Calibration-free gait assessment by foot-worn inertial sensors [original]

ORIGINAL RESEARCH

published: 04 November 2021

doi: 10.3389/fdgth.2021.736418

Frontiers in Digital Health | www.frontiersin.org 1November 2021 | Volume 3 | Article 736418

Edited by:

Mohamed Elgendi,

University of British Columbia, Canada

Reviewed by:

Thibault Bernard Warlop,

Catholic University of Louvain,

Belgium

Matthew R. Patterson,

Data Scientist Shimmer Research Ltd

Dublin, Ireland

*Correspondence:

Daniel Laidig

[email protected]

Specialty section:

This article was submitted to

Connected Health,

a section of the journal

Frontiers in Digital Health

Received: 05 June 2021

Accepted: 24 September 2021

Published: 04 November 2021

Citation:

Laidig D, Jocham AJ,

Guggenberger B, Adamer K,

Fischer M and Seel T (2021)

Calibration-Free Gait Assessment by

Foot-Worn Inertial Sensors.

Front. Digit. Health 3:736418.

doi: 10.3389/fdgth.2021.736418

Calibration-Free Gait Assessment by

Foot-Worn Inertial Sensors

Daniel Laidig1*, Andreas J. Jocham 2, Bernhard Guggenberger 2, Klemens Adamer 3,

Michael Fischer3,4,5 and Thomas Seel6

1Control Systems Group, Technische Universität Berlin, Berlin, Germany, 2Institute of Physiotherapy, FH JOANNEUM

University of Applied Sciences, Graz, Austria, 3Vamed Rehabilitation Center Kitzbuehel, Kitzbuehel, Austria, 4Ludwig

Boltzmann Institute for Rehabilitation Research, Vienna, Austria, 5Hannover Medical School MHH, Clinic for Rehabilitation

Medicine, Hannover, Germany, 6Department Artificial Intelligence in Biomedical Engineering, Friedrich-Alexander-Universität

Erlangen-Nürnberg, Erlangen, Germany

Walking is a central activity of daily life, and there is an increasing demand for objective

measurement-based gait assessment. In contrast to stationary systems, wearable inertial

measurement units (IMUs) have the potential to enable non-restrictive and accurate gait

assessment in daily life. We propose a set of algorithms that uses the measurements

of two foot-worn IMUs to determine major spatiotemporal gait parameters that are

essential for clinical gait assessment: durations of five gait phases for each side as well

as stride length, walking speed, and cadence. Compared to many existing methods,

the proposed algorithms neither require magnetometers nor a precise mounting of the

sensor or dedicated calibration movements. They are therefore suitable for unsupervised

use by non-experts in indoor as well as outdoor environments. While previously proposed

methods are rarely validated in pathological gait, we evaluate the accuracy of the

proposed algorithms on a very broad dataset consisting of 215 trials and three different

subject groups walking on a treadmill: healthy subjects (n=39), walking at three

different speeds, as well as orthopedic (n=62) and neurological (n=36) patients,

walking at a self-selected speed. The results show a very strong correlation of all gait

parameters (Pearson’s rbetween 0.83 and 0.99, p<0.01) between the IMU system

and the reference system. The mean absolute difference (MAD) is 1.4 % for the gait

phase durations, 1.7 cm for the stride length, 0.04 km/h for the walking speed, and

0.7 steps/min for the cadence. We show that the proposed methods achieve high

accuracy not only for a large range of walking speeds but also in pathological gait as it

occurs in orthopedic and neurological diseases. In contrast to all previous research, we

present calibration-free methods for the estimation of gait phases and spatiotemporal

parameters and validate them in a large number of patients with different pathologies.

The proposed methods lay the foundation for ubiquitous unsupervised gait assessment

in daily-life environments.

Keywords: inertial sensors, IMU, human motion analysis, gait analysis, gait assessment, gait phases,

rehabilitation, walking

Laidig et al. Gait Assessment by Inertial Sensors

1. INTRODUCTION

Walking is a central activity of daily life, and restrictions of

this ability lead to a reduction in the quality of life (1,2).

Therefore, gait analysis is an important tool in different medical

and therapeutic fields (3,4). The measurement of various gait

characteristics can either facilitate diagnosis or be used to

track the progress of rehabilitation. Gait can be measured by

spatial (e.g., step or stride length) and temporal (e.g., stride

time, cadence) parameters, relative durations of gait phases, and

kinematic and kinetic gait variables (5). These parameters are

used to quantify gait deviation in both clinical practice and

research, and their use varies with the medical field, the research

question, and the analysis options. While gait assessment in

clinical practice is mostly based on visual observation by medical

experts (6), it is desirable to support expert knowledge and

time by objective measurements. This is also important because

relevant gait changes are often too subtle to be detected by the

naked eye (7).

Traditionally, sensor-based gait assessment is performed with

stationary systems like marker-based optical motion tracking,

instrumented treadmills, or pressure-sensitive walkways (6,8).

Besides being expensive, one major drawback of those systems

is that they are limited to a small capture space or require the

subject to walk on a treadmill (4,9–12). Furthermore, the use of

walking aids is often not possible or restricted in combination

with such systems.

A promising, more ambulatory, and less restrictive

alternative is inertial gait analysis, i.e., gait analysis with

inertial sensor technology. Lightweight and battery-powered

inertial measurement units (IMUs) are used, which transmit the

data wirelessly.

The transition from expensive stationary systems to small

wearable sensors opens up possibilities that go beyond replacing

the measurement technology used for gait assessment in a clinical

setting. Integrating objective long-term gait monitoring in day-

to-day life—as illustrated in Figure 1—could provide more

powerful tools for clinicians to help patients in rehabilitation

but also to gain further insights into disease progression.

Furthermore, non-obtrusive wearable plug-and-play systems

facilitate applications in neuroprosthetics (13) or exoskeletons

and can be used to provide biofeedback (14). In the last years,

wireless battery-powered IMUs have become smaller, lighter,

more accurate, and at the same time cheaper and more energy-

efficient, and it is to be expected that this development is going

to continue. For those new trends, it is important to develop

methods that can provide a wide variety of gait parameters that

are useful to medical experts. At the same time, the methods

need to be robust so that the system can be used by patients in

unsupervised settings, outdoors as well as indoors.

It has been shown by previous contributions (15–17) that

major gait parameters can be determined with two IMUs that are

placed on the feet or the shoes, as illustrated in Figure 1. This

includes stride length, gait phase durations (e.g., stance and swing

percentage), and also the cadence and walking speed.

Our aim is to propose methods for gait assessment that meet

the requirements for day-to-day life monitoring in unsupervised

settings and that are validated on a broad group of subjects

including patients with various gait pathologies. The proposed

methods do not assume any fixed orientation of the sensor with

respect to the foot and do not require the subject to perform

dedicated calibration movements. Furthermore, magnetometers

are not used since the magnetic field is known to be severely

disturbed in indoor environments (18). This makes the use

of inertial gait analysis easy and practical in clinical settings

and facilitates future applications of ubiquitous gait analysis in

home environments.

The remainder of the article is structured as follows. In

section 2, we briefly review existing methods for IMU-based

spatiotemporal gait parameter estimation. In section 3, we

describe the proposed methods, which we then validate in section

4 using experimental data of 98 orthopedic and neurological

patients, as well as 39 healthy subjects walking at different

speeds. The results are discussed in section 5, and section 6

provides conclusions.

2. BRIEF REVIEW OF IMU-BASED

SPATIOTEMPORAL GAIT PARAMETER

ESTIMATION

Several methods have been proposed that employ inertial sensors

to obtain spatiotemporal gait parameters. In the following, we

present a brief overview of the current state of the art and

summarize the different hardware setups that are used, which

parameters are calculated, and how the methods were validated.

Table 1 categorizes 23 publications that provide a range of

examples for the variety of existing approaches in the estimation

of spatiotemporal gait parameters with inertial sensors.

