Estimation of the Average Gait Velocity based on Statistical Stride
Parameters of Foot Sensor Data
Harald Loose, Katja Orlowski and Laura Tetzlaff
Fachhochschule Brandenburg, Magdeburger Str. 50, 14770 Brandenburg, Germany
Keywords: IMU, Average Gait Velocity, Statistical Stride Parameters, Foot Sensor.
Abstract: The paper deals with the estimation of gait parameters based on data acquired by inertial measurement units
(IMU) placed at the middle foot (metatarsus). The developed method described in (Loose and Orlowski,
2015) is robust against a wide spectrum of the gait speed. The gait parameters (stride duration, length,
velocity, distance) are calculated stride by stride with excellent quality. This paper is focused on
experimental data acquired during walking on treadmill with a speed profile. First the robustness of the
method is shown and quantified using statistical characteristics of each speed level and the whole walking
distance. Second the determined speed profiles are evaluated against the adjusted speed profile and an
alternative camera based measurement. Third the influence of the walking speed on various physical and
statistical stride parameters is discussed. Fourth a model to estimate the walking speed as a function of the
root mean square of the magnitude of the angular velocity vector is proposed and evaluated. The rms is
calculated for the acquired sensor data after stride detection for the whole stride. The proposed method is
applicable to any IMU applied to the metatarsus.
1 INTRODUCTION
In the middle of the last century Perry (Perry, 2010)
and Murray (Murray, 1964) observed, measured and
analysed the normal and pathological human gait. In
addition to the graphical representation of the
normal range of motion Perry published the acquired
motion data. The gait pattern covers one stride, the
full period of movement of one leg, one stance and
one swing phase. The given patterns include motion
ranges of joint angles (hip, knee and ankle), the
angle between the thigh and the vertical axis (in the
sagittal plane).
During the last decade accelerometers,
gyrometers as well as integrated inertial
measurement units became freely available at the
market: from low cost sensors to relatively
expensive IMU assembled in small and light weight
packages. IMU are integrated in most smartphones.
They provide acceleration data, and more and more
angular velocity and magnetometer data as well as
an estimation of orientation.
In this paper we focus on the estimation of the
average gait velocity based on statistical stride
parameters of foot sensors. Based on the data of one
IMU sensor placed on the metatarsus various gait
values and parameters are determined:
cadence, distance and velocity of motion,
characteristics of each or averaged stride like
initial and terminal point, length, height, width,
duration of stride, stance and swing phase.
In addition one-stride statistical parameters like
minimum, maximum, mean and root mean square of
these characteristics are calculated. The “average”
stride is determined after the stride time
normalization.
In section II of this paper the used scenarios
including the experimental setup, the task for the
cohorts and the evaluation software are described.
Section III gives an overview about our investigation
of walking on treadmill with a speed profile. First
the robustness of the method is shown and
quantified using statistical characteristics of each
speed level and the whole walking distance. Second
the determined speed profiles are evaluated against
the adjusted speed profile and an alternative camera
based measurement. Third the influence of the
walking speed on various physical and statistical
stride parameters is discussed. Fourth a model to
estimate the walking speed from measured one-
stride-root mean squares of acceleration and/or
Loose, H., Orlowski, K. and Tetzlaff, L.
Estimation of the Average Gait Velocity based on Statistical Stride Parameters of Foot Sensor Data.
DOI: 10.5220/0005822602770283
In Proceedings of the 9th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2016) - Volume 4: BIOSIGNALS, pages 277-283
ISBN: 978-989-758-170-0
Copyright
c
2016 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
277
angular velocity magnitudes is proposed and
evaluated. The proposed method is applicable to any
IMU applied on the metatarsus. A similar idea is
given in (Juen et al., 2014) in the context of health
monitoring using mobile phones. Finally we will
conclude and give an outlook for further
investigations. It is expected that the method can be
applied to sensors placed above the ankle or at the
trunk. It can also be implemented on smart phones.
2 SYSTEMS AND EXPERIMENTS
For about five years we have been using sensor
systems for the acquisition of various motion data.
Sensors were applied directly to limbs/body were
tested as well as position measurement systems,
which are used for comparison in motion data
acquisition. Since a couple of years we have focused
on human walking, tried to understand the
underlying process and to find best positions of
sensors. Xsens MTw sensors providing strapped
down data including sensor orientation are used. A
robust and reliable algorithm which is applicable to
a wide range of walking scenarios (~2-8 km/h) was
developed. The algorithm was evaluated on data
acquired from foot sensors in two main scenarios
addressed to a large number of healthy subjects.
