in
the state-of-the-art included in this review. We describe the paper screening
process and analyze the common publishers of this field. Finally, we detail
the data extracted from them for the further analysis.

###  II-A Eligibility Criteria

This review focuses on peer-reviewed articles, book chapters and conference
papers. Papers are required to be published in English and describe the
methodology employed to obtain human kinematic parameters using only IMUs.
Sensor fusion with other devices is not considered. This review only includes
those papers that validate their results using a reference system. If a
journal paper is an extended version of a conference one, only the journal
paper is included.

###  II-B Literature Search Strategy

Considering the eligibility criteria, we select eight databases (ACM Digital
Library, IEEE Xplore, PubMed, Science Direct, Scopus, Taylor & Francis Online,
Web of Science and Wiley Online Library) for the search of related papers, see
Table I. Following the strategy of the previous review [4] about this topic,
we use the same search command, which consists in:

_(“human motion” OR “human movement”) AND (“wearable sensors” OR “inertial
sensors” OR “wearable system”)_ ,

considering their presence in the title, abstract or keywords. The search
includes journals, book chapters or conference proceedings. The paper abstract
is required to be available during this search. No restriction was imposed on
the date of publications.

TABLE I: Databases consulted in the literature search Database | Source | # papers
---|---|---
ACM Digital Library | dl.acm.org | $17$
IEEE Xplore | ieeexplore.ieee.org | $145$
PubMed | www.ncbi.nlm.nih.gov/pubmed | $188$
ScienceDirect | www.sciencedirect.com | $115$
Scopus | www.scopus.com/ | $1434$
Taylor & Francis Online | www.tandfonline.com | $2$
Web of Science | webofknowledge.com | $326$
Wiley Online Library | onlinelibrary.wiley.com | $21$

The initial search on the databases in Table I leads to a review of $2\,248$
papers. The papers found in this search do not include important references
from the state-of-the-art, as [8] or [9], so we expand the search. The new
search is only performed in the Scopus website, since it is the largest
database of all those evaluated (see Table I). In this case, we use the
following command, which is less restrictive than the previous one:

_((“human motion” OR “human movement” OR “joint kinematics” OR “body tracking”
OR kinematic* OR “joint angle*” OR “joint angle velocity” OR “joint angle
acceleration”) AND (imu OR “inertial sensors” OR “inertial measurement unit”
OR accelerometer OR gyroscope OR magnetometer ))_.

The search criteria is to find these key phrases in the title, abstract or
keywords of articles. This second search adds $1\,882$ documents, so we
finally obtain $4\,130$ papers to review.

Starting from the results of this search, we carry out a Preferred Reporting
Items for Systematic reviews and Meta-Analyses (PRISMA) screening process [10]
to determine the documents included in this study. Fig. 2 depicts the
processes of identification and screening to determine the works included in
this review.

Figure 2: PRISMA search strategy flowchart.

After excluding duplicated citations, the number of documents to screen is
reduced to $3\,775$ papers. The results of this search include works in the
field of human motion analysis with IMUs. However, this IMU-based motion
analysis covers a wide range of topics, such as the estimation of kinematic
and spatio-temporal parameters or the motion-based evaluation of health, as
depicted in Fig. 3.

Figure 3: Distribution of the publications related to human motion analysis
and IMUs, sorted by the semantic information obtained. This work focuses on
the topic included in the left square of the lower row: kinematic parameters
with magneto-inertial measurements.

The topics of kinematic and spatio-temporal parameters refer to the analysis
of different motion magnitudes, such as joint angles, trajectory or speed;
whereas the human body calibration includes the location of joints or the
estimation of segment lengths. The last two topics, human monitoring and
motion-based evaluation, are focused on qualitative analysis, such as
recognizing types of motions or activities and identifying behavior patterns.
Our study is focused on wearable inertial sensors and kinematic parameters as
joint rotation angles, so we discard by abstract reading those works that are
focused on any other topic. In this way, we exclude $3\,262$ papers for not
being related with the topic of this review.

We found $513$ potentially relevant studies of this topic for quality
assessment. To consider a study in this review, we set the inclusion criteria
detailed in Fig. 2, which are referred to the proposed or applied algorithm,
its validation and the sensor system used. Finally, $147$ studies meet the
inclusion criteria and are analyzed in this review.

###  II-C Publisher and Years

Most reviewed works are journal papers ($72.1$ %) (see Fig. 4-top). These
works are published in $42$ journals. The $56.7$ % of them appear in $7$
journals (each of them with at least four papers), as shown in Fig. 4-bottom.
The journals that appear with the highest frequency in this search are
_Sensors_ , _IEEE Sensors Journal_ (IEEE SJ), _IEEE Transactions on Biomedical
Engineering_ (IEEE TBE), _Journal of Biomechanics_ (JBiomech), _Gait &
Posture_ (G&P), _IEEE Transactions on Instrumentation and Measurement_ (IEEE
TIM) and _IEEE Journal of Biomedical and Health Informatics_ (IEEE JBHI). The
remaining $43.3$ % of works are distributed in $35$ journals.

Figure 4: Distribution of the papers with respect to the type of publication
environment in which they were published. Top: conference and journals
distribution. Bottom: journals that published the analyzed works.

There is a clear increasing interest in the research field of inertial motion
capture (see Fig. 1). This review is not restricted to any date in order to
analyze all the works related to this topic and provide a general overview and
its evolution. Fig. 1 shows the number of papers published during the 5-year
periods from $1991$ until August $2022$. Only $2$ works are dated on the first
studied decade, $21$ works on the second one and $98$ works on the third one.
There are also $27$ works published in the period $2021$-$2022$, the last
years studied in this review.

Figure 5: Year of publication of the reviewed papers. Top: trend since the
first motion analysis related work until nowadays. Bottom: distribution of
publications in last 5-year period.

Since $2016$, the last year studied in [4], the number of publications has
highly (see Fig. 5). These figures support the need for an update of a
systematic review on the research topic of human motion analysis by using
IMUs.

###  II-D Data Extraction, Analysis and Examination

We categorize the selected papers in terms of a set of relevant details. We
classify them into two groups in order to ease the study and its reading.
Firstly, we evaluate the details related with the implemented algorithms, the
sensors in use and the estimations. And secondly, we study the specific
anatomic part of the human body studied in each work, the validation system
and metrics used, and the information related to the validation subjects.

Regarding the first set of details, we analyze the following parameters: the
fusion algorithm (FA) implemented for the motion analysis, that indicates with
“SF” if the work uses sensor fusion approaches, as “ML” the application of ML
techniques and with “OA” any other proposal; the use of biomechanical
constraints (BC) and their related requirements of anatomical information
(ANT), as the segment lengths or the joint location with respect to the IMU
sensors; the implementation of other corrections (OC); the type of sensor used
to measure the motions (GS: gyroscope sensor, AS: accelerometer sensor, MS:
magnetometer sensor) and the use of external sensors to train ML-based
algorithms, but not in the motion prediction (OS); the type of estimation
(EST), considering the possible planar (2D) or three-dimensional (3D)
estimations; the measured magnitude (ANG: angle, or DIS: displacement referred
to the change in the position of the corresponding point, i.e. the sensor or
the monitoring joint) and the monitored motion unit (JNT: joint, or SGM:
segment). These details are shown in Table LABEL:tab:alg+sens+est in Appendix
A for the selected papers.

With respect to the the human body part, we study the lower-group (LG) or
upper-group (UG) of segments and joints. We also report the validation system
(VS) used as _ground truth_ in the studied works and the metrics (RMSE: root
mean square error; nRMSE: normalized RMSE; %RMSE: percentage of RMSE; MAE:
mean absolute error; AE: average error; CFC: correlation coefficient; LAM:
limits of agreement; MV: maximum variation; Accuracy; and Error rate), labeled
as M1 and M2 in Table LABEL:tab:part+validation+subjects in Appendix A,
employed in the proposed methods. Finally, we provide the number of subjects
(NS) studied and if this population considered presents a motor-related
disease (DSS). Table LABEL:tab:part+validation+subjects includes the details
of these parameters above explained in the selected papers.

##  III Review findings

Based on the categorization of the papers with respect to their relevant
characteristics, presented in Table LABEL:tab:alg+sens+est and Table
LABEL:tab:part+validation+subjects, in this section we describe the main
findings.

###  III-A Sensors

IMUs contain tri-axial gyroscopes, accelerometers and, commonly,
magnetometers. The information from these sensors are used separately through
the observation of vectors, as gravity in the accelerometer data or the
magnetic field in magnetometers, or by integration of the gyroscope data.
Another approach is to gather their measurements in different combinations of
two or three sensors with different algorithms, as sensor fusion filters or ML
methods. In order to illustrate the proportion of their utilization,
separately or fused, Fig. 6 shows the percentage of use of each sensor or
combination.

Figure 6: Sensor type and combination used in the analyzed works (AS:
accelerometer sensor; GS: gyroscope sensor; MS: magnetometer sensor).

The integration of the turn rate alone entails inherent errors. In the
estimations of kinematic parameters, the turn rate integration results in an
accumulated error from the gyroscope bias. For that reason, only $4.8$ % of
studies use this sensor alone [11, 12, 13, 14, 15, 16, 17].

Accelerometers are more frequently used separately ($8.8$ %). Their
measurement of specific force allows us to obtain a direct observation of the
gravity vector, used as orientation reference [18, 19, 20, 21, 22, 23, 24, 25,
26, 27, 28, 29, 30]. However, the direct observation of the gravity vector is
only possible when accelerometers are static, as in gait strides during the
stance phase.

Magnetometers are the most limited sensor analyzed because of their
sensitivity to magnetic disturbances in the environment. As a consequence,
only a $1.4$ % of studies use this sensor independently [31, 32].

Sensor fusion techniques are useful methods to overcome the individual
limitations of each of them separately. Most of studies that fuse data from
various sensors combine gyroscopes and accelerometers [33, 34, 35, 36, 37, 38,
39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57,
58, 59, 60, 61, 46, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75,
76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94,
95, 96, 8, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110,
111, 112, 113, 114, 115] or both sensors with magnetometers [116, 117, 118,
119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133,
134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148,
149, 150, 151, 152]. Few studies join the accelerometer and magnetometer data
[153, 154] and only one uses the gyroscope and magnetometer data [155].

The 3D position of devices can be inferred from the IMU sensors information.
The combination of the three sensors, gyroscope, magnetometer and
accelerometer includes information of the angular rate of motion and the
references of the vector gravity and Earth magnetic field references. However,
these 3D positions can also be estimated by sensor fusion techniques using
different combinations of the three sensors in IMUs. Most studies give 3D
estimations ($71.4$ %), as shown in Fig. 7. Conversely, only $1.4$ % of works
use accelerometers and magnetometers and $25.2$ % both sensors complemented
with gyroscopes (see Fig. 6). This fact is noticeable because the combination
of the first two sensors is required to obtain the references to overcome the
gyroscope drift and get accurate 3D estimations. It implies that the majority
of algorithms that offer 3D space predictions propose methods for error
reduction that do not rely on vector references. In this way, the magnetic
disturbances that cause errors in the magnetic field measurements are avoided.

Figure 7: Type of estimations in term of their dimensionality, divided between
2D and 3D estimations.

The 2D estimations include kinematic parameters in any plane perpendicular to
the floor and the two angles with respect to the horizontal plane, in the
frontal and sagittal planes. No doubt the 3D estimations are more complete
since they provide information about the whole motion, even if it is mostly
performed in one plane. That is the reason why only $27.9$ % of studies focus
on obtaining estimations in the $2$D space.

Only one study adapts the estimation to 3D or 2D spaces, according to the
motions [41]. In this proposal, the method gives 2D estimations based on the
accelerometer data when the motion is mostly performed in one plane. If
deviations from this plane are detected, the method integrates the gyroscope
data in order to provide 3D estimations.

###  III-B Application

Healthcare applications are the most common ones ($95.2$ %) in the inertial
motion analysis field (see Fig. 8). These applications include motion capture
or analysis, gait and clinical assessment, or rehabilitation. The aim of
$33.5$ % of studies is the motion capture in order to obtain information about
human kinematics for the motion analysis or find possible diseases. Gait is
the second most common application ($19.1$ %) due to its relationship with
cognitive impairments. The prevalence of use for the specific clinical
assessment is similar, being the aim of the $14.5$ % of works. Rehabilitation
and sports are also worth mentioning because they are very motivating in
research works ($19.6$ % of studies).

Figure 8: Analysis of the application of the studied works. Left: percentage
of proposals whose aimed field is included in healthcare-related applications.
Right: specific application or applications considered in proposals. Some
works provide possible uses of their proposals, others focus on a specific
application, such as gait, and others refer to the general motion capture
field. FES refers to functional electrical stimulation and the research of
human-robot interactions (HRI) is labeled as “Human-robot”.

###  III-C Monitored Motion Unit

We analyze the anatomical unit measured in the reviewed works. In this work,
the anatomical units are called monitored motion units following the
nomenclature of previous studies [4]. We divide these monitored motion units
into two groups: segments and joints. Segments usually correspond to elements
of the skeletal system, such as thighs (femur), and are modeled as a rigid-
solid bodies. Joints are the unions between segments. The objective of $64.6$
% of studies is to measure the motion of joints, whereas the $27.2$ % of
proposals focus on tracking segments and the remaining $8.2$ % combine the
monitoring of both monitored motions, segments and joints, as shown in Fig.
9-top.

Figure 9: Monitored motion units and the obtained measurement. Top: percentage
of studies that measure each motion unit or their combination. Bottom: type of
measurement, orientation and location.

Studies focus more frequently on the lower-half ($61.2$ %) of the body than on
than upper-half ($34.7$ %). Compared to the outcomes in the review of Lopez-
Nava [4], this trend is in the most recent works different than in the
previous ones. We found that recent research, dated on the last three years,
extend motion analysis to full-body monitoring, which is an important
difference with the findings of previous sudies [4]. We consider full body if
both upper-and lower-halves are monitored, which is made in the $4.1$ % of
studies. Fig. 10-left depicts the percentage of works that monitor each body
half or the full body.