There are different hardware setups, based on the number

of inertial sensors and their placement. The chosen setup has

an impact on which and how many parameters can be derived

from the measured data. The most commonly used setup consists

of two IMUs. As shown in Table 1, sensors are typically placed

on the feet or shoes and sometimes on the shank. This setup

is occasionally extended by adding a third sensor on the pelvis

or lumbar spine (34,35). Note that it has even been shown

that temporal gait events can be obtained from a single IMU at

the pelvis (38), but the potential for extracting further spatial

parameters is limited. Full (lower) body motion tracking opens

up additional possibilities, as demonstrated with 7 IMUs on the

lower body and pelvis in (37) and with 8–15 IMUs in (36).

Another, less common, option consists of combining inertial

sensors with further measurement devices, e.g., a camera on

one foot and LEDs on the other foot to facilitate the direct

measurement of relative positions (39).

Some methods require that a known orientation of the sensor

axes with respect to the anatomical foot axes has to be ensured

by precise placement. Many methods in the literature are based

on such assumptions, including (13,15–17,22,23,25,26,30–

33). In practice, however, ensuring a precise placement is a

challenge, especially in non-supervised application scenarios and

during activities of daily life. Alternatives are to develop methods

that are agnostic to the sensor-to-segment orientation—e.g., by

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Laidig et al. Gait Assessment by Inertial Sensors

FIGURE 1 | Inertial gait analysis can be realized with two miniaturized IMUs on the shoes, enabling daily-life assessment outside of laboratory environments. From the

raw sensor data, orientation, gait phases, and velocity and position trajectories can be estimated. Parameters commonly used in gait analysis, such as stride length,

cadence, and walking speed, can easily be derived from this.

only relying on signal norms—or to determine this orientation

in a process commonly called anatomical calibration (40). For

setups with more sensors, there are recently developed methods

that facilitate automatic anatomical calibration by exploiting

kinematic constraints of the respective joints without requiring

the subject to perform precise calibration movements (41,42).

For those setups, the linking of the sensors to the body segments

poses another challenge to a plug-and-play approach, which can

be solved by automatic pairing methods (43).

The calculation of spatiotemporal gait parameters is usually

implemented in a two-stage approach. In a first step, gait events

and corresponding gait phases are detected. In a second step,

spatial parameters are calculated.

Existing methods vary in the set of gait events or phases that

are detected. In many cases, the focus is only on the separation

between stance and swing (cf. Table 1), although sometimes

additional events, such as mid-swing (33), are also detected. It is

also common to detect four events that occur during the gait cycle

and are only defined by the ipsilateral (same) foot. Those events

are initial contact, full contact, heel rise, and toe-off, although

the terminology varies. Despite being common practice in gait

analysis (5,44), employing bilateral information, i.e., combining

information from both feet to define the gait phase, is far less

common in IMU-based gait analysis. One example is (36) in

which single and double limb support durations are calculated.

There are various approaches for detection of gait events

using inertial sensors. It has been shown that exploiting features

of the angular rate signal in the sagittal plane is sufficient to

achieve reliable gait event detection (16,22,25,30,32). Many

other methods use both accelerometers and gyroscopes and

detect characteristic signal features in the inertial sensor data,

including (13,15,17,19–21,23,31,33). Sometimes automatic

adaption mechanisms are used to adjust thresholds based on

TABLE 1 | Overview of IMU-based spatiotemporal gait parameter estimation

literature.

Employed sensor setup

2 IMUs on feet/shoes (15,17,19–31)

2 IMUs on shank (13,16,27,30,32,33)

3 or more IMUs (34–37)

Detected gait phases

Stance/swing (13,16,17,22,23,27,30,32,33,35,37)

4 unilateral events (15,19–21,25,26)

Single/double support (29,36)

Ground truth used for evaluation

Optical motion capture (20,25,26,28,29,31,34,37)

Pressure-sensitive walkways (16,17,23,32,33,35)

Instrumented treadmills (24,27)

Pressure insoles (15,30)

Others/none (19,21,22,36)

Non-healthy subjects included in evaluation

None (healthy only) (21,22,24–28,34,36,37)

≤20 (20,30,31,33,35)

>20 (15–17,23,29,32)

A total of 23 publications that describe estimation of spatiotemporal gait parameters with

IMUs are categorized based on sensor setup, detected gait phases, and the ground truth

and number of non-healthy subjects for evaluation.

the subject’s walking style (19–21,33). An alternative to the

signal-based methods is to rely on a kinematic model to detect

gait events (36,37). Machine learning methods, often based

on hidden Markov models (26,35), are also used for event

detection [cf. (45)].

In addition to the detection of gait events, spatial parameters

such as stride length and walking speed are often calculated.

Those parameters are obtained by either signal integration,

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Laidig et al. Gait Assessment by Inertial Sensors

human gait models, or by machine learning methods (46).

By far the most common approach is numerical strapdown

integration of the accelerations (16,17,22,27,28,31,32,37).

The cyclic nature of gait and the fact that there is frequent

ground contact are exploited to correct for drift that is due

to double integration. It has been shown that Fourier-based

integration is an alternative to numerical integration (34), that

spatial parameters can be obtained from kinematic models (27,

36), and that convolutional neural networks can also be used to

estimate spatial parameters (23).

Most publications focus on common spatiotemporal

parameters such as stride length, walking speed, and cadence.

Other than those spatiotemporal parameters, there is a multitude

of spatiotemporal gait parameters that are relevant in a clinical

context for various pathologies (6). Examples that can be

estimated using inertial sensors include step width (37), swing

width (31,37), incline (22), and foot clearance (47).

Some publications (13,19–21,25,33) focus on real-

time detection of events, e.g., to trigger functional electrical

stimulation (FES). While the approaches used are usually similar

to the ones used in offline gait analysis, this typically implies a

focus on minimizing the detection delay rather than the accuracy

of the reported values.

As shown in Table 1, evaluation is often performed with

marker-based optical motion capture as ground truth. Systems

based on the detection of pressure, such as pressure-sensitive

walkways, instrumented treadmills, and pressure insoles, are a

common alternative. In some cases, no validation with respect

to a gold standard is performed. Instead, the settings of a

(calibrated) treadmill are used for walking speed and incline

(22), a manually counted number of steps is combined with the

detection of irregularities (21), validation is performed by visual

inspection of the results (19), or the focus is only on test-retest

reliability (36).

Even though it has been shown that the accuracy of gait

analysis methods decreases when applied to non-healthy subjects

(45), the evaluation of inertial gait analysis methods is often only

based on healthy subjects. When data obtained from non-healthy

subjects is part of the evaluation, the number of subjects is often

small, for example five transfemoral amputees (20), 10 stroke

patients (33), 10 hemiparetic patients and 10 Huntington’s

disease patients (35), or 10 patients with Parkinson’s

disease (31).

To the best of our knowledge, few publications (15–17,23,29,

32) exist which propose methods for IMU-based spatiotemporal

gait parameter estimation and validate the methods on a larger

set of subjects with gait pathologies. In the following, we briefly

summarize those publications.

In (15), sensors are placed on the forefoot in a known

orientation, and four different unilateral gait events are detected

based on features of the angular velocity in the sagittal plane, the

norm of the accelerometer signal, and the derivative of angular

velocity norm. Using pressure insoles as reference, the method is

validated on 10 healthy and 32 orthopedic subjects.

The commercial Gait Up system is evaluated in (29) with 25

subacute stroke patients as subjects and marker-based optical

motion capture as reference.

Gait events and stride length are calculated in (16) based

on shank-mounted IMUs. Events are detected based on the

angular rate in the sagittal plane, and stride length is obtained

via double integration of the accelerations. The latter relies on

the proprietary orientation estimation algorithm provided by

the sensor manufacturer. Experimental evaluation is performed

using the GAITRite pressure-sensitive walkway as reference on

10 healthy elderly and 30 non-healthy subjects.

In (32), the same method is validated on a much larger

group of subjects, consisting of 236 community-living older

adults, including 31 mild cognitive impaired subjects and 125

Parkinson’s disease patients.

In (17), IMUs are placed laterally on the shoe in a fixed

orientation, stance, and swing durations are calculated based on

characteristic signal features, and the stride length is obtained via

double integration. The method is evaluated using a large data

set of 101 geriatric inpatients, with reference data obtained from

a GAITRite pressure-sensitive walkway.