2.1 9DOF Xsens MTw Sensors
The 9DOF Xsens MTw sensor incorporates three
microelectromechanical sensors: triple-axis
gyroscope, accelerometer and magnetometer.
Onboard, the data of the primary sensors are
sampled at 1800 Hz. Strap-down integration (SDI) is
used to estimate the orientation with a transfer rate
of 60 Hz (for seven sensors). They are connected via
Bluetooth to one Awinda station and the data
acquisition software “MT Manager”. All involved
sensors are synchronized with high accuracy (< 10
s). The software provides linear acceleration a,
angular velocity ω, magnetic field m and quaternion
q. The sensors need calm or slow motion for
calibration, to determine the initial orientation of the
sensor with respect to the world coordinate system
(Roetenberg, Luinge and Slycke, 2009).
2.2 Experimental Setup
The sensors are clipped on body straps attached
similarly to the left and right lower limbs and one in
the middle of the back. Figure 1 shows two different
placements of the sensor on the metatarsus. The
distances of the sensors from the floor as well as the
length of the limbs are fixed in the experimental
record of each subject.
Figure 1: Two placements of foot sensors (on the side –
left, on the top of the foot - right).
2.3 Scenario
This paper is focused on human walking on
treadmill with a stepping-up speed profile over a
time period of 8 minutes and a distance of about 640
meters. The speed was increased every minute from
2 km/h (0.56 m/s) to 8 km/h (2.22 m/s) with a step
of 1 km/h and after decreased every 30 seconds to 5
km/h (1.39 m/s) and 2.5 km/h (0.79 m/s). It was
repeated three times, first after 6 month and second
after one week.
An additional test scenario was involved for the
examination of distance accuracy: Straightforward
constant walking outdoor on enough long distance
(~175 m) on a flat and paved ground. The distance
was measured alternatively with GPS and tape line.
2.4 Cohorts
11 volunteers participating in the described treadmill
scenario experiments were healthy persons between
32±13 years old, 176±12 cm height, 77±20 kg
weight and a body mass index of 24±4. All of them
provided informed consent.
2.5 Basic Ideas and Algorithms
The first steps in data processing – digital filtering
and estimation of the orientation matrix – are
executed on-board on the sensor (Roetenberg,
Luinge and Slycke, 2009). Using the delivered
quaternion the vectors of acquired data are converted
into the inertial coordinate system CS
0
where the z-
axis is vertical and the x-axis is directed to the
magnetic North. The gravitation force is eliminated
from acceleration and its integration can be
separated between the vertical and plane motion.
CS
0
is rotated so that the x-axis coincides with the
estimated direction of motion. Analysing the gait
pattern of the foot, i.e. acceleration, angular velocity
BIOSIGNALS 2016 - 9th International Conference on Bio-inspired Systems and Signal Processing
278
and foot angle to vertical, gait events are identified
which allow to detect precisely all gait cycles. While
Perry (Perry, 2010) defines the beginning of a gait
cycle at the initial floor contact we place it with
respect to the needs of integration at mid stance. At
this moment the foot is not moving, it stands on the
floor. The initial conditions of the velocities and the
distances, necessary for integration, are
predetermined. More details are explained in (Loose
and Orlowski, 2014 and 2015). The detection of gait
cycles is executed for both feet.
2.6 Evaluation Software
We developed, implemented and tested all
algorithms in Matlab®, V.: 2014b
(www.mathworks.com). Figures are mainly
produced in Matlab®, while tables were mostly
processed in Microsoft Excel®, V.: 2010
(www.microsoft.com).
An editable M
ATLAB
®
script is available to
process experimental data automatically step by
step. After each step the intermediate results are
saved. Figures can be created and written to hard
disc.
The following steps are included:
Preprocessing: reading and reorganizing sensor
by sensor the acquired data, given in the sensor
related coordinate system, transformation of
sensor data into world coordinate system,
elimination of gravity, calculation of orientation
relative to the initial one, calculation of angles
between z-axes of a sensor and the vertical or the
horizontal plane, calculation of joint angles.
Processing: estimation of direction of motion,
calculation of candidates for gait events,
plausibility check, determination of gait cycles,
transformation of data into motion coordinate
system, integration of acceleration, calculation of
velocity and position data stride by stride.
Postprocessing: calculation of physical and
statistical characteristics for each stride and the
whole walking distance, determination of
average motion.
Evaluation: building figures, extracting and
processing tables.
The developed algorithm is described in more
detail in (Loose and Orlowski, 2015).