Figure 10: Anatomical monitored units. Left: location of the monitored units
in the upper-or lower-half part of the body. Right: number of papers per
combination of segments and/or joints monitored.

We study the groups of segments or joints included in each body half for a
deeper analysis. We define the groups as sets of monitoring units. We consider
that studies focus on one of the groups if they estimate the orientation or
location of one of the included monitored units. For example, one study that
tracks the motion of wrists is included in the hand group, since we establish
that the hand group includes the wrist among other motion units.

With respect to the upper-half of the body, we divide it into hand (hand,
wrist and fingers), arm segments (arm and forearm), arm joints (shoulder,
elbow and forearm twist), trunk (back, trunk and torso) and head and upper
back (head/neck/scapula). The upper-half groups ($51$ works) are named as
follows: arm segments (U1), trunk (U2), arm joints and hand (U3), head and
upper back, trunk, arm segments and arm joints (U4), arm joints (U5), head and
upper back (U6), arm segments and joints (U7), trunk, arm joints and hand
(U8), head and upper arm, trunk and arm (U9), head and upper arm and arm
joints (U10), head and upper back and trunk (U11), head and upper back and arm
segments (U12) and head and upper back alone (U13). Fig. 10-right shows the
presence of the combination of these groups in the studied works.

The arm joints group, U5, is the one on which most works are focused ($12/51$
studies), followed by the trunk ($9/51$ studies), U2. The next three frequent
groups are the arm segments ($7/51$ studies), U1, the combination of arm and
hand joints ($7/51$ studies), U3, and the head and upper back ($6/51$
studies), U6. The rest of the groups are only monitored in $1/51$ or $2/51$
studies, according to the case. In this way, research works commonly focus on
the study of the arms more than the other upper-half body structures.

With regard to the lower-half, we divide it into pelvis, leg segments (thigh
and shin), leg joints (hip/knee/ankle) and feet. The names of the groups of
their combinations are the following: leg segments and feet (L1), leg joints
(L2), leg segments (L3), leg joints and feet (L4), feet (L5), pelvis, leg
segments and leg joints (L6), leg segments and joints (L7), pelvis and leg
joints (L8) and pelvis (L9). Fig. 10-right shows the number of works focused
on each of these groups (the total number of works is $90$).

In the lower-half body, it is noticeable that most of the works focus on the
leg joints, L2, is the object of monitoring of most works ($63/90$ studies).
These joints are commonly studied in multiple applications, being the most
important the gait analysis because of its relevance in health assessment. It
is worth mentioning the contrast of the number of studies about the L2 group
in comparison with the L4 group, that combines the leg joints with the feet,
meaning that the motion of feet joints is commonly discarded in the studies
focused on the lower-limb joints. Beside the leg joints, the following most
studied groups that are also focused on legs are: leg segments, L3 ($8/90$
studies), leg segments and joints, L7 ($7/90$ studies) and leg segments and
feet, L1 ($5/90$ studies). The rest of the groups, that include leg joints and
feet (L4), feet (L5), pelvis, leg segments and leg joints (L6) and pelvis (L9)
are studied in few works ($2/90$ studies).

The monitored units in these groups are measured regarding their orientation
or location. Orientation refers to the rotation angles, which are commonly
presented as Euler angles or quaternions. Locations refer to the spatial
coordinates, so they are a measurement of distance. Most of studies estimate
the orientation of monitored units ($81.6$ %), the $15.6$ % give a combination
of orientation and location of units and only the $2.7$ % are focused only on
providing locations. Fig. 9 shows the distribution of the measured magnitudes.

###  III-D Adopted Algorithms

The algorithms used in the estimation of the kinematic parameters can be
separated into five different groups: integration, vector observation, sensor
fusion filters, ML techniques and other methods.

####  III-D1 Sensor fusion filters

Sensor fusion filters (SF in Table LABEL:tab:alg+sens+est), including Kalman
Filters (KF), particle filters (PF), and Complementary Filters (CF) are the
algorithms most frequently used. Specifically, KFs are still the algorithms
that are employed the most in the inertial human motion analysis field,
following the trend reported in previous studies [4].

The problem formulation of Bayesian filters consists in the identification of
the desirable estimations using a series of measurements observed over time
containing statistical noise and different inaccuracies [156]. The inputs and
observations form the knowledge on the system’s behavior and both convey
errors and uncertainties, namely: the measurement noise and the system errors.
These filters fuse the information of sensors with the knowledge of the system
in two stages: the estimation stage and the update stage. The initial stage
uses the information of the previous time instant to estimate the current
state of the state vector. The second stage updates these estimations using
the measurements from the sensors.

The motion analysis includes proposals with Extended Kalman filter (EKF), KF
and _Unscented_ Kalman filter (UKF), in descending order of frequency of use.
KF is a sensor fusion technique that estimates the states of a linear system
through the minimization of the variance of the estimation error [156]. KFs
use a series of measurements observed over time and their statistical noise to
produce estimates of unknown variables. EKFs appeared because KFs are limited
to linear systems, being their generalization to non-linear systems. EKFs
assume that the non-linearities in the dynamic and the observation model are
smooth, so they expand the state and observation functions in Taylor series
and approximate in this way the next estimate of the state vector. However,
this approximation can introduce large errors in the true posterior mean and
covariance of the variables, which may lead to the divergence of the filter.
One of the possible solutions is the use of UKFs, whose distribution of their
state vector is a set of sample points called _sigma points_. Sigma points
capture the actual mean and covariance of the Gaussian random variables and
are obtained though the _Unscented Transformation_ (UT). The UT is a method
for calculating the statistics of a random variable that suffers a nonlinear
transformation. UKFs are an extension of UTs to the recursive estimation where
the UT is applied to the augmented state vector.

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

Classical KFs are normally used for the sensor fusion of gyroscope and
accelerometer data to estimate the segment orientation [33, 40, 43, 50, 52,
57, 97, 139], the joint orientation [44, 82, 95, 98, 85], the segment location
[74], and all of them, the segment and joint orientation and location [42].
KFs have also been used in the fusion of gyroscope, accelerometer and
magnetometer data to estimate segments orientation and location [136, 152].

UKFs appear less frequently in the literature. UKFs are commonly used for the
sensor fusion of gyroscopes, accelerometers and magnetometers to estimate the
joints location [137], or orientation [130, 149], the orientation of joints
and segments [131], and the orientation and location of both elements, joints
and segments [121]. Some works do not use the magnetometer information and
only fuse the gyroscope and accelerometer data to estimate joints orientation
[106, 99].

PFs are another modification of KFs for their use in non-linear systems [156].
PFs are close in functioning to UKFs but with a set of differences that
approximates PFs to a generalization of UKFs. PFs update the estimations with
a randomly generated noise according to the _prior_ knowledge of the process
noise Probability Density Function (PDF) instead of the update of the UKF that
is deterministic. Another difference with UKFs is that the number of particles
in PFs is not related to the length of the state vector. Finally, PFs
estimates the PDF of the state instead of the mean and covariance, and it
converges to the actual PDF as the number of particles increases.

PFs are less popular than any other kind of KFs. PFs are applied to fuse the
measurements from gyroscopes, accelerometers and magnetometers to estimate the
orientation of segments and joints [125]. PFs are combined with other KFs,
such as EKFs, for the fusion of gyroscope and accelerometers measurements to
estimate the orientation of segments [94].

CFs combine the information from different sensors by minimizing the mean-
square-error instead the error covariance, which is minimized in KFs [157].
CFs are used to fuse the measurements of gyroscopes, accelerometers and
magnetometers to estimate the orientation of joints [123, 126, 133], their
orientation and location [119, 144], and their orientation together with the
segments orientation [143]. They are also used to estimate the joint either by
combining the information of the gyroscope and the accelerometer orientation
[45, 47, 62, 65, 101, 109], or just only with the gyroscope [11].

Another alternative to KFs is the Weighted Fourier Linear Combiner (WFLC)
filter, which is a model-based adaptive filter. WFLCs exploit the _prior_
knowledge of the signal shape and evolution over time, in those occasions when
the motion performed is given [93]. These filters are specially effective in
periodic signals but adapt to variations between repetitions. Their
applications to the human motion analysis include the use of the turn rate
measurements to estimate the segment orientation [14] and the combination of
these data from the gyroscope with the accelerometer measurements to estimate
the orientation of joints [93].

####  III-D2 Data science algorithms

ML techniques represent the second group of algorithms that is applied most
frequently for the estimation of the human kinematics. Furthermore, the
supervised learning algorithms are the most widespread in recent years.
Supervised learning is one of the most employed learning paradigm which tries
to discover the unknown function $f(\mathbf{x},\omega)$ that relates the input
space $X\subset\mathbb{R}^{n}$ (which, in this work, are the inertial
measurements), with the output space $Y\subset\mathbb{R}$ (which describes the
motion kinematics). Each pair $(\mathbf{x}_{i},{y}_{i})$ is composed of the
value of a set of $n$ predictive variables
$\mathbf{x}_{i}=(x_{1},\cdots,x_{n})_{i}\in\mathbb{R}^{n}$ of the input space,
which are measured by the IMUs, and its corresponding output value
$y_{i}\in\mathbb{R}$, which are the target value of joint or segment
orientation and location. During the process called _training_ , supervised
algorithms retrieve the map $f\in F$ from the provided training dataset
$\mathcal{D}$, typically establishing an optimization problem that minimizes a
_loss function_ $\mathcal{L}$. Different parametric function spaces $F$ with
different learning methods correspond to the existent variety of supervised
methods, as described in depth in Table II.

Gaussian Processes (GPs) are kernel-based probabilistic ML models. The
Gaussian process is a kind of continuous random process $f(t)$, such that
every finite set of random variables has a multivariate Gaussian distribution
[158]. GP method estimates the output $y$ by introducing a set of latent
variables $\\{f(t_{k})\\}_{k=1}^{n}$ from a Gaussian process, and explicit
link functions, $g(\cdot)$. Gaussian Process Latent Variable (GPLV) models are
used with the gyroscope and accelerometer data to estimate the segment
positions [58].

Other classical ML methods are Decision Trees (DTs) and Support Vector
Machines (SVMs). A DT is a classical ML method that builds a tree, a
particular graph without cycles, by branching decision paths for each
considered input variable to make the final classification [159]. During the
training process, databases are used to compute thresholds (the parameters in
DTs) that better branch the input variable for optimizing a criterion, usually
the best gain of information possible in the current node (optimizing the
entropy), for a better prediction of the output variable.

SVMs are one of the most used ML method for classification [160, 161]. It
establishes an optimization problem to find the so-called support vectors,
those training data which are close to the separation hyperplane and maximize
the soft margin. Frequently, this method uses the kernel trick which consists
in choosing an appropriate non-linear mapping $\boldsymbol{\phi}$ that maps
input samples into a higher dimensional space where they are likely to be
linearly separable. In regression problems, the support vectors are used to
provide a continuous value trough a link function instead of classes.

However, these classical ML methods are less promising than artificial Neural
Networks (ANNs) in the human motion analysis field, as proved in [109] for the
correction of the joint angles initially obtained from sensor fusion filters.
ANNs consist in a set of connected base units known as artificial neurons
which emulate the biological neurons of animal brains [162]. ANNs are usually
organized in layers which interconnect themselves to create a huge variety of
networks that try to represent the functional relation between the input and
output variables. ANNs have revolutionized the ML field due to their ability
to model very complex non-linear input-output relations and their capacity to
learn them from a huge amount of data. The single Multi-Layer Perceptrons
(MLP) were the first ANNs.

In the inertial motion capture field, ANNs use the accelerometer data as
inputs to estimate the segments orientation and location [27], combine the
gyroscope and accelerometer data to estimate joint orientations [68, 71, 84,
91] or fuse the information of the three sensors integrated in IMUs to
estimate the segment angles [147]. Other specific types of ANNs merge the
estimation of joint angles with gyroscopes and accelerometers, such as the
general regression NNs [90, 49] or the Elman Neural Networks [115].

Deep Neural Networks (DNNs) arise later than ANNs, and encompass a huge amount
of modern network architectures with a high number of interconnected layers
[163]. The current technology allows massive computation during the training
process, hence, new variety of interconnections and predictions in real time.
DNNs starts with the Convolutional Neural Networks (CNNs), a large sequence of
convolutional layers configured in cascade where each layer computes the
convolution operation (see [164]) from the previous one. They are able to
extract intrinsic local features, the called deep features, which surpass the
results of the classical ML methods. VGG [165] and Residual Networks (RESNET)
[166] are famous CNNs included in this category. Most of DNNs including CNNs
are feed-forward networks which means that the information flows forward and
they do not include cycles. However, DNNs also include recurrent networks
which memorize internal states, frequently exploited for temporal sequence,
such as the improved Recurrent Neural Network (RNN) [167], which evolved to
the novel Long-Short Term-Memory (LSTM) [168], Gate Recurrent Unit (GRU) [169]
and nonlinear autoregressive neural network with exogenous inputs (NARX)
[170].

Among the deep learning algorithms, LSTMs are the most utilized. LSTMs are
made by a sequence of cells capable to keep previous states, specifically keep
two kind of temporal information, the long and short-term memory. They have
replaced the RNNs which suffer from the vanishing gradient problem during the
training and include forget gates to quickly adapt to the new changes of data.
These DNNs can use just the information of accelerometers and the orientation
of a set of body segments to estimate the whole-body posture [29] or fuse the
information of specific force with the turn rate to estimate the joint angles
[53, 86, 103, 69]. A less common approach includes the fusion of gyroscopes
and magnetometers to estimate the joint angles [155]. LSTMs can also be used
to estimate the orientation of the whole-body joints using the orientation
obtained with sparse commercial sensors [148]. In [69], LSTMs are combined
with CNN to estimate the joint angles. CNNs are also used to obtain the joint
angles only using the accelerometer data [21] or fusing the gyroscope and
accelerometer data [56, 111, 114]. In [34], Mundt et al. made a comparison of
these previous methods, CNNs and LSTMs, together with MLPs for the estimation
of joint orientation. Using the information of gyroscopes and accelerometers,
CNNs provided the most favorable metrics. Other RNNs are also used to estimate
the joints orientation. To estimate the joint angles from gyroscopes and
accelerometers, [54] proposes a NARX; and [134] also includes the magnetometer
data with NARX and LSTMs.