Using the same gait event detection method and the same

data set for evaluation as (17), Hannink et al. (23) estimates

stride length, stride width, mediolateral change in foot angle, heel

contact times, and toe contact times using deep convolutional

neural networks.

In summary, the main shortcoming of existing approaches

for the vision of plug-and-play ambulatory gait analysis is that

most methods—especially those with broad validation—require

a precise attachment of the sensor to the subject’s foot. Some

methods only focus on gait events and do not provide spatial

parameters, and some methods rely on proprietary algorithms of

the sensor manufacturers. Furthermore, very few of the proposed

methods are validated on a large group of subjects with diverse

gait pathologies.

In the following section, we propose a set of methods that

combine the valuable achievements of existing methods with

additional features that overcome the remaining limitations.

3. METHODS

In the following, we propose a set of methods to determine

gait parameters from two IMUs attached to the foot. The

proposed methods are based on the following assumptions and

requirements: An IMU is attached to each foot (or shoe) in an

arbitrary orientation. This implies that the proposed method does

not make any assumption about the orientation of the sensor

coordinate system, which means it does not require any specific

sensor axis to be aligned with an anatomical or functional axis

of the foot. In order to avoid artifacts caused by toe or ankle

motions, and also to not limit the subject’s freedom of movement,

we propose to attach the IMU on the instep, i.e., the dorsal

side of the midfoot. We obtain the accelerometer and gyroscope

readings of both IMUs at a fixed sampling rate (typically in the

range 50–1,000 Hz). We assume that data for several steps is

processed at once, which allows us to employ non-causal signal

processing to increase the accuracy compared to sample-by-

sample real-time capable methods. This processing can either be

performed in batches while the subject is walking, e.g., for use

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Laidig et al. Gait Assessment by Inertial Sensors

FIGURE 2 | Overview of the proposed modular set of methods to determine spatiotemporal gait parameters from foot-worn IMUs. While gait phase durations and

cadence are determined from gait events, stride length and walking speed are derived from a position trajectory obtained via piecewise strapdown integration of the

acceleration.

in biofeedback applications, or after the recording is completed.

During the recording, the subject walks either on a treadmill or

an indoor or outdoor ground.

The set of methods that we propose is explained in the

following subsections, and the presentation is structured as

follows. Separately for each foot, we use the recorded sensor

data to separate phases in which the foot is in full contact with

the ground from phases in which the foot moves, i.e., we detect

when strides take place (section 3.3). For each detected stride,

we then detect toe-off (section 3.5) and initial contact (section

3.6). The gait events from the ipsilateral and contralateral foot

are combined to define gait phases. We calculate the relative

duration of each gait phase and the cadence (section 3.7). We

then estimate the sensor orientation by sensor fusion of the

gyroscope and accelerometer readings (section 3.8) and double-

integrate the acceleration to obtain a position trajectory (section

3.9). From this position trajectory, we obtain the stride length and

the walking speed (section 3.10). Figure 2 provides an overview

of the proposed set of methods.

In the remainder of this section, we define parameters used by

the method. For an overview of those parameters and proposed

values, please refer to Table 2 in section 4. Our aim is to

define the parameters in a way that they are not sensitive to

different gait styles or velocities. In section 4, we demonstrate

that this approach works by only employing one common set of

parameters for validation on a very broad data set with healthy

and non-healthy subjects walking at different speeds.

3.1. Notation

Denote the accelerometer readings a(tk)∈R3and the gyroscope

readings ω(tk)∈R3, sampled at times tk=kTs,k∈ {1 . . N},

Ts∈R>0.

In the following, all times twith any index are multiples of

Ts. If any calculation yields a time that is not a multiple of Ts,

we assume that this value is rounded to the nearest multiple of Ts

and do not explicitly write this for the sake of a compact notation.

Furthermore, any summation over τshould be interpreted as

a summation with a non-integer step size of Ts, i.e., we simply

write Pt2

τ=t1x(τ) instead of the longer but mathematically precise

notation Pk2

k=k1x(tk), k1=t1

Ts,k2=t2

Ts.

Unit quaternions in vector notation are used to represent

rotations and orientations (48). When a quaternion is used

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Laidig et al. Gait Assessment by Inertial Sensors

to represent the sensor orientation, it is the rotation from an

inertial reference frame with the z-axis pointing up (and arbitrary

heading) to the coordinate system of the sensor. In the context

of quaternion multiplication, which we denote by ⊗, three-

dimensional vectors are implicitly regarded as quaternions with

zero real part.

Furthermore, v⊺denotes the transpose of the vector v.

3.2. Gait Events and Gait Phases

According to standard literature (44) and as illustrated in

Figure 3A, the gait cycle starts at initial contact. Each stride can

be separated into stance and swing. Stance consists of the gait

phases loading response,mid-stance,terminal stance, and pre-

swing. Swing can be separated into initial swing,mid-swing, and

terminal swing. The combination of mid-stance and terminal

stance is called single limb support and corresponds to the swing

phase of the contralateral foot. In standard literature (44), the

initial contact is commonly considered to be a very short gait

phase with a duration of 2 %. As it is common practice in IMU-

based gait analysis (15,19,21,26), we define the initial contact

as an event without duration. Note that sometimes the initial

contact is also called foot strike (26) or heel strike (15).

The separation between stance and swing and the separation

of stance into loading response, mid-stance, terminal stance, and

pre-swing is defined based on three events that describe a change

of ground contact of the feet: initial contact,heel rise, and toe-off.

In contrast, the separation of swing into initial swing, mid-swing,

and terminal swing is based on positional information of the feet

and on the tibia orientation. The gait phases are defined based

on bilateral events, i.e., the gait phase of the ipsilateral foot is

not only described based on the events of the same (ipsilateral)

foot but also based on toe-off and initial contact of the other

(contralateral) foot.

We will now describe how we determine five of those

gait phases (swing and the four sub-phases of stance) using

IMUs in a two-step approach. First, we detect four gait events

independently for each foot. We then use this gait event cycle of

both feet to derive gait phases for each foot.

To this end, for each stride i∈ {1 . . M}, we define

the following events that we want to detect independently for

the right and left foot from the raw measurement data of the

corresponding IMU:

•initial contact – tic,i

•full contact – tfc,i

•heel rise – thr,i

•toe-off – tto,i.

Note that in addition to the three events used to define gait phase

transitions in Figure 3A, we introduce an event called full contact

that indicates that the foot is in full contact with the ground.

For various processing steps, such as zero-velocity updates and

position integration, we further define a rest instant trest,iat the

middle of the foot flat phase, i.e.,

trest,i:=1

2tfc,i+thr,i. (1)

See Figure 3B for a plot of the raw accelerometer and gyroscope

data measured during one stride along with a graphical

representation of the gait event cycle defined by the introduced

events. In the following subsections, we will describe in detail

how we determine those time instants from the raw sensor data.

After having determined the gait events for both feet, we use

the gait event cycles from both feet to determine the gait phase

according to the commonly used definitions by (44). As shown in

Figure 4, finite automata for the gait phases of the left and right

foot are each driven by the gait event cycles of both feet.

Since time instances from both sensors are used for the

definition of the gait phase transitions, both feet must be

equipped with sensors, and precise time synchronization is

required. However, note that the separation into stance and

swing directly follows from the gait event cycle (as shown

in Figure 4) and is independent of the contralateral foot.

Therefore, we can determine stance and swing regardless of

the synchronization between the sensors. This is also useful if

only one foot is equipped with a sensor and facilitates on-chip

data processing.

Note that the three sub-phases of stance in the gait event

cycle hold further information that is not directly captured by

the standard gait phase definitions as given in Figure 3A. We

denote the phase from tfc,ito thr,i, in which the foot is fully

on the ground, as foot flat. Note that the other two sub-phases

of the stance phase, tic,ito tfc,iand thr,ito tto,i, are sometimes

called loading response and pre-swing (19,21) but do not

correspond to the phases with the same name as defined in

standard literature (44).