3 DISCUSSION AND RESULTS
In this section results from all scenarios and for all
sensors are presented. First evaluation results of the
basic algorithm for both foot sensors in the test
scenario, followed by the results of standard
scenarios are listed.
3.1 Test Scenario
A quick test scenario was implemented to examine
the accuracy of the determined distance. On the
campus a path was identified where the subject
walked two times a relative long distance
straightforward on a flat and paved ground. The
distance was measured with GPS (171-181 m) and a
classical tape line (174.7 m) what can here used as
the “gold standard”. The measured distance for the
right foot is 179,6 m and the left foot 179.4 m, i.e.
the absolute error is 5m and relative error < 3 %.
The subject made 108 strides. The average stride
duration is 1.03 s, the length 1.66 m, the height 0.12
m, the width 0.04 m and the speed 1.60 m/s. All
values are plausible. The result is excellent, but not
validated yet.
3.2 Walking on Treadmill
Eleven subjects participated in the walking on
treadmill scenario with a speed profile from 2 km/h
(scuffle) to 8 km/h (rush, jog) stepping 1 km/h. A
small number of subjects switched from walking to
jogging when the speed became uncomfortable (> 7
km/h). This scenario was done by 11 subjects. Seven
of them executed it once in April and twice in
October 2015. 46 of 68 data sets acquired from foot
sensors were analyzed. 12 data sets were corrupted
(interruption of the data transfer via Bluetooth).
Sabatini (Sabatini et al., 2005) used a similar
scenario to assess the determination of walking
features using inertial foot sensors.
3.2.1 Evaluation of the Method
A distance of 643 m was monitored by treadmill; a
distance of 680 m was determined by a camera
based control measurement. From all data sets an
average distance of 682 m was calculated in a range
from 656 to 702 m. The mean stride speed is 1.52 ±
0.05 m/s. The number of strides varies between 401
and 471 and a mean of 441. The variance of the
walking distance of about ±4% results from
a small variation of the walking time and the
treadmill speed, what was not determined,
the intra-subject variance of walking and
a systematic error (no filtering of the impact of
the heel strike) and the variance of the
Estimation of the Average Gait Velocity based on Statistical Stride Parameters of Foot Sensor Data
279
calculation method (limited precision of the
stride detection of ±16 ms).
Table 1 and 2 summarize averaged
characteristics of the gait what were first determined
for each stride, then averaged over all strides of each
data set and finally statistically evaluated over all
data sets.
Table 1: Averaged over all foot sensor data sets stride
characteristics (min – minimum, max – maximum, mean –
mean value, std – standard deviation).
averaged stride characteristics
dura-
tion
[s]
length
[m]
height
[m]
width
[m]
speed
[m/s]
strike
angle
[°]
lift
angle
[°]
min 1,03 1,43 0,08 0,02 1,46 17,97 58,87
max 1,21 1,73 0,17 0,06 1,59 36,32 78,80
mean 1,10 1,55 0,12 0,04 1,52 26,20 71,25
std 0,06 0,08 0,03 0,01 0,04 4,59 4,35
Table 1 shows the duration, length, height, width
and the velocity of an averaged stride as well as the
strike and the lift angle of the foot. The variance of
the stride characteristics over all data sets can be
explained by different physical properties of
involved subjects, e.g. their height, leg length and
level of fitness.
Table 2: Correlation coefficients of by the stride duration
normalized measured and average strides. The relevant
components in the sagittal plane are averaged over all data
sets (min – minimum, max – maximum, mean – mean
value, std – standard deviation).
correlation coefficient
forward sideward vertical
acc vel ang. vel. acc vel
min 0,86 0,94 0,91 0,76 0,88
max 0,93 0,99 0,97 0,87 0,95
mean 0,90 0,98 0,94 0,81 0,92
std 0,01 0,01 0,01 0,03 0,02
Data summarize in table 2 correlation
coefficients between each stride execution
(normalized by the stride duration) and the average
stride (determined for the data set) and their
statistically evaluation over all subjects. They reflect
the small variance of the stride execution in the
sagittal plane, while the variance in the other
direction is significant (not shown in the table). By
the way these results show the excellence of stride
detection. The best correlation is observed for the
angular velocity and linear velocities calculated by
integration of the acceleration, smoothing
disturbances of the acceleration. The highest
variance is seen in the vertical component of
acceleration, what can be explained by the natural
variance of the vertical movement of the foot and the
influence of the heel strike which causes an
additional pulse on the acceleration.