The ML-based algorithms that are used for human motion analysis are supervised
methods. These methods need training data, which must include reference data
of the parameter to estimate, i.e. the joint or segment orientation or
location. In this review, we found 26 works that use reference data, that can
be obtained from a stereophotogrammetric system (17/26) [90, 49, 58, 53, 21,
56, 27, 68, 91, 69, 86, 103, 34, 54, 111, 114, 115], electro-goniometer and
encoders (2/26) [84, 71] or inertial sensors (7/26) [147, 109, 29, 148, 134,
100, 155]. Fig. 11 shows the percentage of use of the different external
sensors for obtaining reference data.

Figure 11: External sensors used to obtain the reference measurements for the
training and test stages of the ML algorithms.

The use of optical systems also allows the data generation in order to have
data for the training and test of the algorithms and to increase the available
data to train the models. These tasks can be performed with simulation
software, e.g. OpenSim [171], as in [148, 86, 103], by applying kinematic
relationships from the stereophotogrammetric measurements, as in [19, 53, 56,
69, 103, 68, 91], or with data augmentation techniques [68]

TABLE II: Outcomes of the analysis of inputs used in the ML algorithms, algorithms applied in each work, and outputs aimed as targets with the capture system employed. SF : specific force, TR: turn rate, OR: orientation, Cap.: capture, SNN: Shallow Neural Network, DNN: Deep Neural Network, vs.: _versus_ Work | Inputs | Specifications of inputs | Algorithm | Outputs
---|---|---|---|---
SF | TR | OR | Magnitudes | Cap. system
[90] | ✓ | ✓ |  | Time instant | GRNN | Joint angle | Optical
[49] | ✓ | ✓ |  | Time instant |  | GRNN
---
Aux. Sim. Info.
Joint angle | Optical
[84] | ✓ | ✓ |  | Time instant | ANN | Joint angle | Other
[58] | ✓ | ✓ |  | Sparse IMUs | GPLVM | Whole-body posture | Optical
[147] | ✓ |  | ✓ |  | Sparse IMUs
---
$5$ samples ($0.55$ s) windows
SNN & DNN |  | Segment location
---
Whole-body posture
Inertial
[109] |  | ✓ | ✓ | Joint angle from Bayesian filters |  | NN (vs.)
---
SVM (vs.)
DT
Joint angle | Inertial
[53] | ✓ | ✓ |  |  | Simulated inertial data
---
Different IMU combination + PCA
From $100$ to $1000$ time-steps
LSTM | Joint angle | Optical
[21] | ✓ |  |  |  |  $600$ ms windows
---
Sparse IMUs for leg kinematics
1D-CNN | Joint angle | Optical
[56] | ✓ | ✓ |  |  | Experimental and simulated data combined
---
$100$ time-steps for each walking cycle
CNN |  | Joint angle
---
Joint moment
GRF
Optical
[27] | ✓ | ✓ |  | Time instant | ANN |  | Joint angle
---
Joint moment
GRF
Optical
[68] | ✓ | ✓ |  |  | Simulation of IMUs
---
Data augmentation
$10$ frames windows
Full gait cycles
ANN |  | Joint angle
---
Joint moment
Optical
[91] | ✓ | ✓ |  |  | Simulated inertial data
---
Segmentation into gait cycles
ANN |  | Joint angle
---
Joint moment
Optical
[29] | ✓ |  | ✓/✗ |  | Sparse IMUs
---
Window of $50$ samples $=$ $0.50$ s
LSTM | Whole-body posture | Inertial
[69] | ✓ | ✓ |  |  | Simulated inertial data
---
Calibration for alignment
Marker trajectories filtered
$1$ s & $2$ s windows
| 1D-CNN (vs.)
---
LSTM
& Optimizer
| Joint angle
---
time series
Optical
[86] | ✓ | ✓ |  |  $100$ samples ($100$ Hz) windows |  | CNN
---
LSTM
| Joint angle
---
time series
Optical
[103] | ✓ | ✓ |  |  | Experimentally measured IMU data,
---
Simulated inertial data
$200$ time-steps
Time wrapping of strides as inputs
LSTM |  | Joint angle
---
time series
Optical
[155] | ✓ | ✓ |  |  | Sparse IMUs
---
Synthetic and experimental data
$300$ frames windows
LSTM |  | Joint angle
---
time series
Whole-body posture
Inertial
[148] |  |  | ✓ |  | IK outputs as biRNN inputs
---
+Joint parmeter
Sparse IMUs
$300$ time-steps windows
LSTM | Whole-body posture | Inertial
[53] | ✓ | ✓ |  |  | Experimental and simulated data
---
$101$ frames windows
| MLP
---
LSTM
CNN
| Joint angle
---
time series
Optical
[71] | ✓ | ✓ | ✓ | Time instant | ANN |  | Joint angle
---
Walking speed
Other
[54] | ✓ | ✓ |  | Time instant |  | NARX (vs.)
---
CF
Segment angle | Optical
[134] | ✓ | ✓ | ✓ |  | Sparse IMUs for leg kinematics
---
Gait cycle segmentation
| NARX
---
LSTM
Joint angle | Inertial
[100] | ✓ | ✓ |  |  | Sparse IMUs for knee angle
---
Short intervals $0.05$ s
LSTM | Joint angle | Inertial
[111] | ✓ | ✓ |  |  | Sparse IMUs for leg kinematics
---
Evaluation of classifier combinations
| CNN
---
RNN
| Joint angle
---
time series
Optical
[114] | ✓ | ✓ | ✓ |  | Initial gyro integration for joint orientation estimation
---
Elman NN | Joint position | Optical
[115] | ✓ | ✓ |  | Gait variations | LSTM |  | Joint angle
---
time series
Optical

####  III-D3 Other algorithms

Over the years of research on motion analysis with inertial sensors, proposals
have been based on various algorithms other than sensory fusion filters and
data science methods. These proposals cover from the integration of the
gyroscope data to estimate the joint orientation [12, 15, 16, 17, 41], to its
combination with the direct use of the data from accelerometers to estimate
the orientation of joints [104, 105, 80] and segments [59, 60, 81, 63], and to
estimate the orientation and location of segments [110, 112]. The measurements
from gyroscopes and accelerometers are also used directly to obtain the
orientation and location of joints [35] and segments [46], and to estimate the
orientation of both joints and segments [48, 51, 113]. The information of the
three sensors in the IMU are also directly used for the estimation of the
segments orientation [141].

Different works exploit the observation of the gravity vector by the
accelerometer for the estimation of the orientation of joints [24, 30, 22, 61,
18], segments [28] or both [20]. Other works also use the data of the
magnetometer to estimate thee joint orientation and location [31], or combine
this information with the measurements of accelerometers to obtain the joint
orientation [153]. The gravity vector can also be observed by eliminating of
the linear acceleration of the motions, which can be estimated from the turn
rate measurements [73].

Besides the gyroscope integration and the direct observation of vectors, the
measurements from IMU sensors can be combined through the use of virtual
sensors. The use of virtual sensors consists in the estimation of the
measurements that a sensor would obtain if it was located in the joint. This
measurement projection is commonly performed because it is not possible to
place the sensors in the joints. This is commonly used to simulate the
measurements in joints whereas the IMUs are placed in segments. This approach
is used to combine the gyroscope and accelerometer measurements to estimate
only the joint orientation [37, 46, 83], or both the joint orientation and
location [89]. Another application of virtual sensors is to combine the turn
rate, specific force and magnetic field to obtain these magnitudes in joints
to estimate their orientation [129, 150, 151, 132] and also not considering
the measurements from gyroscope for the joint orientation estimation [154].

Another common method used is the gradient descent. Gradient descent is
applied to obtain the joint orientation by using the measurements from
gyroscopes [13] and combined with the specific force measurements [39, 102,
64]. This approach also allows the gathering of the measurements of the three
sensors to estimate the segment orientation [116].

The remaining proposals use a wide variety of methods and approaches to
monitor the measurement units. These methods include probabilistic graphical
models [122], which are employed with the gyroscope, accelerometer and
magnetometer measurements to estimate the orientation of joints, smoothing
algorithms [36], bidirectional low-pass filters [19], least squares [75, 87],
optimization techniques [67, 25, 107] and modified iterative algorithms [23].
The latest worth mentioning approach consists in the double-sensor difference
based algorithm [26], that combines the measurements from two accelerometers
placed on the same segment with the knowledge of their positions with respect
to the joint.

####  III-D4 Approaches for error reduction

This section describes the main approaches found in the literature in order to
reduce the errors in the estimation of kinematic parameters. First, we focus
on the explanation of the proposals based on biomechanical constraints and
then we summarize the approaches for error reduction based on the properties
of the inertial sensors and their motions.

Biomechanical constraints are a promising resource to improve the inertial
human motion analysis. A common approach is to model the rotations of
different joints with different Degrees Of Freedom (DOF), which are depicted
with cylinders in the geometrical model in Fig. 12. The three rotational DOF
recorded by IMUs can be modeled as one or two DOF joints, according to the
possible anatomical motions.

In the literature, the knee is assumed to be a hinge joint with just one DOF
(flex-extension, see Fig. 12) [39, 45, 130, 62, 135, 136, 71, 80, 88, 96, 8,
101, 87, 151, 55] because its internal rotation allows a negligible Range Of
Motion (ROM). Some works also consider the knee internal rotation together
with its flex-extension, so the modeled joint presents two DOF [82]. The same
approach can be used to simplify the ankle orientation estimation, using only
the knee-flex extension rotation, so one DOF [136] or also including the
internal rotation, resulting in two DOF [55], as Fig. 12 depicts. Less
commonly used due to its actual DOF and complexity, hips are modeled as joints
with two DOF [101, 151].

Figure 12: Scheme of the biomechanical constraints commonly implemented in the
kinematic models for the inertial motion analysis. It includes the geometrical
model with a reduced number of DOF in the knee and ankle joints and the
limitations with respect to the ROM, using the knee as example. The lengths
and IMU-joint vector used in the soft constraints are labeled as $d_{S}$,
$d_{T}$ and $\boldsymbol{r}_{i}$ with $i=0,1,2$, respectively.

This DOF reduction can be also applied to upper-limbs. Elbows can be assumed
to have only two DOF, gathering the elbow flex-extension rotation and the
forearm internal-external rotation [98, 99, 149, 150, 106, 13, 121, 122, 143,
55] or considering only the elbow flex-extension [125]. Wrist can be also
modeled as one DOF joint [121, 122] or allowing a second rotation with two DOF
[150].

Another approach related with the simplification of motions to a lower amount
of DOF is to model the motions as if they occur in one or two planes. This
approach reduces the $3$D space in, at least, one dimension. Different
motions, such as gait or squats, can be approximated as $2$D in the sagittal
plane [134, 105, 109] or with the combination of the sagittal and coronal
planes [97, 52].

The separation of motions in the DOF available for the joints allows another
restriction based on the joint anatomical ROM. This constraint is based on the
correction of the estimations that are not consistent with the anatomically
possible ROM per DOF of joints. As depicted in Fig. 12, the ROM of a joint, in
this case the knee, includes the consistent estimations and the estimations on
the limit of the ROM. The values of angles outside this range are wrong
estimations of the algorithm and the objective is to detect and correct them.
This approach can be found in several proposals in the literature [120, 136,
79, 87, 143, 59].

Another common approach for the error reduction in most of biomechanical
models is to take into account the anatomic parameters, such as the joints
location with respect to the sensors or the segments length [35, 119, 37, 38,
129, 46, 132, 19, 20, 46, 64, 17, 73, 76, 137, 77, 138, 79, 78, 23, 83, 24,
87, 25, 26, 88, 89, 92, 93, 94, 95, 143, 96, 8, 98, 99, 105, 150, 106, 107,
108, 154, 151, 91]. Fig. 12 shows these parameters, labeled as
$\boldsymbol{r}_{i}$, where $i=0,1,2$, $d_{S}$ and $d_{T}$, respectively. The
IMU-joint vector and the segment length are used to impose that the
relationship between magnitudes has to be consistent with the anatomy of
participants and the location of sensors on the body. These constraints can be
applied by the relationship between the velocity in the common joint between
two segments and the turn rate measured by the gyroscopes of the corresponding
IMUs using Eq. (1), see Fig. 12.

$\boldsymbol{v}_{\textit{knee}}=\boldsymbol{\omega}_{\textit{IMU}_{1}}\times\boldsymbol{r}_{1}=\boldsymbol{\omega}_{\textit{IMU}_{2}}\times\boldsymbol{r}_{2}$
(1)

An alternative approach is to relate the linear acceleration suffered by the
IMUs with the linear acceleration in the common joint between segments. This
approach requires the consideration of the gravity influence from the specific
force measured by accelerometers. If the gravity influence is eliminated, Eq.
(2) can be applied with the derivation of the turn rate.

$\boldsymbol{a}_{\textit{knee}}=\boldsymbol{a}_{\textit{IMU}_{1}}+\dot{\boldsymbol{\omega}}_{\textit{IMU}_{1}}\times\boldsymbol{r}_{1}+\boldsymbol{\omega}_{\textit{IMU}_{1}}\times\left(\boldsymbol{\omega}_{\textit{IMU}_{1}}\times\boldsymbol{r}_{1}\right)=\\\
a_{\textit{IMU}_{2}}+\dot{\boldsymbol{\omega}}_{\textit{IMU}_{2}}\times\boldsymbol{r}_{2}+\boldsymbol{\omega}_{\textit{IMU}_{2}}\times\left(\boldsymbol{\omega}_{\textit{IMU}_{2}}\times\boldsymbol{r}_{2}\right)$
(2)

The IMU-joint vectors combined with the segment lengths or the joint-joint
vectors are commonly used to estimate the kinematic of chains of segments.
This is frequently performed with the Denavit-Hartenberg (D-H) notation, that
uses four angular and distance parameters to relate reference frames with the
links of spatial kinematic chains [172]. In order to apply the D-H convention,
one reference frame is defined for each DOF included in the biomechanical
model. The axes of the consecutive reference frames, $i-1$ and $i$, must
follow two rules: the xi axis must be perpendicular to zi-1 and the xi axis
must intersect with zi-1. In this way, the transformation matrix $T_{i-1,i}$
detailed in Eq. (3) defines the transformation between consecutive frames.