Furthermore, as also shown in Figure 4, time-synchronized

events from both feet also allow for the distinction of double

support,single support, and zero-contact phases, which occur only

during running (44).

3.3. Foot Flat Detection

As the first step of gait phase detection, the phases in which

the foot is fully on the ground (foot flat) are detected.

When the foot is fully on the ground, the Euclidean norm

of the accelerometer readings will be close to 9.81 m/s2,

and the norm of the gyroscope readings will be close to

zero. During a stride, we typically will see an increase in

the signal norms. However, it is possible that during the

motion phase there are long periods with only small changes

of velocity or small rotations. To obtain a robust stride

detection, we, therefore, first find activity using either the

accelerometer or the gyroscope readings and then combine

this information.

For an acceleration-based rest signal ra(tk), we consider the

absolute difference of the norm from 9.81 m/s2,

a(tk):=ka(tk)k − 9.81, (2)

and perform acausal thresholding using a threshold ath and

a hysteresis factor haby applying hysteresis in forward and

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Laidig et al. Gait Assessment by Inertial Sensors

FIGURE 3 | (A) Definition of gait phases as used in standard literature [cf. (44)], and transitions based on gait events of the ipsilateral and contralateral foot. (B) Raw

accelerometer and gyroscope sensor readings and representation of the gait event cycle with a staircase-shaped signal. We define time instants tic,i,tfc,i,thr,i,tto,ithat

mark characteristic events and a rest instant trest,iin the middle of the phase in which the foot is fully on the ground (foot flat).

backward direction, i.e.,

r∗

a(tk):=









1a(tk)>(1 +ha)ath

0a(tk)<(1 −ha)ath

ra(tk−1) otherwise

(3)

ra(tk):=









1r∗

a(tk)=1

0a(tk)<(1 −ha)ath

ra(tk+1) otherwise

(4)

with r∗

a(0) =0 and ra(tN)=r∗

a(tN). In the resulting signal,

zero-phases shorter than T0,min are set to one, and afterward,

one-phases shorter than T1,min are set to zero.

The same acausal thresholding with the removal of short

phases is applied to the gyroscope norm signal ω(tk):= kω(tk)k

using a threshold ωth and hysteresis factor hω, which yields

a gyroscope-based rest signal rω(tk). See Figure 5A for an

illustration of the thresholding method.

Both rest signals, ra(tk) and rω(tk), are combined into r(tk),

which is set to one if at least one of the two signals is one.

Afterward, zero-phases shorter than T0,min are set to one, and

then one-phases shorter than 2T1,min are set to zero. This process

is illustrated in Figure 5B. Each zero-to-one transition of the

resulting signal marks a heel rise thr,i, and each one-to-zero

transition marks a full contact tfc,i+1.

3.4. Automatic Threshold Adaptation

A common issue with thresholding approaches is that the

thresholds have to be adapted based on gait velocity and

also other gait and sensor characteristics (19,20). Therefore,

instead of performing the thresholding of the accelerometer and

gyroscope norm using manually tuned thresholds ath and ωth,

we propose an algorithm that automatically determines these

thresholds for each trial based on the measured data.

The threshold ath is determined using an iterative algorithm

similar to (49), with lbeing the iteration index and wabeing a

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FIGURE 4 | Derivation of clinically relevant gait phases from the gait event cycles. Following standard literature (44), events from both the left foot (filled arrows) and

the right root (outlined arrows) are necessary to define the gait phase of each foot. Furthermore, support phases based on the number of feet that are in contact with

the ground can be defined based on the gait events.

weighting parameter:

ath,0 =1

2max

tk∈[t1,tN]a(tk)+min

tk∈[t1,tN]a(tk)(5)

T+= {tk∈[t1,tN]|a(tk)>ath,l}(6)

T−= {tk∈[t1,tN]|a(tk)≤ath,l}(7)

ath,l+1=wa

|T−|X

tk∈T−

a(tk)+1−wa

|T+|X

tk∈T+

a(tk). (8)

We perform 200 iterations to ensure convergence, i.e., ath :=

ath,200.Figure 6 illustrates the result of this process. Further, we

define a lower bound ath,min for this threshold.

Similarly, we determine the threshold ωth based on the

gyroscope norm ω(tk) and a weighting factor wω.

3.5. Toe-Off Detection

After determining heel rise and full contact, we want to detect

the beginning of the swing phase, i.e., the toe-off. During toe-off,

the foot first rotates approximately along the mediolateral axis

as the heel rises, then loses contact with the ground and rotates

in the opposite direction. An inertial sensor attached to the foot

cannot directly measure when the foot fully loses contact with

the ground, in contrast to, e.g., pressure-sensitive walkways. Note

that the accuracy of toe-off detection using pressure sensors also

depends on calibration and the chosen thresholds (12).

As rotation can be measured precisely with IMUs, we exploit

the fact that the direction of rotation of the foot changes when

transitioning from the phase in which the heel rises while the

toe stays on the ground to the phase in which the toe leaves the

ground. This approach is commonly used in existing literature, as

detailed in section 2. However, most methods directly rely on the

angular rate measured in the sagittal plane and thereby require at

least one sensor axis to be well-aligned with a functional axis of

the foot.

To be independent of the sensor orientation and also to obtain

a reliable detection if the subject exhibits strong inversion or

eversion during toe-off, we define a signal called tilt-rate Ŵi(tk),

from each heel rise thr,ito the subsequent full contact tfc,i+1, as

Ŵi(tk):=ω(tk)⊺Ptk

τ=thr,iω(τ)



Ptk

τ=thr,iω(τ)



,tk∈[thr,i,tfc,i+1]. (9)

The rationale behind the definition of the tilt-rate Ŵi(tk) is to

identify the main axis of rotation since the last heel rise and

compute the current rate of rotation around this main axis. This

enables us to detect a zero-crossing of the main rotation without

making any assumptions on the orientation of the sensor with

respect to the foot.

In general, the tilt-rate Ŵi(tk) will exhibit a change of sign after

a distinct peak (cf. Figure 7A). As there might be noise, leading to

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A B

FIGURE 5 | (A) Illustration of the thresholding algorithm. Acausal hysteresis and the removal of short phases ensure the robust detection of the desired rest phase.

(B) Illustration of the combination of rω(tk) and ra(tk) into r(tk). By using the OR combination of the accelerometer- and gyroscope-based signals, we are able to robustly

detect when the foot is not fully on the ground.

FIGURE 6 | Illustration of the result of the automatic thresholding algorithm for

a short segment of accelerometer data. The threshold ath is chosen such that

the mean of the values above and the mean of the values below are in a

certain proportion.

frequent sign changes right after thr,i, as well as large peaks later

during the stride, we propose the following strategy to robustly

determine the sign change of interest:

During the first half of the movement phase, let Ŵmax,idenote

the maximum value of Ŵi(tk), i.e.,

Ŵmax,i:=max

tk∈[thr,i,1

2(thr,i+tfc,i+1)]

Ŵi(tk). (10)

We then find the first time instant for which Ŵi(tk)≥1

2Ŵmax,i.

Starting from this time instant, we find the first time instant at

which Ŵi(tk)≤0. We assume this time instant to be the toe-

off tto,i, i.e., the start of the swing phase. Figure 7A illustrates

this process.

Note that tto,iis defined based on a feature of the rotation

of the foot and not directly as the lift-off of the toes.

Using the maximum of the tilt rate (or any weighted average

of the maximum and zero-crossing time instant) are also

plausible approaches.

3.6. Initial Contact Detection

The initial contact marks the beginning of the loading response

and can be detected by the jerk, i.e., the change of acceleration,

caused by the foot touching the ground. We calculate the jerk

using the first-order backward difference approximation, i.e.,

j(tk):=1

Tsa(tk)−a(tk−1). (11)

For every stride, we only consider a sub-window of the phase

between toe-off and the beginning of the subsequent foot-flat

phase and denote the start time of this window as twin,i:=

jwintto,i−1+(1 −jwin)tfc,i,jwin ∈[0, 1]. In this time window, we

first determine the maximum value of the jerk norm, i.e.,

jmax,i:=max

tk∈[twin,i,tfc,i]kj(tk)k. (12)

We then mark the first time instant in this window with kj(tk)k ≥

jthjmax,ias the start of the loading response tic,i. See Figure 7B for

an illustration of the initial contact detection.

3.7. Stride and Gait Phase Durations and

Cadence

For each detected stride, we calculate the stride duration as the

duration from one initial contact to the subsequent initial contact

of the same foot, i.e.,

Tstride,i:=tic,i+1−tic,i. (13)

For each detected stride, the duration of the swing phase

is the time between toe-off and initial contact of the

subsequent stride, i.e.,

Tswing,i:=tic,i+1−tto,i. (14)

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A B

FIGURE 7 | Detection of toe-off and initial contact events that define the swing phase. (A) Illustration of the toe-off detection. Between heel rise and full contact, the

tilt rate might exhibit multiple local maxima and zero-crossings. For a robust detection of the correct zero-crossing, we first find the maximum value during the first half

of the phase from thr,ito tfc,i+1and search for the first zero-crossing after the tilt rate has reached half of this maximum. (B) Illustration of the initial contact detection

based on the jerk norm. Note how the jerk norm reflects the sudden change when the foot touches the ground much better than the accelerometer norm signal a(tk).

The stance duration is the remaining duration of the stride:

Tstance,i:=Tstride,i−Tswing,i. (15)

Since relative gait phase durations are easier to

interpret, we calculate

Tswing,rel,i:=Tswing,i

Tstride,i

, (16)

Tstance,rel,i:=Tstance,i

Tstride,i

. (17)

Similarly, for every stride we calculate relative gait phase

durations for loading response Tlr,rel,i, single limb support

Tsl,rel,i, terminal stance Tts,rel,i, and pre-swing Tps,rel,i, based on

the bilateral gait phases as defined in Figure 3A. Note that,

analogously, we can also calculate absolute and relative durations

for all other gait phases defined in Figure 3A.

To calculate the cadence, we multiply the inverse of the stride

duration by two in order to express the cadence as the number of

steps per minute instead of strides per minute, i.e.,

ci:=2

Tstride,i

. (18)

3.8. Orientation Estimation

By fusing the gyroscope and accelerometer measurements, we

obtain an estimate of the sensor orientation with respect to a

global frame that has a vertical z-axis and an arbitrary heading.

Starting with an arbitrary initial orientation qω(0), e.g.,

1 0 0 0T, we perform gyroscope strapdown integration

qω(tk):=qω(tk−1)⊗hcos Ts

2kω(tk)kω⊺(tk)

kω(tk)ksin Ts

2kω(tk)ki⊺.

(19)

Using this orientation, we transform the measured acceleration

into a (slowly drifting) inertial frame, i.e.,

aω(tk):=qω(tk)⊗a(tk)⊗qω(tk)−1. (20)

In the rotating sensor frame, the gravitational acceleration can

point in different directions depending on sensor orientation.

In the inertial frame, however, the gravitational acceleration will

point in (almost) the same direction regardless of the sensor

orientation, and, when integrating, acceleration and deceleration

will cancel out. Exploiting this property, we low-pass filter each

component of aω(tk) by applying a moving average filter with a

window length of Tain forward and reverse direction. Assuming

that the change of velocity over the filter window length is

small, the resulting filtered acceleration will be dominated by

the gravitational acceleration. This filtered acceleration aω,f(tk) is

then transferred back to the sensor frame

af(tk):=qω(tk)−1⊗aω,f(tk)⊗qω(tk). (21)

We then correct the inclination of the gyroscope strapdown

integration quaternion qω(tk) by using the filtered acceleration

as a vertical reference. To this end, we transform the filtered

acceleration into the global frame

ar(tk):=qa(tk−1)⊗qω(tk)⊗af(tk)⊗(qa(tk−1)⊗qω(tk))−1, (22)

with qa(0) :=1 0 0 0T, and correct the inclination

n(tk):=ar(tk)×0 0 1T(23)

α(tk):=arccos 0 0 1Tar(tk)



ar(tk)

!(24)

qa(tk):=qa(tk−1)⊗hcos α(tk)

2n(tk)

kn(tk)ksin α(tk)

2i⊺. (25)

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FIGURE 8 | Velocity trajectories with (solid) and without (dashed) linear drift

correction. The dotted line represents the subtracted linear drift approximation

for stride i. For demonstration purposes, the drift has been artificially increased

by a factor of 10.

Multiplication of the gyroscope strapdown integration

quaternion and the accelerometer correction quaternion

yields the sensor orientation,

q(tk):=qa(tk)⊗qω(tk). (26)

3.9. Foot Velocity and Position Tracking

Using the estimated orientation, we perform double integration

of the measured accelerations to estimate the length of each

stride, i.e., the horizontal displacement between two adjacent

foot-flat phases.

To integrate accelerations, they are first transformed into the

reference frame

aε(tk):=q(tk)⊗a(tk)⊗q(tk)−1. (27)

Assuming that the velocity is zero in the middle of the foot-flat

phase, i.e., at trest,i, we integrate those accelerations for each stride

which yields a velocity

vi(tk):=Ts

τ=trest,iaε(τ)−0 0 9.81T,tk∈[trest,i,trest,i+1].

(28)

Due to measurement errors, mainly accelerometer bias, this

velocity is usually not zero at trest,i+1even if the foot is perfectly

at rest. Therefore, we correct this drift linearly over the time

duration of the stride:

vdf,i(tk):=vi(tk)−tk−trest,i

trest,i+1−trest,i

vi(trest,i+1). (29)

See Figure 8 for an example velocity trajectory with and without

drift correction.

By integrating this drift-free velocity over the stride duration,

we obtain a position trajectory,

pi(tk):=Ts

τ=trest,i

vdf,i(τ)=:pi,x(t)pi,y(t)pi,z(t)T. (30)

3.10. Stride Length and Walking Speed

We calculate the stride length Lias the horizontal displacement

during the stride i. Since pi(trest,i)=0,

Li:=qpi,x(trest,i+1)2+pi,y(trest,i+1)2. (31)

Note that this method does not make any assumption on the

orientation in which the sensor is attached to the foot. Also, note

that we integrate from trest,ito trest,i+1and not from tic,ito tic,i+1

since this makes the zero-velocity assumption more robust.

By dividing the stride length by the stride duration, we obtain

the walking speed,

vi:=Li

Tstride,i

. (32)

3.11. Summary of the Estimated

Parameters

After performing all steps presented above, the set of proposed

methods provides the time instants of the defined gait events,

the sensor orientation quaternion for each time instant, and

velocity and position trajectories. From those time-based signals,

the following gait parameters are extracted for each stride i:

•swing duration Tswing,rel,i[%]

•stance duration Tstance,rel,i[%]

•analogously, relative durations for the other gait phases as

defined in Figure 4

•stride length Li[cm]

•walking speed vi[km/h]

•cadence ci[steps/min]

Note that all quantities are calculated separately for each stride

of each foot. In many cases, only the mean of those values

over multiple steps will be of interest. However, this stepwise

calculation also allows for analysis of the variance and the

detection of trends.

The accuracy of those gait parameters is validated in the

next section.

4. EXPERIMENTAL VALIDATION

In this section, we aim to show that the less restrictive IMU-

based setup combined with the methods proposed in section 3 is

able to determine the same parameters as stationary systems that

are used in clinical practice while providing similar accuracy. To

this end, with a large data set consisting of three different subject

groups, we compare the parameters calculated by the proposed

methods with values reported by instrumented treadmills.

4.1. Setup

One PABLO R

Lower Extremity inertial sensor (Tyromotion

GmbH, Graz, Austria) was attached to each shoe (cf. Figure 9A).

The sensors measure angular rate and acceleration at a sampling

frequency of 110 Hz. Each sensor has a size of 56 ×34 ×21 mm

and transmits the data wirelessly using Bluetooth. The sensors

were attached to the subjects’ shoes with special Velcro straps.

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FIGURE 9 | Experimental setup. (A) Patient with inertial sensors attached to

the shoe. (B) Instrumented treadmill at NTK Kapfenberg. Gait parameters are

derived from the measurement data of the inertial sensors with the proposed

methods and validated against parameters obtained from the instrumented

treadmill serving as ground truth.