$T_{i-1,i}=\begin{bmatrix}\cos\theta_{i}&\text{-}\cos\beta_{i}\hskip
2.0pt\sin\theta_{i}&\sin\beta_{i}\hskip
2.0pt\sin\theta_{i}&r_{i}\cos\theta_{i}\\\ \sin\theta_{i}&\cos\beta_{i}\hskip
2.0pt\cos\theta_{i}&\text{-}\sin\beta_{i}\hskip
2.0pt\cos\theta_{i}&r_{i}\sin\theta_{i}\\\
0&\sin\beta_{i}&\cos\beta_{i}&d_{i}\\\ 0&0&0&1\end{bmatrix}$ (3)

Where $\theta_{i}$ is the angle between $x_{i-1}$ and $x_{i}$ axis, about the
$z_{i-1}$ axis and $\beta_{i}$ is the angle between $z_{i-1}$ and $z_{i}$
axis, about the $x_{i}$ axis. This transformation of consecutive frames allows
the estimation of the forward kinematics of a chain of joints by using Eq. (1)
and Eq. (2), as performed in [87, 121, 122, 74, 79].

The location of joints and the segment lengths are not imposed as the
limitation of DOF or ROM, which directly models or corrects the estimations.
However, they are used to impose constraints in the measured magnitudes. For
that reason, the restrictions forced through these conditions are commonly
known as _soft constraints_. It is worth mentioning that the errors in the
estimation of the IMU-joint vector directly influence the estimation of joint
angles that use these soft constraints [87].

Other corrections found in the literature that are not related with
biomechanical properties include the following: modeling the bias of sensors
or including them in the state vector [33, 173, 118, 36, 119, 123, 125, 44,
13, 52, 19, 57, 46, 70, 75, 139, 82, 95, 30, 117, 60, 61, 153, 62, 63, 83];
calibrating this bias [30, 46, 44, 124, 121, 97, 104, 105, 150, 133]; low-pass
filtering the recorded signals [37, 11, 41, 45, 63, 14, 145, 143, 71]; or
optimizing them [67], updating the estimations when a direct observation of
gravity is available or with its dynamic compensation [35, 43, 48, 51, 59,
140, 81, 141, 174] or the zero-angle during the zero-turn rate time instants
[11, 47, 48]; modeling the disturbances in the magnetometer and gyroscope
[118, 31]; using virtual sensors, discriminating the quasi-static and dynamic
motions [41]; eliminating the errors from the soft tissue artifacts [44, 127]
and, in the case of Kalman filters, the optimization of the Kalman parameters
[33, 50, 79].

###  III-E Participants of the study

This work also analyzes the number of subjects that participate in the studies
to validate the methods. Fig. 13-top shows the _boxplot_ of the distribution
of subjects in the studies analyzed in this work ($147$). The boxplot presents
the $1^{\text{st}}$, $2^{\text{nd}}$, $3^{\text{rd}}$ and $4^{\text{th}}$
quartile of the studied subjects together with the _outliers_. In this work,
the outliers represent the punctual studies that test their proposals in more
than $18$ subjects ($8/147$ studies). According to Fig. 13-top, most results
provided in the studies correspond to a population of less than $10$ subjects.
It is worth mentioning than the median is $3$ subjects per study, what makes
the results hardly generalizable to all population. Furthermore, more than one
third of studies test their proposals with only one person ($34.7$ %).

Figure 13: Characteristics of the population of study in the human motion
analysis literature. Top: percentage of works that evaluates their proposal in
each number of participants. Bottom: percentage of works that considers
population with (Diseased vols.) or without (Healty vols.) disease.

The studies that validate their proposal with the highest amount of volunteers
commonly test ML-based algorithms. This amount of volunteers is required by
these algorithms because they work with a high amount of data in order to
develop generalizable models. However, a $65.4$ % of these studies use the
data from the optical systems to generate simulated inertial data, as shown in
Fig. 11.

Studies analyze volunteers with or without diseases related with the motor
system. We assume that if there is no statement about whether unhealthy people
is included, the studied population is healthy or with no illness that affects
the performance of motions. In this way, only a small percentage ($8.2$ %) of
proposals are tested on population with these motor limitations (see Fig.
13-bottom). This is remarkable since most proposals claim healthcare
applications among their possible uses as seen in section III-B ($95.2$ %).

###  III-F Validation Systems and Evaluation Metrics

For the validation of the reviewed works, researchers use different systems,
as shown in Fig. 14. The gold standard is the $3$D optical motion capture
system, such as the commercial Vicon [175] or Optitrack [176], being the most
widely employed. This system is commonly used for the validation of proposals
($68.0$ %) and, sometimes ($4.8$ %), in combination of force platforms or with
a simulation software ($0.7$ %). $2$D optical systems that can obtain a
reference in the image plane are also used ($4.8$ % of the works). In some
works, the $2$D optical systems are combined with depth sensors ($0.7$ %).

Figure 14: Validation system used to assess the proposals. Force platforms and
simulations are abbreviated as force plat. and simul., respectively.

Another approach to validate the algorithms that is worth mentioning is the
use of output values of commercial inertial systems that provide highly
accurate measurements, as done in the $6.8$ % of studies. IMUs of the Xsens
commercial brand are the most frequently used for the validation of proposals
[177]. Four of the eleven works that validate their algorithms against
inertial sensors outputs use these sensors [110, 148, 109, 147], whereas the
remaining seven works use IMUs of seven different brands.

A less common solution includes the use of analog and electronic goniometers
($8.2$ %). Other validation systems, which in combination sum a $6.8$ % of
works, include different programs of motion simulation, encoders and
potentiometers.

The accuracy metric reported most frequently for the validation of proposals
is the root mean square error (RMSE). In some works, the correlation
coefficient or the mean absolute error (MAE) are also provided. For the case
of angles measurement, the studied works report a RMSE between $2.59$ ° and
$7.67$ °. Even if in average most of studies provide similar metrics, it is
worth mentioning that the RMSE range of ML methods is between $2.48$ ° and
$5.70$ °, whereas the RMSE provided by the classical methods is between $2.24$
° and $7.80$ °. These results prove that ML methods are promising approaches
in the human motion analysis field in spite of their limitations related to
the data availability.

##  IV Discussion

After the previous in-depth study, we discuss the review findings in terms of
the general trends and the future guidelines in the inertial motion monitoring
field.

###  IV-A General Trends

This paper analyzes the current state and the research trends in the inertial
motion analysis field. The analyzed works show the interest in developing an
alternative to the gold standard system, based on cameras, due to their high
cost and the required space of use. As a consequence, the research focused on
developing an IMU-based system for the human motion analysis has increased
over the last years, as seen in Fig. 5.

The sensors integrated in IMUs, accelerometer, gyroscope and magnetometer, are
fused in different ways in the analyzed works, as shown in Fig. 6. The fusion
of gyroscopes and accelerometers is more common than the use of magnetometers,
being one of the main differences with respect to the findings in previous
reviews [4]. However, the use of magnetometers is spreading during the last
year with $10$ works. Bayesian filters and trigonometric approaches are the
ones that most frequently employ the data from the magnetometer. ML proposals
barely rely on the measurements of the magnetic field and only use them in the
training step of the algorithms. In this way, the works focused on ML
proposals are not limited by magnetic disturbances.

The common objective in $72.4$ % of studies (see Fig. 7) is to obtain $3$D
kinematic parameters. The $2$D estimations are useful in human motion analysis
because some movements can be simplified as motions in one plane, e.g. knee or
elbow flex extension or even gait and squats. However, these estimations can
miss relevant information in motions, about correctness or symptoms of motion-
related diseases. Obtaining the complete kinematic information is specially
important in healthcare applications, that is considered in the $95.2$ % of
works (see Fig. 8).

Most of the analyzed works ($33.5$ %, as shown in Fig. 8) mention the generic
motion capture field for human motion analysis, closely followed by the gait
evaluation, as aimed applications for their work. That reflects the interest
of developing more affordable and user-friendly alternatives to the optical
systems, as previously discussed. Consequently, the analyzed works propose
algorithms to monitor frequently the orientation of joints, which is commonly
measured by stereophotogrammetric systems, such as Vicon [175]. The $64.6$ %
of works focus on joints and the $81.6$ % on the estimation of the
orientation. These percentages imply a great advance in the direction of
inertial solutions for the human motion analysis, especially compared to the
trends reported in [4], where most works studied the orientation of segments.

Another interesting analysis is focused on the distribution of works with
respect to the analyzed body part, divided into the upper-and lower-halves.
The $61.2$ % of works (see Fig. 10) study the lower-half of the body, and most
of them focus on the leg joints, which is also consistent with the trend of
gait evaluation besides the motion analysis. Conversely, only the $34.7$ %
(see Fig. 10) studies the upper-half, that include arms and trunk, which are
difficult to monitor due to the DOF and the complexity of joints as shoulders
or neck. The results in Fig. 10 mean that during the last years, the research
has been focused mostly on the lower-half of the body, the opposite of what
happened in [4], that most of the reviewed works analyzed upper-limbs.
However, monitoring this upper-half of the body is crucial for the evaluation
of motions, being specially important in the rehabilitation of cognitive
alterations or illness, such as strokes. The remaining $4.1$ % (see Fig. 10)
of proposals are aimed at monitoring the whole-body posture, which are the
most complete approach for the human monitoring. Even though the gait analysis
is commonly performed by monitoring the lower-limbs, upper-limbs are also
important to study relevant features, as balance, in clinical assessments. The
rising interest in considering the full body is also another noteworthy
difference compared to previous findings.

For the full-body monitoring, ML methods are specially attractive. Sensor
fusion algorithms use one IMU per segment to monitor the whole-body posture or
model biomechanical relationships between segments to reduce this number with
different constraints. Conversely, the approach in ML-based proposals focused
on the whole-body posture is the optimization of the number of devices with
the use of the so-called _sparse_ IMUs, as in [58, 147, 29, 155, 148]. This
approach is also used to monitor specific limbs, as legs, reducing the number
of sensors [21, 134, 100].

The biomechanical approaches for error reduction can restrict motions and
might not be generalized for populations with motor related diseases. For
instance, the ROM of joints can be different in people with anomalous physical
abilities. Likewise, the assumption of a number of DOF can miss relevant
information about motions out of the main directions. Also, the knowledge of
the segment length or the location of the sensors on the body is not always
available in practical applications. Different IMU-joint calibration methods
have been proposed to address this limitation. The first approach is to obtain
an average location of joints with respect to the sensors, which has been
validated for the upper-and lower-limbs [178, 179], respectively, but require
specific calibration motions. The second method consists in estimating an
adaptive position vector, considering the changes of the location of IMUs due
to soft tissue artifacts [180, 181, 182, 183], which has been validated for
the calibration of hips performing leg circles [182]. These proposals assume
that the joints are fixed, but it is not the case in all the activities in the
daily living. In [184], the calibration of moving joints with soft tissue
artifacts is addressed.

As in previous findings [4], the sensor fusion algorithms are employed more
commonly than other approaches. However, their use during the last decade
remains stable (around $24$ papers), whereas the use of ML techniques has
increased from $4$ papers to $18$ papers. These ML techniques provide a slight
improvement in the accuracy metrics, referred to a reduction of the maximum
RMSE in $2$ ° in angle measurements. However, none study analyzed in this work
includes a research that makes a fair comparison using common data to test
both approaches.

Sensor fusion filters and data science algorithms differ in terms of their
computational costs. Computational time varies among the different methods
depending on their implementations. Sensor fusion filters are faster than data
science methods which require more calculations, specially, DNN-based ones
whose number of parameters is superior. Also, ML-and DNN-based methods usually
demand more memory than the sensor fusion solutions, specially in their
training stage, making their implementations more expensive.

ML algorithms are more robust to variation in the intrinsic noise of the
sensors with which they are trained. In addition, their robustness can
increase by generating synthetic data to which more noise models are added.
Conversely, the sensor fusion algorithms include parameter tuning to adapt
them to the sensors used, e.g. the covariance matrix of KFs. Thus, sensor
fusion algorithms would require a previous study to estimate these sensor-
dependent matrices.

ML methods require a high amount of reference data to be trained. Two
alternative trends are followed in order to generate reference data: _1)_ to
simulate the inertial data from the optical data to use them as inputs or _2)_
to use the orientation data obtained by commercial systems as reference. In
the first case, the simulation of inertial data might not present the
intrinsic errors of IMUs, whereas by using inertial data as reference, it
presents an error around $0.5$ ° depending on the commercial brand, which is
less accurate than optical systems.

With regard to the validation, new reference systems have appeared during the
last years. Among them, we find $2$D visual systems, encoders and
computational models. The $3$D optical systems are still the ones most
frequently used ($68.0$ % of studies, see Fig. 14). However, the use of this
validation system entails the limitation of testing the proposals in daily
activities and alternative validation methods should be investigated [7].

The reviewed studies generally analyze a low amount of participants for the
validation of the algorithms. This limitation was detected in [4] and still
remains in recent works. Most studies test their results only in one
volunteer, and the average of study subjects is $4$ participants. It makes the
proposals hardly to generalize for the whole population. In those studies that
more participants are involved, the inertial data are simulated from the
optical data or their reference consists in the orientation outputs obtained
from the IMUs, including the errors previously indicated.

Most studies analyze healthy participants. That is noticeable since most
studies consider healthcare applications as possible uses of their proposals.
However, only a few of them ($8.2$ %) test their proposals on subjects with
motor related diseases.