Zebris Rehawalk instrumented treadmills (Zebris Medical,

Isny, Germany) were used as reference systems. Since the data

collection took place in various institutions (FH Joanneum Graz,

NTK Kapfenberg, Rehabilitation Center Kitzbühel), different

systems with identical function were used. See Figure 9B for a

picture of the setup at NTK Kapfenberg.

•FH Joanneum (Graz, Austria)

– Treadmill: h-p-c Mercury Med Treadmill (HP Cosmos,

Nussdorf, Germany), walking speed: 0–22 km/h in 0.1 km/h

steps, walking surface: 150 ×50 cm

– Pressure measuring platform: FDM-THM-M-3i (Zebris

Medical, Isny, Germany), 120 Hz, sensor area: 108.4 ×47.4

cm, 7,168 sensors.

•NTK (Kapfenberg, Austria)

– Treadmill: h-p-c Locomotion Med Treadmill (HP Cosmos,

Nussdorf, Germany), walking speed: 0–10 km/h in 0.1 km/h

steps, walking surface: 150 ×50 cm

– Pressure measuring platform: FDM-THM-M-2i (Zebris

Medical, Isny, Germany), 120 Hz, sensor area: 111.8 ×49.5

cm, 3,432 sensors.

•Rehabilitation Center Kitzbühel (Kitzbühel, Austria)

– Treadmill: h-p-c Mercury Med Treadmill (HP Cosmos,

Nussdorf, Germany), walking speed: 0–22 km/h in 0.1 km/h

steps, walking surface: 150 ×50 cm

– Pressure measuring platform: FDM-THM-M-2i (Zebris

Medical, Isny, Germany), 120 Hz, sensor area: 111.8 ×49.5

cm, 3,432 sensors.

4.2. Subjects and Experimental Procedure

The data collection was carried out in three different institutions

with different groups of subjects. Approval from the ethics

committee of the University of Graz was obtained, and an

informed consent form was signed by all participants.

Healthy participants were recorded at three different walking

speeds, each for two minutes: 1.5, 3, and 5 km/h. A prerequisite

for participation was the ability to walk on a treadmill at different

speeds. The healthy participants (n=39) were recruited from the

students at the Physiotherapy Institute of FH Joanneum Graz.

Non-healthy participants with affected ability to walk were

asked to walk on a treadmill at a self-selected comfortable

walking speed. Patients who were unable to walk on a treadmill

were excluded during participant selection. The following set of

participants were recruited:

•Participants with different neurological diseases (n=36)

were recruited from patients who were in neurological

inpatient rehabilitation at NTK Kapfenberg at the time of

data collection. This comprises 20 post-stroke patients, 6

patients with Parkinson’s disease, two with multiple sclerosis,

two with meningioma, two after polytrauma, and one patient

each with epilepsy, spinocerebellar ataxia, low back pain,

and polyneuropathy.

•Participants with various orthopedic diseases (n=62) were

recruited from the patients who were in orthopedic inpatient

rehabilitation at Rehazentrum Kitzbühel at the time of data

collection. Of these, four patients had pathologies in the area

of the ankle or lower leg (e.g., ankle joint fractures, tibia

fractures), 21 patients at the knee (e.g., osteoarthritis, total

knee arthroplasty), 18 patients in the area of the thigh and hip

(e.g., osteoarthritis, total hip arthroplasty, femur fractures), 16

patients in the area of the lumbar spine (low back pain, lumbar

vertebrae fractures) as well as three patients in whom different

body areas were affected (polytrauma, polymyositis).

All participants had time to get used to walking on the treadmill

prior to the data collection. All participants were free to use the

treadmill support (handrail, fall protection system). For the data

collection, two minutes of walking was recorded simultaneously

by both systems. IMU data was recorded with a tool of the TyroS

software (Tyromotion, Graz, Austria) that allows the export of

raw gyroscope and accelerometer data. Zebris data was recorded,

analyzed, and exported with the software FDM v1.18.38 (Zebris

Medical, Isny, Germany).

4.3. Data Processing

For each trial, we obtain the following gait parameters from the

Zebris Rehawalk instrumented treadmill:

•loading response duration

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TABLE 2 | Parameter values used for the proposed IMU-based methods.

Symbol Description Value

haHysteresis factor for acceleration 0.23

hωHysteresis factor for angular rate 0.23

waFactor for ath auto-tuning 0.85

ath,min Lower bound for ath 1.8 m/s2

wωFactor for ωth auto-tuning 0.8

ωth,min Lower bound for ωth 0 rad/s

T0,min Minimum duration of zero-phase 120 ms

T1,min Minimum duration of one-phase 180 ms

jwin Ratio of the window to look for initial contact 0.7

jth Threshold for jerk norm (relative to maximum) 0.95

TaTime constant for acceleration moving average filter 8.0 s

This parametrization is used for the processing of all trials, regardless of gait pathology,

walking speed, or style, in order to show that the method works well without tuning the

parameters for specific gait characteristics.

•single limb support duration

•pre-swing duration

•swing duration

•stride length

•walking speed

•cadence.

These parameters are reported as averages over the whole trial.

The gait phase durations are relative to the stride duration and

reported separately for the left and right foot. We add the loading

response, single limb support, and pre-swing durations to obtain

the stance duration (cf. Figure 3A).

From phases in which the treadmill is not moving and

the foot is resting on the ground for approximately 5 s at

the beginning and end of each trial, gyroscope turn-on bias

is automatically estimated and removed. Using the methods

described in section 3, each recorded trial is processed with the

parameter values given in Table 2. Note that we use the same

set of parameters for all different subject groups and walking

speeds in order to demonstrate that the method works well

without adjusting the parameters for the specific gait velocity

and style.

The sensor attachment used for recording the data sets, as

shown in Figure 9A, ensures that one sensor axis is always

roughly aligned with the mediolateral axis of the foot. To

show that the proposed methods do not make assumptions

regarding the sensor orientation, we simulate a random sensor

attachment by multiplying all gyroscope and accelerometer

measurements with a random rotation matrix that is different for

each trial.

Finally, we calculate the same gait parameters as reported

by the reference system by averaging the respective

parameters, excluding the first and last three strides of

each foot, and compare the resulting values to the values

reported by the Zebris system. The results are found in the

following section.

4.4. Results

For each trial, we first consider the five main parameters

stance duration, swing duration, stride length, walking speed,

and cadence, and evaluate the difference between the proposed

methods (IMU) and the Zebris Rehawalk reference system (REF).

The results are presented separately for each of the three subject

groups in scatter plots and Bland-Altman plots (50) and can

be found in Figure 10, for the healthy participants walking at

three different speeds; in Figure 11, for the participants with

orthopedic diseases; and in Figure 12, for the participants with

neurological diseases.

The error (mean ±standard deviation) for the relative stance

duration is 1.04 ±1.34 % for healthy subjects, −0.29 ±1.52 % for

orthopedic patients, and 2.06 ±1.63 % for neurological patients.

For relative swing duration, the errors are −1.01 ±1.35 % for

healthy subjects, 0.32 ±1.54 % for orthopedic patients, and

−2.02 ±1.64 % for neurological patients. This means that the

average swing/stance duration error is in the range of 1–2 % for

all subject groups.

For the stride length, the errors are −1.59 ±1.53, −1.74

±1.63, and 0.51 ±1.37 cm for healthy subjects, orthopedic

patients, and neurological patients, respectively. This means that

the average stride length error is below 2 cm for all subject groups.

The mean errors and standard deviations for the

walking speed are −0.02 ±0.05 km/h for healthy

subjects, −0.03 ±0.05 km/h for orthopedic patients, and

0.03 ±0.03 km/h for means that the average walking speed error

is below 0.05 km/h for all subject groups.

The cadence estimates show deviations of

0.68 ±0.56 steps/min for healthy subjects, 0.55 ±0.47 steps/min

for orthopedic patients, and 0.57 ±0.51 steps/min for

neurological patients. This means that the average cadence

error is below 1 step/min for all subject groups.

As an additional evaluation metric, we calculate the mean

of the absolute difference (MAD) between the values reported

by Zebris and the IMU-based analysis over all trials. Table 3

summarizes the results for the three subject groups and all 215

evaluated trials.

The MAD of the stance and swing durations are ∼1.3 %

for healthy subjects and orthopedic patients and 2.2 % for

neurological patients. Note that we also evaluated the differences

for the three sub-phases of stance that the Zebris Rehawalk

reference system reports, i.e., loading response, single limb

support, and pre-swing. Table 3 shows that we can estimate

the duration of those phases with the same accuracy as stance

and swing.

To summarize, for all subject groups, the MAD is in the range

of 1–2 % for gait phase durations, below 2 cm for the stride length,

below 0.05 km/h for the walking speed, and below 1 step/min for

the cadence.

5. DISCUSSION

In the present contribution, we have proposed a set of methods

for spatiotemporal gait analysis based on two inertial sensors

attached to the feet. Our methods allow for the calculation of

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FIGURE 10 | Scatter plots and Bland-Altman plots for stance and swing duration, stride length, walking speed, and cadence of 39 healthy subjects walking at 1.5, 3,

and 5 km/h. Red: 45-degree lines (y=x). Values obtained with the proposed IMU-based methods (IMU) are compared to the ground truth from the Zebris reference

system (REF). The average deviation is ∼1 % for gait phase durations, below 2 cm for the stride length, below 0.05 km/h for the walking speed, and below 1 step/min

for the cadence.

the main spatiotemporal gait parameters that are also reported by

stationary laboratory systems: gait phase durations, stride length,

walking speed, and cadence. Using a large data set consisting of

healthy subjects walking at three different speeds, subjects with

orthopedic diseases, and subjects with neurological diseases, we

have validated the calculation of those parameters, using a Zebris

Rehawalk instrumented treadmill as reference. All parameters

show a very strong correlation (Pearson’s rbetween 0.83 and 0.99,

p<0.01) (51). Figures 10–12 display consistent results over this

large and diverse group of subjects. Averaged over all trials, the

MAD with respect to the reference system is 1.4 % for the gait

phase durations, 1.7 cm for the stride length, 0.04 km/h for the

walking speed, and 0.7 steps/min for the cadence.

In clinical practice and research, the presented parameters

are used to quantify gait abnormalities and to document

changes in the walking behavior of patients. Associations between

spatiotemporal gait parameters and functional capacity, or

increased mortality, have been demonstrated (52–54). A positive

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FIGURE 11 | Scatter plots and Bland-Altman plots for stance and swing duration, stride length, walking speed, and cadence of 62 orthopedic patients. Red:

45-degree lines (y=x). Values obtained with the proposed IMU-based methods (IMU) are compared to the ground truth from the Zebris reference system (REF). The

average deviation is below 1 % for gait phase durations, below 2 cm for the stride length, below 0.05 km/h for the walking speed, and below 1 step/min for the

cadence.

correlation with cardiovascular-related mortality was found for

cadence (55). A reduction in walking speed has been shown to

correlate with fall risk, frequency of hospitalization, and mortality

(56–58). Stride length describes a strong correlation with walking

speed according to the research of (59). Slower walking speed,

altered gait phase duration, and increased variability of walking

increase the risk of falls (60). Furthermore, it was found that

psychological modalities, such as fear of falling, can also influence

stride length and gait phase duration (61). The minimal clinically

important difference (MCID) can be used to determine how

precisely these changes must be detected in order to make

a statement about their relevance. Despite thorough research,

specific values for the MCID could only be found for the walking

speed, ranging from 0.36 to 0.72 km/h (62–64). For IMU-based

measurement with the proposed methods, the smallest detectable

change (SDC) for walking speed is 0.21 km/h and clearly within

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FIGURE 12 | Scatter plots and Bland-Altman plots for stance and swing duration, stride length, walking speed, and cadence of 36 neurological patients. Red:

45-degree lines (y=x). Values obtained with the proposed IMU-based methods (IMU) are compared to the ground truth from the Zebris reference system (REF). The

average deviation is ∼2 % for gait phase durations, below 1 cm for the stride length, below 0.05 km/h for the walking speed, and below 1 step/min for the cadence.

the MCID for all examined groups. For the other parameters, no

reported MCID values could be found, which is consistent with

the statement of (29).

The SDC for the cadence is 2.01 steps/min across all studied

groups of subjects. This allows for much more accurate

changes to be detected than those described as relevant in the

literature [e.g., reduction in cadence of 10 steps per minute

increases mortality by 4 % (65)]. The achieved SDC for stride

length of 5.3 cm in the patients with neurological diseases

seems to be sufficiently accurate to capture the differences

occurring, for example, in Parkinson’s disease (66). The stance

and swing phase durations show an SDC of 6.5 % across

all trials.

Unlike many existing contributions, we showed that the

proposed methods reliably work on patients in addition to

healthy subjects and still produce accurate results. This is

noteworthy since it has been shown that pathological walking

deteriorates the accuracy of many gait analysis methods (45)

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Laidig et al. Gait Assessment by Inertial Sensors

TABLE 3 | Deviation between IMU-based and Zebris gait parameters.

Stance [%] Swing [%] Stride Walking Cadence

LR [%] SLS [%] PS [%] length [cm] speed [km/h] [steps/min]

Healthy subjects (n=39)

MAD 1.32 1.29 1.28 1.32 1.31 1.73 0.04 0.74

µ±σ1.04 ±1.34 0.97 ±1.34 −0.96 ±1.33 1.03 ±1.34 −1.01 ±1.35 −1.59 ±1.53 −0.02 ±0.05 0.68 ±0.56

rx,y0.93 0.93 0.93 0.93 0.93 >0.99 >0.99 >0.99

LoA −1.58 to 3.67 −1.65 to 3.59 −3.56 to 1.65 −1.60 to 3.66 −3.65 to 1.63 −4.59 to 1.40 −0.13 to 0.08 −0.42 to 1.77

SDC 5.25 5.24 5.21 5.26 5.28 6.00 0.21 2.19

Orthopedic patients (n=62)

MAD 1.14 1.12 1.14 1.07 1.16 1.94 0.04 0.63

µ±σ−0.29 ±1.52 −0.33 ±1.49 0.35 ±1.49 −0.31 ±1.44 0.32 ±1.54 −1.74 ±1.63 −0.03 ±0.05 0.55 ±0.47

rx,y0.84 0.84 0.85 0.85 0.83 >0.99 >0.99 >0.99

LoA −3.27 to 2.69 −3.26 to 2.60 −2.57 to 3.26 −3.13 to 2.51 −2.68 to 3.33 −4.93 to 1.46 −0.13 to 0.06 −0.37 to 1.47

SDC 5.96 5.86 5.84 5.65 6.02 6.39 0.19 1.84

Neurological patients (n=36)

MAD 2.26 2.20 2.23 2.21 2.22 1.09 0.03 0.60

µ±σ2.06 ±1.63 2.04 ±1.65 −2.04 ±1.64 2.06 ±1.65 −2.02 ±1.64 0.51 ±1.37 0.03 ±0.03 0.57 ±0.51

rx,y0.89 0.89 0.89 0.89 0.89 >0.99 >0.99 >0.99

LoA −1.13 to 5.26 −1.19 to 5.28 −5.26 to 1.18 −1.16 to 5.29 −5.22 to 1.19 −2.18 to 3.20 −0.04 to 0.09 −0.43 to 1.58

SDC 6.39 6.47 6.44 6.46 6.41 5.38 0.13 2.01

All trials (215 trials)

MAD 1.43 1.39 1.40 1.40 1.41 1.68 0.04 0.68

µ±σ0.83 ±1.65 0.78 ±1.65 −0.76 ±1.64 0.82 ±1.64 −0.79 ±1.66 −1.28 ±1.73 −0.02 ±0.05 0.62 ±0.53

rx,y0.87 0.87 0.88 0.88 0.87 >0.99 >0.99 >0.99

LoA −2.41 to 4.07 −2.45 to 4.0 −3.98 to 2.46 −2.39 to 4.03 −4.05 to 2.46 −4.68 to 2.11 −0.12 to 0.09 −0.41 to 1.66

SDC 6.48 6.46 6.44 6.42 6.50 6.79 0.21 2.08

LR, loading response; SLS, single limb support; PS, pre-swing.