###  IV-B Future Advancements and Developments

This review highlights a set of clear trends. The studies describe the motions
in the $3$D space more frequently than reducing them to planar motions. This
is crucial to describe complex motions that can be performed during the daily
life, so it is required for an out-of-the-lab analysis. Furthermore, the
reduction of the gait or simpler motions such as knee flex-extension to a
plane eliminates relevant information about these motions.

The reviewed works focus on the lower-limbs, specifically on the orientation
of the hip, knee and ankle. Future research should include upper-limbs or even
focus on the development of whole-body posture monitoring for a complete
description of motions. In this line of work, the proposal of sparse-IMUs
utilization, is promising to decrease the number of sensors in use, which is
required for the motion analysis in all environments. Moreover, the monitoring
of complex joints, such as shoulders or hips, which are usually modeled as
$3$-DOF joints, should include all their DOF for a proper kinematic analysis.

With regard to the algorithms in use, the current trend moves from the
Bayesian filters, which we consider the classical ones, to ML algorithms,
specially into deep learning algorithms. For the development of these novel
proposals, more data with an accurate reference are required, as described in
[185, 186], in order to avoid the use of data from IMUs and simulations from
the optical systems as ground truth. One of the main limitations of the
biomechanical constraints found in the literature is their generalization of
use in wide and varied populations, where the constraints based on ROM and DOF
exclude people with motor diseases. In this way, new proposals should be
adaptable to the populations under study. Also, alternatives to obtain the
IMU-joint vector based on inertial devices are needed in order to make
suitable the proposals that exploit the biomechanical relationships in out-of-
the-lab environments.

Common data with inertial measurements and its reference are needed in order
to obtain a fair comparison of the existent and new proposals. In that line of
research, future proposals are required to be validated on a larger number of
volunteers than is currently the case. This also should ensure the variability
of motions and not be focused on the gait.

##  V Conclusions

This work has reviewed the studies focused on the human motion analysis based
on IMUs. The date of publication of the reviewed papers is not limited, so we
provide an overview of the proposals since the first study to the current
date. This overview summarizes the algorithms, the combination of sensors, the
anatomical units monitored, the subjects of study and the validation
approaches in the research of inertial monitoring. The review also focuses on
the studies of the last decade, so we analyze the last trends in this research
field. Most of the analyzed works focus on obtaining the $3$D estimation of
the kinematics of lower-limb joints, presenting a lack of studies of the
upper-half of the body. The Bayesian filters are still the most used methods,
but their trend is to be applied less frequently, whereas the ML algorithms
are being used now with a higher incidence. This review includes the
description of the main algorithms used with their inputs and outputs for a
better understanding of the existent methods. In this way, we show that,
nowadays, these groups of algorithms present also differences in the selected
sensors: Bayesian filters tend to use more the magnetometer and try to
compensate its limitations, but ML algorithms commonly rely only on gyroscopes
and accelerometers. Both groups of algorithms present also differences in the
range of accuracy, obtaining slightly lower maximum errors by using ML
methods. This work also analyzes the proposed approaches for error reduction,
highlighting the need of proposals suitable for all the population and of IMU-
joint calibration methods. Finally, this work remarks the requirement of
testing future proposals on a highly number of subjects, that help to create
common databases that allow the comparison among the existent and new
proposals.

##  Appendix A Tables of the data extracted

TABLE III: Relevant details related with the implemented algorithms, the sensors in use and the estimations of the selected studies. With respect to the FA acronyms, SF: sensor fusion, ML: machine learning, OA: other algorithms. Other acronyms: BC: biomechanical constraints, ANT: anatomical parameters in use, OC: other constraints, ML learns: refers to that theses ML-based algorithms learn for real motions so they are constraint to anatomical joint limits and EST: refers to the use of anatomical or soft constraints after estimate the required parameters, GS: gyroscope sensor, AS: accelerometer sensor, MS: magnetometer sensor, OS: other sensors for training, EST: type of estimation, ANG: angle, DIS: displacement or position, JNT: joint and SGM: segment.  Title | Algorithms | Sensors | Estimation characteristics
---|---|---|---
FA |  BC |  ANT |  OC |  GS |  AS |  MS |  OS |  EST |  ANG |  DIS |  JNT |  SGM
A basic study on variable-gain Kalman filter based on angle error calculated from acceleration signals for lower limb angle measurement with inertial sensors [33] |  SF |  |  |  ✓ |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  |  ✓
A Comparison of Three Neural Network Approaches for Estimating Joint Angles and Moments from Inertial Measurement Units [34] |  ML |  ✓ |  ML learns |  ✓ |  ✓ |  ✓ |  |  ✓ |  3D |  ✓ |  |  ✓ |
A fast quaternion-based orientation optimizer via virtual rotation for human motion tracking [116] |  OA |  |  |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  |  ✓
A Full-State Robust Extended Kalman Filter for Orientation Tracking during Long-Duration Dynamic Tasks Using Magnetic and Inertial Measurement Units [117] |  SF |  |  |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  |  ✓
A Human Motion Tracking Algorithm Using Adaptive EKF Based on Markov Chain [118] |  SF |  |  |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  |  ✓
A method for gait analysis in a daily living environment by body-mounted instruments [35] |  OA |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  2D |  ✓ |  ✓ |  ✓ |
A Method for Lower Back Motion Assessment Using Wearable 6D Inertial Sensors [36] |  OA |  |  |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  |  ✓
A Miniature Sensor System for Precise Hand Position Monitoring [119] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  ✓ |  ✓ |
A new approach to accurate measurement of uniaxial joint angles based on a combination of accelerometers and gyroscopes [37] |  OA |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  ✓ |
A new quaternion-based kalman filter for human body motion tracking using the second estimator of the optimal quaternion algorithm and the joint angle constraint method with inertial and magnetic sensors [120] |  SF |  ✓ |  |  |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  |  ✓
A nonlinear dynamics-based estimator for functional electrical stimulation: Preliminary results from lower-leg extension experiments [38] |  SF |  ✓ |  EST |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
A novel 7 degrees of freedom model for upper limb kinematic reconstruction based on wearable sensors [121] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  ✓ |  ✓ |  ✓
A Novel Application of Flexible Inertial Sensors for Ambulatory Measurement of Gait Kinematics [39] |  OA |  ✓ |  EST |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
A novel approach to motion tracking with wearable sensors based on Probabilistic Graphical Models [122] |  ML |  ✓ |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |
A novel complimentary filter for tracking hip angles during cycling using wireless inertial sensors and dynamic acceleration estimation [123] |  SF |  |  EST |  |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |
A novel data glove for fingers motion capture using inertial and magnetic measurement units [124] |  SF |  |  |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  |  ✓
A novel hierarchical information fusion method for three-dimensional upper limb motion estimation [125] |  SF |  ✓ |  |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |  ✓
A Novel Kalman Filter for Human Motion Tracking With an Inertial-Based Dynamic Inclinometer [40] |  SF |  |  |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  |  ✓
A novel method for estimating knee angle using two leg-mounted gyroscopes for continuous monitoring with mobile health devices [11] |  SF |  |  |  ✓ |  ✓ |  |  |  |  3D |  ✓ |  |  ✓ |
A novel method of using accelerometry for upper limb FES control [18] |  OA |  |  |  |  |  ✓ |  |  |  2D |  ✓ |  |  |  ✓
A novel sensor-based assessment of lower limb spasticity in children with cerebral palsy [41] |  OA |  |  |  ✓ |  ✓ |  ✓ |  |  |  2D+3D |  ✓ |  |  ✓ |
A patient-centric sensory system for in-home rehabilitation [126] |  SF |  |  |  |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |
A preliminary test of measurement of joint angles and stride length with wireless inertial sensors for wearable gait evaluation system [42] |  SF |  |  |  |  ✓ |  ✓ |  |  |  2D |  ✓ |  ✓ |  ✓ |  ✓
A study of gait analysis with a smartphone for measurement of hip joint angle [12] |  OA |  |  |  |  ✓ |  |  |  |  2D |  ✓ |  |  ✓ |
A Wearable Human Motion Tracking Device Using Micro Flow Sensor Incorporating a Micro Accelerometer [43] |  SF |  |  |  ✓ |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  |  ✓
A Wearable Magnetometer-Free Motion Capture System: Innovative Solutions for Real-World Applications [44] |  SF |  |  |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Accuracy Improvement on the Measurement of Human-Joint Angles [127] |  OA |  |  |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |
Accuracy of a custom physical activity and knee angle measurement sensor system for patients with neuromuscular disorders and gait abnormalities [45] |  SF |  ✓ |  |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Adaptive Gain Regulation of Sensor Fusion Algorithms for Orientation Estimation with Magnetic and Inertial Measurement Units [128] |  SF |  |  |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  |  ✓
Alignment-Free, Self-Calibrating Elbow Angles Measurement Using Inertial Sensors [13] |  OA |  ✓ |  EST |  |  ✓ |  |  |  |  3D |  ✓ |  |  ✓ |
Ambulatory estimation of knee-joint kinematics in anatomical coordinate system using accelerometers and magnetometers [129] |  OA |  ✓ |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |
Ambulatory measurement and analysis of the lower limb 3D posture using wearable sensor system [46] |  OA |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
An adaptive complementary filter for inertial sensor based data fusion to track upper body motion [47] |  SF |  |  |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
An auto-calibrating knee flexion-extension axis estimator using principal component analysis with inertial sensors [130] |  SF |  ✓ |  EST |  |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |
An inertial human upper limb motion tracking method for robot programming by demonstration [110] |  OA |  |  ✓ |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
An inertial sensor system for measurements of tibia angle with applications to knee valgus/varus detection [48] |  OA |  |  |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |  ✓
An instance-based algorithm with auxiliary similarity information for the estimation of gait kinematics from wearable sensors [49] |  ML |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  ✓ |  3D |  ✓ |  |  ✓ |
An investigation into the accuracy of calculating upper body joint angles using MARG sensors [131] |  SF |  |  |  |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |  ✓
An optimized Kalman filter for the estimate of trunk orientation from inertial sensors data during treadmill walking [50] |  SF |  |  |  ✓ |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  |  ✓
Analysis of a mobile system to register the kinematic parameters in ankle, knee, and hip based in inertial sensors [51] |  OA |  |  |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |  ✓
Analyzing 3D knee kinematics using accelerometers, gyroscopes and magnetometers [132] |  OA |  ✓ |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |
Angle measurements during 2D and 3D movements of a rigid body model of lower limb: Comparison between integral-based and quaternion-based methods [52] |  SF |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  |  ✓
Artificial neural networks in motion analysis—applications of unsupervised and heuristic feature selection techniques [53] |  ML |  ✓ |  ✓ |  ✓ |  ✓ |  ✓ |  |  ✓ |  3D |  ✓ |  |  ✓ |
Biomechanical Ambulatory Assessment of 3D Knee Angle Using Novel Inertial Sensor-Based Technique [54] |  ML |  ✓ |  ML learns |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Calibrated 2D angular kinematics by single-axis accelerometers: From inverted pendulum to N-Link chain [19] |  OA |  ✓ |  ✓ |  |  |  ✓ |  |  |  2D |  ✓ |  |  |  ✓
Closed-chain pose estimation from wearable sensors [55] |  SF |  ✓ |  NO? |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  ✓ |  ✓ |
CNN-Based Estimation of Sagittal Plane Walking and Running Biomechanics From Measured and Simulated Inertial Sensor Data [56] |  ML |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  ✓ |  2D |  ✓ |  |  ✓ |
Comparison of angle measurements between integral-based and quaternion-based methods using inertial sensors for gait evaluation [57] |  SF |  |  |  |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  |  ✓
Data-Driven Reconstruction of Human Locomotion Using a Single Smartphone [58] |  ML |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  ✓ |  3D |  |  ✓ |  |  ✓
DeepBBWAE-Net: A CNN-RNN Based Deep SuperLearner For Estimating Lower Extremity Sagittal Plane Joint Kinematics Using Shoe-Mounted IMU Sensors In Daily Living [111] |  ML |  |  ML learns |  |  ✓ |  Y |  |  ✓ |  2D |  ✓ |  |  ✓ |
Deriving kinematic quantities from accelerometer readings for assessment of functional upper limb motions [20] |  OA |  ✓ |  ✓ |  |  |  ✓ |  |  |  3D |  ✓ |  |  ✓ |  ✓
Design and validation of an ambulatory inertial system for 3-D measurements of low back movements [59] |  OA |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  |  ✓
Detecting absolute human knee angle and angular velocity using accelerometers and rate gyroscopes [60] |  OA |  |  |  ✓ |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  |  ✓
Development of a body joint angle measurement system using IMU sensors [61] |  OA |  |  |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Development of a wearable glove system with multiple sensors for hand kinematics assessment [133] |  SF |  |  |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |
Development of a wearable sensor system for quantitative gait analysis [187] |  OA |  ✓ |  ✓ |  ✓ |  ✓ |  ✓ |  |  |  2D |  ✓ |  ✓ |  |  ✓
Digital inclinometer for joint angles measurements with a real-time 3D-animation [153] |  OA |  |  |  ✓ |  |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |
Drift-Free 3D Orientation and Displacement Estimation for Quasi-Cyclical Movements Using One Inertial Measurement Unit: Application to Running [112] |  OA |  |  |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  Y |  |  ✓
Drift-Free and Self-Aligned IMU-Based Human Gait Tracking System with Augmented Precision and Robustness [62] |  SF |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Drift-Free Foot Orientation Estimation in Running Using Wearable IMU [63] |  OA |  |  EST |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  |  ✓
Drift-Free Inertial Sensor-Based Joint Kinematics for Long-Term Arbitrary Movements [64] |  SF |  ✓ |  EST |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Effect of walking variations on complementary filter based inertial data fusion for ankle angle measurement [65] |  SF |  |  EST |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Efficiency of deep neural networks for joint angle modeling in digital gait assessment [134] |  ML |  ✓ |  ML learns |  ✓ |  ✓ |  ✓ |  ✓ |  ✓ |  2D |  ✓ |  |  ✓ |
Estimate of lower trunk angles in pathological gaits using gyroscope data [14] |  SF |  |  |  ✓ |  ✓ |  |  |  |  3D |  ✓ |  |  |  ✓
Estimating Lower Body Kinematics Using a Lie Group Constrained Extended Kalman Filter and Reduced IMU Count [135] |  SF |  ✓ |  ✓ |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  |  ✓
Estimating lower extremity running gait kinematics with a single accelerometer: A deep learning approach [21] |  ML |  ✓ |  |  ✓ |  |  ✓ |  |  ✓ |  3D |  ✓ |  |  ✓ |
Estimating Lower Limb Kinematics Using a Reduced Wearable Sensor Count [136] |  SF |  ✓ |  ✓ |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  ✓ |  ✓ |
Estimation and Observability Analysis of Human Motion on Lie Groups [66] |  SF |  |  |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Estimation of gait kinematics and kinetics from inertial sensor data using optimal control of musculoskeletal models [67] |  OA |  |  ✓ |  ✓ |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  ✓ |  ✓
Estimation of Gait Mechanics Based on Simulated and Measured IMU Data Using an Artificial Neural Network [68] |  ML |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  ✓ |  3D |  ✓ |  |  ✓ |
Estimation of kinematics from inertial measurement units using a combined deep learning and optimization framework [69] |  ML |  ✓ |  ML learns |  ✓ |  ✓ |  ✓ |  |  ✓ |  3D |  ✓ |  |  ✓ |
Estimation of knee joint angle during gait cycle using inertial measurement unit sensors: a method of sensor-to-clinical bone calibration on the lower limb skeletal model [113] |  OA |  ✓ |  |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |  ✓
Estimation of lower limb joint angles during walking using extended kalman filtering [70] |  SF |  |  |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Estimation of the continuous walking angle of knee and ankle (Talocrural joint, subtalar joint) of a lower‐limb exoskeleton robot using a neural network [71] |  ML |  ✓ |  ML learns |  ✓ |  ✓ |  ✓ |  |  ✓ |  2D |  ✓ |  |  ✓ |
Estimation of the knee flexion-extension angle during dynamic sport motions using body-worn inertial sensors [72] |  SF |  |  |  ✓ |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  ✓ |
Evaluation of wearable gyroscope and accelerometer sensor (PocketIMU2) during walking and sit-to-stand motions [15] |  OA |  |  |  |  ✓ |  |  |  |  3D |  ✓ |  |  ✓ |
Feasibility of a Wearable, Sensor-based Motion Tracking System [16] |  OA |  |  |  |  ✓ |  |  |  |  3D |  ✓ |  |  ✓ |
Feasibility study of inertial sensor-based joint moment estimation method during human movements: A test of multi-link modeling of the trunk segment [17] |  OA |  ✓ |  ✓ |  |  ✓ |  |  |  |  2D |  ✓ |  |  ✓ |
Gait posture estimation using wearable acceleration and gyro sensors [73] |  OA |  ✓ |  ✓ |  ✓ |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  ✓ |
Geometrical kinematic modeling on human motion using method of multi-sensor fusion [74] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  3D |  |  ✓ |  |  ✓
Grasp pose estimation in human-robot manipulation tasks using wearable motion sensors [75] |  OA |  |  |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  ✓ |  ✓ |
Hand Motion Measurement using Inertial Sensor System and Accurate Improvement by Extended Kalman Filter [76] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  ✓ |  ✓ |
Human Arm Motion Tracking by Inertial/Magnetic Sensors Using Unscented Kalman Filter and Relative Motion Constraint [137] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  3D |  |  ✓ |  ✓ |
Human body model based inertial measurement of sit-to-stand motion kinematics [77] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  |  ✓
Human Motion Kinematics Assessment Using Wearable Sensors [138] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |
Human motion tracking based on complementary Kalman filter [139] |  SF |  |  |  |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  |  ✓
Human pose recovery for rehabilitation using ambulatory sensors [78] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  |  ✓
Human pose recovery using wireless inertial measurement units [79] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  ✓ |  ✓ |
IMU-Based joint angle measurement for gait analysis [80] |  OA |  ✓ |  EST |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Inertia-based angle measurement unit for gait assistive device [22] |  OA |  |  |  |  |  ✓ |  |  |  2D |  ✓ |  |  ✓ |
Inertial Motion Capture Using Adaptive Sensor Fusion and Joint Angle Drift Correction [140] |  SF |  ✓ |  |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  |  ✓
Inertial sensing in ambulatory back load estimation [81] |  OA |  |  |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  |  ✓