MAD, mean absolute difference between IMU-based and Zebris values.

µ±σ, mean and standard deviation of difference between IMU-based and Zebris values.

rx,y: Pearson correlation coefficient (p <0.01 for all values).

LoA, limits of agreement, µ−1.96σto µ+1.96σ.

SDC, smallest detectable change, range between both LoA.

and specifically the neurologically induced gait abnormalities are

challenging for IMU-based gait analysis (29).

A fundamental challenge of IMU-based gait event detection

is that IMUs do not directly measure the gait parameters of

interest. For toe-off detection, the time instant of load relief

cannot directly be measured, and instead, the inversion of the

direction of rotation is used. Similarly, initial contact is not

detected based on the onset of load but based on the change of

acceleration. It is therefore important to properly validate the

IMU-based methods by comparing the estimated gait parameters

to a reliable ground truth.

As reference system, treadmills instrumented with Zebris

pressure measurement platforms were used, which are frequently

employed for gait analysis in clinical practice as well as scientific

data collection (12). This system shows good reliability (67),

but no studies could be found in which the validity of the gait

parameters was investigated. It should be noted that due to the

length of the pressure sensors (FDM-THM-M-3i: 0.85 cm; FDM-

THM-M-2i: 1.27 cm) there may be inaccuracies in the recording

of spatial parameters, which may have an effect on the results

of the comparative measurements. Moreover, calibration and

proper thresholding pose challenges in gait event detection based

on pressure measurements (12).

For the neurological patients, the reported duration of stance

is, on average, 2 % longer than the reference duration. While

this is still a small deviation, it is worth noting because this

bias suggests a pattern that is common to this subject group.

One likely explanation is that toe-off is being detected later than

with the Zebris system. This might be due to a comparatively

long phase of load relief that causes the pressure to fall below

the threshold too early. Furthermore, the reversal of rotation

direction might happen later than for healthy subjects or

orthopedic patients. Still, even though both systems measure

inherently different phenomena, the observation deviation

is only 2 %.

As a replacement for traditional stationary gait analysis

systems, which are commonly used in clinical practice, IMU-

based gait analysis offers several advantages. Measurement is

possible both on treadmills and overground and not restricted

to a dedicated laboratory. The small and lightweight IMUs

do not restrict the movement of the subject and can be used

in conjunction with walking aids such as wheeled walkers.

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Laidig et al. Gait Assessment by Inertial Sensors

Furthermore, only a very short setup time is required before

starting the actual measurement.

Unlike most existing methods (cf. section 2), the proposed

method makes gait analysis easier and faster by not requiring any

specific sensor attachment, which we demonstrated by simulating

a different random sensor-to-foot orientation in each trial. It does

not make use of magnetometers and can therefore be used in both

indoor and outdoor environments.

While evaluation was limited to the gait phases reported by

the reference system, our proposed set of methods further allows

for the calculation of many gait phases (Figure 4), i.e., swing and

stance for each foot, four unilateral gait phases for each foot,

five bilateral gait phases following standard literature (44) for

each foot, and finally the distinction between double and single

support. To the best of our knowledge, no existing work on

IMU-based gait analysis describes the calculation of this set of

gait phases.

Besides the more fine-grained gait phases, there are many

more parameters that can be extracted, e.g., from the velocity

and position trajectories, such as the maximum velocity during

swing, foot clearance, and symmetry parameters. While it is not

surprising that the prevalence of pressure-based systems has led

researchers to focus on features based on ground contact, it is

to be expected that the focus of clinical gait analysis will be

directed toward other parameters as IMU-based systems become

more popular.

Furthermore, miniaturized lightweight sensors with a long

battery life open up possibilities for objective gait analysis outside

of clinical laboratories. Daily-life gait assessment over the course

of multiple days can bring insights that are not possible with short

sessions in a laboratory. If patients place the sensors on or in

the shoes themselves in an unsupervised telemedicine setting, not

requiring the sensor to be oriented in a special way becomes even

more important.

Technological advancement also facilitates real-time

biofeedback applications. While there are methods for real-

time applications that require event detection during a step (41),

e.g., to trigger FES, the proposed set of methods is real-time

capable in the sense that during walking, sections of data

containing a small number of strides can be processed and used

to provide feedback to the subject.

The presented work exhibits a few remaining limitations. In

the statistical analysis, the gait parameters were averaged over the

duration of the trial before comparison with the reference. While

it allows for single-stride errors to cancel out, this methodology

corresponds well with the use case of clinical gait analysis, in

which a subject is asked to walk for several steps, and averaged

parameters are then used to assess the gait. An additional stride-

by-stride comparison was not performed because the employed

reference system can only export averaged gait parameters. In

addition, it should be noted that all recordings were made on

treadmills and not while walking overground, which has an

influence on the movement pattern of gait (68,69). Despite the

known differences between treadmill walking and overground

walking, treadmill gait analysis is considered a standard method

in clinical practice (70,71), especially when weight support and

handrails are required for safety reasons.

6. CONCLUSION

In the present contribution, we have proposed a set of

methods for IMU-based gait analysis. Based on gyroscope

and accelerometer measurements from two inertial sensors

on the feet, we estimate durations of five gait phases, stride

length, walking speed, and cadence. Using a Zebris Rehawalk

instrumented treadmill as reference, we validated the proposed

methods based on a large data set consisting of healthy subjects

(n=39) walking at three different speeds, subjects with

orthopedic diseases (n=62), and subjects with neurological

diseases (n=36). Averaged over all trials, the MAD with respect

to the reference system are 1.4 % for the gait phase durations,

1.7 cm for the stride length, 0.04 km/h for the walking speed,

and 0.7 steps/min for the cadence. We also demonstrated that the

proposed methods work reliably not only in healthy subjects but

also in patients and still provide accurate results under different

pathological gait patterns.

This shows that the proposed setup in combination with

the proposed methods can accurately calculate relevant gait

parameters from the inertial sensor data and thus has the

potential to replace traditional stationary gait analysis systems.

Furthermore, we validated that the proposed methods work

well regardless of the orientation in which the sensor is

attached to the foot, and dedicated calibration movements

and magnetometer measurements are completely avoided.

The combination of these advantages facilitates long-term

ambulatory gait analysis in day-to-day situations without the

need for supervision by health professionals.

Future research will focus on the estimation of additional

gait parameters, on the validation on stairs and slopes,

and the validation against marker-based optical motion

capture systems.

DATA AVAILABILITY STATEMENT

The datasets presented in this article are not readily available

because sharing of the data is not covered by the ethical approval.

Requests to access the datasets should be directed to Andreas J.

Jocham, [email protected].

ETHICS STATEMENT

The studies involving human participants were reviewed and

approved by the Ethics Committee of the University of Graz (GZ.

39/55/63 ex 2017/18, 28 May 2018). The patients/participants

provided their written informed consent to participate in

this study.

AUTHOR CONTRIBUTIONS

DL and TS devised and developed the mathematical method.

DL implemented the method, performed the data analysis, and

drafted the manuscript. AJ, BG, KA, and MF planned and

organized the data collection. AJ, BG, and KA conducted the

data collection and post-processed the data. DL, AJ, BG, KA,

Frontiers in Digital Health | www.frontiersin.org 18 November 2021 | Volume 3 | Article 736418

Laidig et al. Gait Assessment by Inertial Sensors

MF, and TS revised the manuscript. All authors approved the

submitted version.

FUNDING

We acknowledge support by the German Research Foundation

and the Open Access Publication Fund of TU Berlin.

ACKNOWLEDGMENTS

We thank all subjects for their participation, Dr. Matthias

König and Andrea Eschbach as well as the whole team of the

Neurological Therapy Center Kapfenberg for the support during

data collection, and Andrew Cote and Eva Kastenbauer for the

skillful support in algorithm development and evaluation.

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