Inertial sensor-based knee flexion/extension angle estimation [82] |  SF |  ✓ |  |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Joint angle estimation with accelerometers for dynamic postural analysis [23] |  OA |  ✓ |  ✓ |  |  |  ✓ |  |  |  2D |  ✓ |  |  ✓ |
Joint Inertial Sensor Orientation Drift Reduction for Highly Dynamic Movements [83] |  OA |  ✓ |  EST |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Knee angle estimation based on IMU data and artificial neural networks [84] |  ML |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  ✓ |  3D |  ✓ |  |  ✓ |
Knee joint angle measuring portable embedded system based on inertial measurement units for gait analysis [85] |  SF |  |  |  |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  ✓ |
Lower body kinematics estimation from wearable sensors for walking and running: A deep learning approach [86] |  ML |  ✓ |  ML learns |  ✓ |  ✓ |  ✓ |  |  ✓ |  3D |  ✓ |  |  ✓ |
Lower Extremity Angle Measurement with Accelerometers—Error and Sensitivity [24] |  OA |  ✓ |  ✓ |  |  |  ✓ |  |  |  2D |  ✓ |  |  ✓ |
Magneto: Joint angle analysis using an electromagnet-based sensing method [31] |  OA |  |  |  |  |  |  ✓ |  |  3D |  ✓ |  ✓ |  ✓ |
Magnetometer robust deep human pose regression with uncertainty prediction using sparse body worn magnetic inertial measurement units [155] |  ML |  ✓ |  ML learns |  ✓ |  ✓ |  |  ✓ |  ✓ |  3D |  ✓ |  |  ✓ |
Monitoring of Hip and Knee Joint Angles Using a Single Inertial Measurement Unit during Lower Limb Rehabilitation [87] |  OA |  ✓ |  ✓ |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Multi-Inertial Sensor-Based Arm 3D Motion Tracking Using Elman Neural Network [114] |  ML |  |  |  |  ✓ |  ✓ |  |  ✓ |  3D |  ✓ |  ✓ |  ✓ |
Nonlinear optimization for drift removal in estimation of gait kinematics based on accelerometers [25] |  OA |  ✓ |  ✓ |  ✓ |  |  ✓ |  |  |  2D |  ✓ |  ✓ |  |  ✓
Novel approach to ambulatory assessment of human segmental orientation on a wearable sensor system [26] |  OA |  ✓ |  ✓ |  ✓ |  |  ✓ |  |  |  2D |  ✓ |  |  ✓ |
Online tracking of the lower body joint angles using IMUs for gait rehabilitation [88] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  ✓ |  ✓ |
Optimization of Inertial Sensor-Based Motion Capturing for Magnetically Distorted Field Applications [141] |  OA |  |  |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  |  ✓
Physical-Sensor and Virtual-Sensor Based Method for Estimation of Lower Limb Gait Posture Using Accelerometers and Gyroscopes [89] |  OA |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  ✓ |  ✓ |
Pose estimation by extended Kalman filter using noise covariance matrices based on sensor output [142] |  SF |  |  |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |
Predicting Knee Joint Kinematics from Wearable Sensor Data in People with Knee Osteoarthritis and Clinical Considerations for Future Machine Learning Models [115] |  ML |  |  |  |  ✓ |  ✓ |  |  ✓ |  2D |  ✓ |  |  ✓ |
Predicting lower limb joint kinematics using wearable motion sensors [90] |  ML |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  ✓ |  2D |  ✓ |  |  ✓ |
Prediction of lower limb joint angles and moments during gait using artificial neural networks [91] |  ML |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  ✓ |  3D |  ✓ |  |  ✓ |
Prediction of lower limb kinetics and kinematics during walking by a single IMU on the lower back using machine learning [27] |  ML |  ✓ |  ✓ |  ✓ |  |  ✓ |  |  |  2D |  ✓ |  ✓ |  |  ✓
Quasi-real time estimation of angular kinematics using single-axis accelerometers [92] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  ✓ |
Real-time estimate of body kinematics during a planar squat task using a single inertial measurement unit [93] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  ✓ |
Real-Time Human Motion Capture Based on Wearable Inertial Sensor Networks [152] |  SF |  |  ✓ |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  ✓ |  ✓ |
Reconstructing an accelerometer-based pelvis segment for three-dimensional kinematic analyses during laboratory simulated tasks with obstructed line-of-sight [28] |  OA |  |  ✓ |  |  |  ✓ |  |  |  2D |  ✓ |  |  |  ✓
Reconstruction of angular kinematics from wrist-worn inertial sensor data for smart home healthcare [94] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  |  ✓
Reducing drifts in the inertial measurements of wrist and elbow positions [95] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  3D |  |  ✓ |  ✓ |
Research on Human Motion Monitoring Method Based on Multi-Joint Constraint Filter Model [143] |  SF |  ✓ |  ✓ |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |  ✓
Rhythmic EKF for pose estimation during gait [96] |  SF |  ✓ |  ✓ |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Rhythmic Extended Kalman Filter for Gait Rehabilitation Motion Estimation and Segmentation [8] |  SF |  ✓ |  ✓ |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Rigid body motion capturing by means of a wearable inertial and magnetic MEMS sensor assembly-from reconstitution of the posture toward dead reckoning: An application in bio-logging [144] |  SF |  |  |  |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  ✓ |  |  ✓
Robust and Accurate Capture of Human Joint Pose Using an Inertial Sensor [145] |  SF |  |  |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  |  ✓
Sensorial system for obtaining the angles of the human movement in the coronal and sagittal anatomical planes [97] |  SF |  ✓ |  |  |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  ✓ |  ✓
Shoulder and elbow joint angle estimation for upper limb rehabilitation tasks using low-cost inertial and optical sensors [98] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Shoulder and elbow joint angle tracking with inertial sensors [99] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Synergy-based knee angle estimation using kinematics of thigh [100] |  ML |  ✓ |  ML learns |  ✓ |  ✓ |  ✓ |  |  ✓ |  3D |  ✓ |  |  ✓ |
System for measurement of joint range of motion using inertial sensors [101] |  SF |  ✓ |  |  |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  ✓ |
The head mouse - Head gaze estimation ’In-the-Wild’ with low-cost inertial sensors for BMI use [146] |  SF |  |  |  |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  |  ✓
The manumeter: A wearable device for monitoring daily use of the wrist and fingers [32] |  OA |  |  |  |  |  |  ✓ |  ✓ |  3D |  ✓ |  |  ✓ |
The online estimation of the joint angle based on the gravity acceleration using the accelerometer and gyroscope in the wireless networks [102] |  OA |  |  |  |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  ✓ |
The use of synthetic IMU signals in the training of deep learning models significantly improves the accuracy of joint kinematic predictions [103] |  ML |  ✓ |  ML learns |  ✓ |  ✓ |  ✓ |  |  ✓ |  3D |  ✓ |  |  ✓ |
Three dimensional gait analysis using wearable acceleration and gyro sensors based on quaternion calculations [104] |  OA |  |  |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Time coherent full-body poses estimated using only five inertial sensors: Deep versus shallow learning [147] |  ML |  ✓ |  |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  ✓ |  |  ✓
Towards a portable human gait analysis & monitoring system [105] |  OA |  ✓ |  EST |  |  ✓ |  ✓ |  |  |  2D |  ✓ |  |  ✓ |
Towards kinematically constrained real time human pose estimation using sparse IMUs [148] |  ML |  ✓ |  ML learns |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |
Training Data Selection and Optimal Sensor Placement for Deep-Learning-Based Sparse Inertial Sensor Human Posture Reconstruction [29] |  ML |  ✓ |  ML learns |  ✓ |  - |  ✓ |  - |  ✓ |  3D |  ✓ |  |  |  ✓
Ubiquitous human upper-limb motion estimation using wearable sensors [149] |  SF |  ✓ |  |  |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |
Unrestrained measurement of arm motion based on a wearable wireless sensor network [30] |  OA |  |  |  ✓ |  |  ✓ |  |  |  2D |  ✓ |  |  ✓ |
Upper limb joint angle measurement in occupational health [150] |  OA |  ✓ |  ✓ |  ✓ |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |
Upper limb joint angle tracking with inertial sensors [106] |  SF |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  |  ✓ |
Use of multiple wearable inertial sensors in upper limb motion tracking [107] |  OA |  ✓ |  ✓ |  |  ✓ |  ✓ |  |  |  3D |  ✓ |  ✓ |  ✓ |
Validation of a low-cost inertial exercise tracker [108] |  SF |  ✓ |  EST |  ✓ |  ✓ |  ✓ |  |  |  3D |  ✓ |  ✓ |  ✓ |
Visual and quantitative analysis of lower limb 3D gait posture using accelerometers and magnetometers [154] |  OA |  ✓ |  ✓ |  - |  |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |
Visual estimation of lower limb motion using physical and virtual sensors [151] |  OA |  ✓ |  ✓ |  - |  ✓ |  ✓ |  ✓ |  |  3D |  ✓ |  |  ✓ |
Wearable inertial sensor system towards daily human kinematic gait analysis: Benchmarking analysis to MVN BIOMECH [109] |  ML, SF |  ✓ |  |  ✓ |  ✓ |  ✓ |  |  ✓ |  2D |  ✓ |  |  ✓ |  ✓
TABLE IV: Relevant details about the monitored anatomic unit, the number of subjects of study in the selected studies the validation system and the metrics for evaluation. LG: lower-limb group, UG: upper-limb group, NS: number of subjects for the analysis, DSS: presence of subjects with diseases, VS: validation sensory system, M1 and M2: metrics provided for the validation of the proposals.  Title | Monitored anatomic unit | Subjects of study | Validation approach
---|---|---|---
LG |  UG |  NS |  DSS |  VS |  M1 |  M2
A basic study on variable-gain Kalman filter based on angle error calculated from acceleration signals for lower limb angle measurement with inertial sensors [33] |  Leg Feet |  |  3 |  |  Optical 3D |  RMSE |
A Comparison of Three Neural Network Approaches for Estimating Joint Angles and Moments from Inertial Measurement Units [34] |  Hip/knee/ankle |  |  116 |  |  Optical 3D, Force plates |  Difference in nRMSE between methods |
A fast quaternion-based orientation optimizer via virtual rotation for human motion tracking [116] |  |  Arm |  1 |  |  Optical 3D |  RMSE |
A Full-State Robust Extended Kalman Filter for Orientation Tracking during Long-Duration Dynamic Tasks Using Magnetic and Inertial Measurement Units [117] |  Leg Feet |  |  9 |  |  Optical 3D |  RMSE |
A Human Motion Tracking Algorithm Using Adaptive EKF Based on Markov Chain [118] |  |  Arm |  1 |  |  Optical 3D |  RMSE |
A method for gait analysis in a daily living environment by body-mounted instruments [35] |  Hip/knee/ankle |  |  6 |  |  Optical 3D, Force plates |  RMSE |  -
A Method for Lower Back Motion Assessment Using Wearable 6D Inertial Sensors [36] |  |  Back/trunk/torso |  8 |  |  Optical 3D |  RMSE |  -
A Miniature Sensor System for Precise Hand Position Monitoring [119] |  |  Arm joints: shoulders/elbow/forearm twist Hand/wrist/fingers |  6 |  |  Optical 3D |  RMSE |  -
A new approach to accurate measurement of uniaxial joint angles based on a combination of accelerometers and gyroscopes [37] |  Hip/knee/ankle |  |  8 |  |  Visual 2D |  RMSE |  Corr. coeff.
A new quaternion-based kalman filter for human body motion tracking using the second estimator of the optimal quaternion algorithm and the joint angle constraint method with inertial and magnetic sensors [120] |  |  Arm |  1 |  |  Optical 3D |  RMSE |
A nonlinear dynamics-based estimator for functional electrical stimulation: Preliminary results from lower-leg extension experiments [38] |  Hip/knee/ankle |  |  3 |  |  Other |  RMSE |  -
A novel 7 degrees of freedom model for upper limb kinematic reconstruction based on wearable sensors [121] |  |  Head/neck/scapula Back/trunk/torso Arm Arm joints: shoulders/elbow/forearm twist |  1 |  |  Optical 3D |  RMSE |  -
A Novel Application of Flexible Inertial Sensors for Ambulatory Measurement of Gait Kinematics [39] |  Hip/knee/ankle |  |  3 |  |  Optical 3D |  RMSE |
A novel approach to motion tracking with wearable sensors based on Probabilistic Graphical Models [122] |  |  Arm joints: shoulders/elbow/forearm twist |  1 |  |  Optical 3D |  RMSE |
A novel complimentary filter for tracking hip angles during cycling using wireless inertial sensors and dynamic acceleration estimation [123] |  Hip/knee/ankle |  |  1 |  |  Optical 3D |  MAE |  -
A novel data glove for fingers motion capture using inertial and magnetic measurement units [124] |  |  Hand/wrist/fingers |  1 |  |  Visual 2D, Reconstruction |  RMSE |  -
A novel hierarchical information fusion method for three-dimensional upper limb motion estimation [125] |  |  Arm Arm joints: shoulders/elbow/forearm twist |  4 |  |  Optical 3D |  RMSE |  -
A Novel Kalman Filter for Human Motion Tracking With an Inertial-Based Dynamic Inclinometer [40] |  |  Arm |  10 |  |  Optical 3D |  RMSE |  -
A novel method for estimating knee angle using two leg-mounted gyroscopes for continuous monitoring with mobile health devices [11] |  Hip/knee/ankle |  |  5 |  |  Optical 3D |  LAM |  Avg. error
A novel method of using accelerometry for upper limb FES control [18] |  |  Arm |  2 |  2 post-stroke |  Optical 3D |  MAE |
A novel sensor-based assessment of lower limb spasticity in children with cerebral palsy [41] |  Hip/knee/ankle |  |  33 |  28 patients cerebral palsy |  Optical 3D |  RMSE |  Test-retest inter-rater reliabilities
A patient-centric sensory system for in-home rehabilitation [126] |  |  Arm joints: shoulders/elbow/forearm twist Hand/wrist/fingers |  1 |  |  Other |  RMSE |
A preliminary test of measurement of joint angles and stride length with wireless inertial sensors for wearable gait evaluation system [42] |  Hip/knee/ankle Feet |  |  3 |  |  Optical 3D |  RMSE |  Corr. coeff.
A study of gait analysis with a smartphone for measurement of hip joint angle [12] |  Hip/knee/ankle |  |  14 |  |  Optical 3D |  RMSE |
A Wearable Human Motion Tracking Device Using Micro Flow Sensor Incorporating a Micro Accelerometer [43] |  |  Arm |  1 |  |  IMU |  RMSE |
A Wearable Magnetometer-Free Motion Capture System: Innovative Solutions for Real-World Applications [44] |  |  Arm joints: shoulders/elbow/forearm twist |  10 |  |  Optical 3D |  RMSE |
Accuracy Improvement on the Measurement of Human-Joint Angles [127] |  |  Arm joints: shoulders/elbow/forearm twist |  15 |  |  Optical 3D |  RMSE |
Accuracy of a custom physical activity and knee angle measurement sensor system for patients with neuromuscular disorders and gait abnormalities [45] |  Hip/knee/ankle |  |  10 |  |  Goniometer |  RMSE |
Adaptive Gain Regulation of Sensor Fusion Algorithms for Orientation Estimation with Magnetic and Inertial Measurement Units [128] |  Leg Feet |  |  9 |  |  Optical 3D |  RMSE |
Alignment-Free, Self-Calibrating Elbow Angles Measurement Using Inertial Sensors [13] |  |  Arm joints: shoulders/elbow/forearm twist |  1 |  |  Optical 3D |  RMSE |
Ambulatory estimation of knee-joint kinematics in anatomical coordinate system using accelerometers and magnetometers [129] |  Hip/knee/ankle |  |  5 |  |  Optical 3D |  RMSE |
Ambulatory measurement and analysis of the lower limb 3D posture using wearable sensor system [46] |  Hip/knee/ankle |  |  8 |  |  Optical 3D |  RMSE |
An adaptive complementary filter for inertial sensor based data fusion to track upper body motion [47] |  |  Arm joints: shoulders/elbow/forearm twist |  4 |  |  Optical 3D |  RMSE |
An auto-calibrating knee flexion-extension axis estimator using principal component analysis with inertial sensors [130] |  Hip/knee/ankle |  |  15 |  |  Optical 3D |  RMSE |
An inertial human upper limb motion tracking method for robot programming by demonstration [110] |  |  Hand/wrist/fingers |  1 |  |  IMU |  MAE |
An inertial sensor system for measurements of tibia angle with applications to knee valgus/varus detection [48] |  Leg |  |  3 |  |  Optical 3D |  RMSE |
An instance-based algorithm with auxiliary similarity information for the estimation of gait kinematics from wearable sensors [49] |  Hip/knee/ankle |  |  8 |  |  Optical 3D |  Absolute deviation |
An investigation into the accuracy of calculating upper body joint angles using MARG sensors [131] |  |  Back/trunk/torso Arm joints: shoulders/elbow/forearm twist Hand/wrist/fingers |  1 |  |  RBG + depth |  RMSD |
An optimized Kalman filter for the estimate of trunk orientation from inertial sensors data during treadmill walking\citeMazza2012 |  |  Back/trunk/torso |  18 |  |  Optical 3D |  RMSE |
Analysis of a mobile system to register the kinematic parameters in ankle, knee, and hip based in inertial sensors [51] |  Hip/knee/ankle |  |  1 |  |  Visual 2D |  Max. error |
Analyzing 3D knee kinematics using accelerometers, gyroscopes and magnetometers [132] |  Hip/knee/ankle |  |  1 |  |  Optical 3D |  Avg. error |
Angle measurements during 2D and 3D movements of a rigid body model of lower limb: Comparison between integral-based and quaternion-based methods [52] |  Leg |  |  1 |  |  Optical 3D |  RMSE |
Artificial neural networks in motion analysis—applications of unsupervised and heuristic feature selection techniques [53] |  Hip/knee/ankle |  |  115 |  24 knee arthroplasty |  Optical 3D |  RMSE |  Corr. coeff.
Biomechanical Ambulatory Assessment of 3D Knee Angle Using Novel Inertial Sensor-Based Technique [54] |  Hip/knee/ankle |  |  5 |  |  Optical 3D |  RMSE |
Calibrated 2D angular kinematics by single-axis accelerometers: From inverted pendulum to N-Link chain [19] |  |  Back/trunk/torso |  1 |  |  Optical 3D |  RMSE |
Closed-chain pose estimation from wearable sensors [55] |  Hip/knee/ankle |  |  3 |  |  Optical 3D |  Avg. error |  RMSE
CNN-Based Estimation of Sagittal Plane Walking and Running Biomechanics From Measured and Simulated Inertial Sensor Data [56] |  Hip/knee/ankle |  |  10 |  |  Optical 3D, Force plates |  RMSE |
Comparison of angle measurements between integral-based and quaternion-based methods using inertial sensors for gait evaluation [57] |  Leg Feet |  |  3 |  |  Optical 3D |  RMSE |
Data-Driven Reconstruction of Human Locomotion Using a Single Smartphone [58] |  |  Head/neck/scapula Back/trunk/torso Arm |  1 |  |  Optical 3D |  RMSE |
DeepBBWAE-Net: A CNN-RNN Based Deep SuperLearner For Estimating Lower Extremity Sagittal Plane Joint Kinematics Using Shoe-Mounted IMU Sensors In Daily Living [111] |  Hip/knee/ankle |  |  10 |  |  Optical 3D |  RMSE |
Deriving kinematic quantities from accelerometer readings for assessment of functional upper limb motions [20] |  |  Hand/wrist/fingers |  1 |  |  Optical 3D |  RMSE |
Design and validation of an ambulatory inertial system for 3-D measurements of low back movements [59] |  |  Back/trunk/torso |  2 |  |  Optical 3D |  RMSE |
Detecting absolute human knee angle and angular velocity using accelerometers and rate gyroscopes [60] |  Hip/knee/ankle |  |  2 |  1 Paraplegic |  Goniometer |  RMSE |
Development of a body joint angle measurement system using IMU sensors [61] |  Hip/knee/ankle |  |  1 |  |  Optical 3D |  Avg. error |
Development of a wearable glove system with multiple sensors for hand kinematics assessment [133] |  |  Hand/wrist/fingers |  1 |  |  Goniometer |  MAE |
Development of a wearable sensor system for quantitative gait analysis [46] |  Leg |  |  10 |  |  Optical 3D |  RMSE |  Corr. coeff.
Digital inclinometer for joint angles measurements with a real-time 3D-animation [153] |  |  Head/neck/scapula Arm joints: shoulders/elbow/forearm twist |  1 |  |  Goniometer |  Max. error |
Drift-Free and Self-Aligned IMU-Based Human Gait Tracking System with Augmented Precision and Robustness [62] |  Hip/knee/ankle |  |  1 |  |  Optical 3D |  RMSE |
Drift-Free Foot Orientation Estimation in Running Using Wearable IMU [63] |  Feet |  |  26 |  |  Optical 3D |  RMSE |
Drift-Free 3D Orientation and Displacement Estimation for Quasi-Cyclical Movements Using One Inertial Measurement Unit: Application to Running [112] |  Leg |  |  4 |  |  Optical 3D |  RMSE |
Drift-Free Inertial Sensor-Based Joint Kinematics for Long-Term Arbitrary Movements [64] |  Hip/knee/ankle |  |  11 |  |  Optical 3D |  RMSE |
Effect of walking variations on complementary filter based inertial data fusion for ankle angle measurement [65] |  Hip/knee/ankle |  |  10 |  |  Optical 3D |  RMSE |
Efficiency of deep neural networks for joint angle modeling in digital gait assessment [134] |  Hip/knee/ankle |  |  20 |  |  IMU |  RMSE |
Estimate of lower trunk angles in pathological gaits using gyroscope data [14] |  |  Back/trunk/torso |  27 |  13 hemiplegia, 14 Parkinson |  Optical 3D |  RMSE |
Estimation of knee joint angle during gait cycle using inertial measurement unit sensors: a method of sensor-to-clinical bone calibration on the lower limb skeletal model [113] |  Leg Hip/knee/ankle |  |  8 |  |  Optical 3D |  RMSE |
Estimating Lower Body Kinematics Using a Lie Group Constrained Extended Kalman Filter and Reduced IMU Count [135] |  Leg Hip/knee/ankle |  |  14 |  |  Optical 3D |  MAE |
Estimating lower extremity running gait kinematics with a single accelerometer: A deep learning approach [21] |  Hip/knee/ankle |  |  10 |  |  Optical 3D |  RMSE |
Estimating Lower Limb Kinematics Using a Reduced Wearable Sensor Count [136] |  Hip/knee/ankle |  |  9 |  |  Optical 3D |  RMSE |
Estimation and Observability Analysis of Human Motion on Lie Groups [66] |  |  |  - |  |  Optical 3D |  MAE |
Estimation of gait kinematics and kinetics from inertial sensor data using optimal control of musculoskeletal models [67] |  Pelvis Leg Hip/knee/ankle |  |  10 |  |  Optical 3D, Force plates |  RMSE |
Estimation of Gait Mechanics Based on Simulated and Measured IMU Data Using an Artificial Neural Network [68] |  Hip/knee/ankle |  |  30 |  24 Knee arthroplasty |  Optical 3D, Force plates |  RMSE |
Estimation of kinematics from inertial measurement units using a combined deep learning and optimization framework [69] |  Hip/knee/ankle |  |  1000 |  running-related injury |  Optical 3D |  RMSE |
Estimation of lower limb joint angles during walking using extended kalman filtering [70] |  Leg Hip/knee/ankle |  |  3 |  |  Optical 3D |  MAE |
Estimation of the continuous walking angle of knee and ankle (Talocrural joint, subtalar joint) of a lower‐limb exoskeleton robot using a neural network [71] |  Hip/knee/ankle |  |  1 |  |  Other |  MAE |
Estimation of the knee flexion-extension angle during dynamic sport motions using body-worn inertial sensors [72] |  Leg Hip/knee/ankle |  |  7 |  |  Optical 3D |  RMSE |
Evaluation of wearable gyroscope and accelerometer sensor (PocketIMU2) during walking and sit-to-stand motions [15] |  Leg Hip/knee/ankle |  |  1 |  |  Optical 3D |  RMSE |
Feasibility of a Wearable, Sensor-based Motion Tracking System [16] |  |  Arm Arm joints: shoulders/elbow/forearm twist |  8 |  |  Optical 3D |  RMSE |
Feasibility study of inertial sensor-based joint moment estimation method during human movements: A test of multi-link modeling of the trunk segment [17] |  |  Back/trunk/torso |  3 |  |  Optical 3D |  RMSE |
Gait posture estimation using wearable acceleration and gyro sensors [73] |  Hip/knee/ankle |  |  3 |  |  Optical 3D |  RMSE |
Geometrical kinematic modeling on human motion using method of multi-sensor fusion [74] |  Hip/knee/ankle |  |  1 |  |  Other |  RMSE |
Grasp pose estimation in human-robot manipulation tasks using wearable motion sensors [75] |  |  Hand/wrist/fingers |  1 |  |  Other |  Absolute errors |
Hand Motion Measurement using Inertial Sensor System and Accurate Improvement by Extended Kalman Filter [76] |  |  Arm joints: shoulders/elbow/forearm twist Hand/wrist/fingers |  1 |  |  Optical 3D |  RMSE |
Human Arm Motion Tracking by Inertial/Magnetic Sensors Using Unscented Kalman Filter and Relative Motion Constraint [137] |  |  Arm joints: shoulders/elbow/forearm twist Hand/wrist/fingers |  1 |  |  Optical 3D |  RMSE |
Human body model based inertial measurement of sit-to-stand motion kinematics [77] |  |  Back/trunk/torso |  1 |  |  Optical 3D |  RMSE |
Human Motion Kinematics Assessment Using Wearable Sensors [138] |  Hip/knee/ankle |  |  5 |  |  Optical 3D, Force plates |  Absolute errors |
Human motion tracking based on complementary Kalman filter [139] |  Leg |  |  1 |  |  Optical 3D |  RMSE |
Human pose recovery for rehabilitation using ambulatory sensors [78] |  Leg |  |  7 |  Joint replacement inpatients |  Other |  RMSE |
Human pose recovery using wireless inertial measurement units [79] |  Hip/knee/ankle |  |  20 |  |  Optical 3D |  RMSE |
IMU-Based joint angle measurement for gait analysis [80] |  Hip/knee/ankle |  |  1 |  Transfemoral amputee |  Optical 3D |  RMSE |
Inertia-based angle measurement unit for gait assistive device [22] |  Hip/knee/ankle |  |  1 |  |  Goniometer |  |
Inertial Motion Capture Using Adaptive Sensor Fusion and Joint Angle Drift Correction [140] |  Hip/knee/ankle |  |  1 |  |  Optical 3D |  Error |
Inertial sensing in ambulatory back load estimation [81] |  |  Back/trunk/torso |  9 |  |  Optical 3D |  % Error |
Inertial sensor-based knee flexion/extension angle estimation [82] |  Hip/knee/ankle |  |  7 |  |  Optical 3D |  RMSE |
Joint angle estimation with accelerometers for dynamic postural analysis [23] |  Hip/knee/ankle |  |  1 |  |  Other |  RMSE |
Joint Inertial Sensor Orientation Drift Reduction for Highly Dynamic Movements [83] |  |  Back/trunk/torso |  6 |  |  Visual 2D |  MAE |
Knee angle estimation based on IMU data and artificial neural networks [84] |  Hip/knee/ankle |  |  1 |  |  Goniometer |  RMSE |
Knee joint angle measuring portable embedded system based on inertial measurement units for gait analysis [85] |  Hip/knee/ankle |  |  12 |  |  Visual 2D |  RMSE |
Lower body kinematics estimation from wearable sensors for walking and running: A deep learning approach [86] |  Pelvis Hip/knee/ankle |  |  27 |  |  Optical 3D |  MAE |
Lower Extremity Angle Measurement with Accelerometers—Error and Sensitivity [24] |  Hip/knee/ankle |  |  1 |  |  Optical 3D |  Avg. errors |
Magneto: Joint angle analysis using an electromagnet-based sensing method [31] |  |  Arm joints: shoulders/elbow/forearm twist |  13 |  |  Goniometer |  MAE |
Magnetometer robust deep human pose regression with uncertainty prediction using sparse body worn magnetic inertial measurement units [155] |  |  |  |  |  Other |  RMSE |
Monitoring of Hip and Knee Joint Angles Using a Single Inertial Measurement Unit during Lower Limb Rehabilitation [87] |  Hip/knee/ankle |  |  10 |  |  Optical 3D |  RMSD |
Multi-Inertial Sensor-Based Arm 3D Motion Tracking Using Elman Neural Network [114] |  |  Arm joints: shoulders/elbow/forearm twist Hand/wrist/fingers |  1 |  |  Optical 3D |  MAE |
Nonlinear optimization for drift removal in estimation of gait kinematics based on accelerometers [25] |  Leg |  |  10 |  |  Optical 3D |  RMSE |
Novel approach to ambulatory assessment of human segmental orientation on a wearable sensor system [26] |  Leg |  |  8 |  |  Optical 3D |  RMSE |
Online tracking of the lower body joint angles using IMUs for gait rehabilitation [88] |  Hip/knee/ankle |  |  5 |  |  Optical 3D |  RMSE |
Optimization of Inertial Sensor-Based Motion Capturing for Magnetically Distorted Field Applications [141] |  |  Head/neck/scapula Back/trunk/torso Arm |  8 |  |  Optical 3D |  RMSE |
Physical-Sensor and Virtual-Sensor Based Method for Estimation of Lower Limb Gait Posture Using Accelerometers and Gyroscopes [89] |  Leg Hip/knee/ankle |  |  5 |  |  Optical 3D |  RMSE |
Pose estimation by extended Kalman filter using noise covariance matrices based on sensor output [142] |  Hip/knee/ankle |  |  3 |  |  Optical 3D |  RMSE |
Predicting Knee Joint Kinematics from Wearable Sensor Data in People with Knee Osteoarthritis and Clinical Considerations for Future Machine Learning Models [115] |  Hip/knee/ankle |  |  17 |  17 osteoarthritis |  Optical 3D |  RMSE |
Predicting lower limb joint kinematics using wearable motion sensors [90] |  Hip/knee/ankle |  |  8 |  |  Optical 3D |  MAE |
Prediction of lower limb joint angles and moments during gait using artificial neural networks [91] |  Hip/knee/ankle |  |  12 |  |  Optical 3D |  RMSE |
Prediction of lower limb kinetics and kinematics during walking by a single IMU on the lower back using machine learning [27] |  Leg Feet |  |  7 |  |  Optical 3D, Force plates |  %RMSE |
Quasi-real time estimation of angular kinematics using single-axis accelerometers [92] |  Hip/knee/ankle |  |  1 |  |  Optical 3D |  RMSE |
Real-time estimate of body kinematics during a planar squat task using a single inertial measurement unit [93] |  Hip/knee/ankle |  |  8 |  |  Optical 3D |  RMSE |
Real-Time Human Motion Capture Based on Wearable Inertial Sensor Networks [152] |  Hip/knee/ankle Feet |  |  1 |  |  Optical 3D |  RMSE |
Reconstructing an accelerometer-based pelvis segment for three-dimensional kinematic analyses during laboratory simulated tasks with obstructed line-of-sight [28] |  Pelvis |  |  1 |  |  Optical 3D |  RMSE |
Reconstruction of angular kinematics from wrist-worn inertial sensor data for smart home healthcare [94] |  |  Arm |  2 |  |  IMU |  MAE |
Reducing drifts in the inertial measurements of wrist and elbow positions [95] |  |  Arm joints: shoulders/elbow/forearm twist Hand/wrist/fingers |  8 |  |  Optical 3D |  RMSE |
Research on Human Motion Monitoring Method Based on Multi-Joint Constraint Filter Model [143] |  |  |  1 |  |  Goniometer |  RMSE |  Max. error
Rhythmic EKF for pose estimation during gait [96] |  Hip/knee/ankle |  |  3 |  |  Optical 3D |  RMSE |
Rhythmic Extended Kalman Filter for Gait Rehabilitation Motion Estimation and Segmentation [8] |  Hip/knee/ankle |  |  5 |  2 post-stroke |  Optical 3D |  RMSE |
Rigid body motion capturing by means of a wearable inertial and magnetic MEMS sensor assembly-from reconstitution of the posture toward dead reckoning: An application in bio-logging [144] |  Feet |  |  1 |  |  Visual 2D |  MAE |
Robust and Accurate Capture of Human Joint Pose Using an Inertial Sensor [145] |  |  Head/neck/scapula Back/trunk/torso |  14 |  |  Optical 3D & RGB + depth |  RMSE |
Sensorial system for obtaining the angles of the human movement in the coronal and sagittal anatomical planes [97] |  |  Back/trunk/torso Arm |  1 |  |  Other |  RMSE |
Shoulder and elbow joint angle estimation for upper limb rehabilitation tasks using low-cost inertial and optical sensors [98] |  |  Arm joints: shoulders/elbow/forearm twist |  1 |  |  Goniometer |  RMSE |
Shoulder and elbow joint angle tracking with inertial sensors [99] |  |  Arm joints: shoulders/elbow/forearm twist |  8 |  |  Optical 3D |  RMSE |
Synergy-based knee angle estimation using kinematics of thigh [100] |  Hip/knee/ankle |  |  8 |  |  IMU |  RMSE |
System for measurement of joint range of motion using inertial sensors [101] |  Hip/knee/ankle |  |  1 |  |  Goniometer |  MAE |
The head mouse - Head gaze estimation ’In-the-Wild’ with low-cost inertial sensors for BMI use [146] |  |  Head/neck/scapula |  1 |  |  IMU |  RMSE |
The manumeter: A wearable device for monitoring daily use of the wrist and fingers [32] |  |  Hand/wrist/fingers |  7 |  |  Goniometer |  MAE |
The online estimation of the joint angle based on the gravity acceleration using the accelerometer and gyroscope in the wireless networks [102] |  Hip/knee/ankle |  |  1 |  |  Optical 3D |  RMSE |
The use of synthetic IMU signals in the training of deep learning models significantly improves the accuracy of joint kinematic predictions [103] |  Hip/knee/ankle |  |  30 |  17 knee arthroplasty |  Optical 3D |  RMSE |
Three dimensional gait analysis using wearable acceleration and gyro sensors based on quaternion calculations [104] |  Hip/knee/ankle |  |  5 |  |  Optical 3D |  RMSE |
Time coherent full-body poses estimated using only five inertial sensors: Deep versus shallow learning [147] |  |  |  6 |  |  IMU |  MAE |
Towards a portable human gait analysis monitoring system [105] |  Hip/knee/ankle |  |  3 |  |  Optical 3D |  RMSE |
Towards kinematically constrained real time human pose estimation using sparse IMUs [148] |  |  |  15 |  |  IMU |  MAE |
Training Data Selection and Optimal Sensor Placement for Deep-Learning-Based Sparse Inertial Sensor Human Posture Reconstruction [29] |  |  |  4 |  |  IMU |  MAE |
Ubiquitous human upper-limb motion estimation using wearable sensors [149] |  |  Arm joints: shoulders/elbow/forearm twist |  4 |  |  Optical 3D |  RMSE |
Unrestrained measurement of arm motion based on a wearable wireless sensor network [30] |  |  Arm joints: shoulders/elbow/forearm twist |  1 |  |  Goniometer |  MAE |
Upper limb joint angle measurement in occupational health [150] |  |  Arm joints: shoulders/elbow/forearm twist |  1 |  |  Visual 2D |  Typical deviation |  MAE
Upper limb joint angle tracking with inertial sensors [106] |  |  Arm joints: shoulders/elbow/forearm twist |  1 |  |  Optical 3D |  Corr. coeff. |
Use of multiple wearable inertial sensors in upper limb motion tracking [107] |  |  Arm joints: shoulders/elbow/forearm twist Hand/wrist/fingers |  4 |  |  Optical 3D |  RMSE |
Validation of a low-cost inertial exercise tracker [108] |  Leg Hip/knee/ankle |  |  7 |  |  Optical 3D |  RMSE |
Visual and quantitative analysis of lower limb 3D gait posture using accelerometers and magnetometers [154] |  Hip/knee/ankle |  |  5 |  |  Optical 3D |  RMSE |  Corr. coeff.
Visual estimation of lower limb motion using physical and virtual sensors [151] |  Hip/knee/ankle |  |  3 |  |  Optical 3D |  RMSE |  Corr. coeff.
Wearable inertial sensor system towards daily human kinematic gait analysis: Benchmarking analysis to MVN BIOMECH [109] |  Hip/knee/ankle |  |  11 |  |  IMU |  RMSE |

## Acknowledgment

This work was supported by Junta de Comunidades de Castilla La Mancha
(FrailAlert project, SBPLY/21/180501/000216), the Spanish Ministry of Science
and Innovation (INDRI project, PID2021-122642OB-C41) , Comunidad de Madrid
(RACC project, CM/JIN/2021-016) and NEXTPERCEPTION European Union project
funded by ECSEL Joint Undertaking (JU), under grant agreement No.876487
(ECSEL-2019-2-RIA).

## References