3.2.2 Evaluation of Stride Velocity
Every measurement of the treadmill speed can be
evaluated against the adjusted treadmill speed
profile. When a subject walks on the treadmill it has
to adapt its walking to the speed of the treadmill in a
natural way, i.e. increasing stride length and
decreasing stride duration at the same time.
Following the calculated stride velocity for each
speed level can be interpreted as a measure of the
treadmill speed.
All measurements are considered against the
adjusted speed profile. The results are presented in
figure 2. The plot shows that there is a very good
coincidence between the mean stride length and the
adjusted treadmill speed during stepping-up speed
(small overestimating) and an underestimation
during stepping-down speed. In the given speed
range from 0.5 m/s to 2.3 m/s the differences are less
than 0.1 m/s during stepping-up speed and twice of
them during stepping-down speed.
Figure 2: Differences between measured and adjusted
treadmill speed against their mean. Data of seven subjects
and the optical system are included. The mean of
differences is shown as red line, the 1σ-environment as a
green.
The beginning of a new speed level was
automatically detected observing the changes of the
stride velocity. If the change from one stride to the
next stride (or the average of a number of strides) is
higher than a given threshold the beginning of a
transition phase was registered. The transition phase
between two levels, where the treadmill speed rises
up or slows down and the subject tries to adapt to
changing the treadmill speed, is still added to the
following level. From this consideration the different
BIOSIGNALS 2016 - 9th International Conference on Bio-inspired Systems and Signal Processing
280
effects during stepping up and down speed can be
explained.
3.2.3 Influence of the Walking Speed
In figure 3 the dependency of essential stride
characteristics like stride length, height, width and
velocity, strike and lift angle, duration of stride,
stance and swing on the numbers of steps is
presented. The number of executed strides
corresponds to the treadmill speed which was
changed every 60, later every 30 seconds. It
increases together with treadmill speed (see subplot
“stride velocity”). Obviously stride length, height,
width, strike and lift angle rise with increasing
speed, while stride, stance and swing duration
descend. Rising stride velocity is achieved by
ascending stride length and descending stride
duration. The relationship between the stance and
swing phases is changing. The stance phase becomes
shorter relatively to the swing phase.
Figure 3: Influence of the treadmill speed on stride
characteristics: length, height, width, velocity, strike and
lift angle, duration of stride, stance and swing (red – left,
blue – right leg).
After any proper stride detection statistical
characteristics of all available signals can be
calculated. The determination can be executed for
each component or any signal vector. For any stride
the mean, minimum, maximum, median and root
mean square (one-stride-rms) values as well as the
standard deviation of all stride characteristics were
calculated. In figure 4 the rms of the components of
angular velocity, acceleration and velocity in
dependence on the number of steps respectively the
stride velocity is presented.
Comparing the “stride velocity” (see figure 3)
with the curves in figure 4 the similarity is obviously
what was expected for the rms of the stride velocity.
It can be suggested that there is a relationship
between the one-stride-rms of the magnitude of the
acquired linear acceleration/angular velocity vector
and the forward stride velocity.
Figure 4: Influence of the treadmill speed on the stride by
stride calculated root mean squares of angular velocity,
acceleration and linear velocity (brown – sideward, blue –
forward, ocher - vertical).
3.2.4 Estimation of Walking Speed
The relationship between walking speed and RMS of
the magnitude of the angular velocity vector
calculated for any whole stride is investigated on the
case of seven data sets of subjects. In figure 5 the
calculated for each speed level averaged RMS of
magnitude of the angular velocity vector against the
stride velocity is presented. The equation of the
quadratic fitting curve for the mean line was
determined:
 = −0.36
+ 3.3 + 0.27 (1)
Obviously the quadratic curve fits the mean
excellent and the seven other curves are very close
to them. Equation (1) models the relationship
between the walking speed, which is equivalent to
the mean stride velocity, and the one-stride-rms of
angular velocity vectors magnitude. To model the
relationship between both values by a quadratic
function seems to be satisfying, but the coefficients
must be validated including more experimental data.
The Bland-Altman-Plot (Bland, Altman, 1986),
shown in figure 6, points the quality of the
approximation model (1). The “measured”, i.e.
calculated by the method described ahead, and the
estimated using equation (1) one-stride-rms of the
magnitude of the angular velocity vector are
compared. The 1σ-environment of the differences
between the values is given with ±0.12 rad/s. It
seems to be that the error of the model rises with the
Estimation of the Average Gait Velocity based on Statistical Stride Parameters of Foot Sensor Data
281
value of the rms. The relative error is less than ±5%
(worst case).
Figure 5: One-stride-rms of angular velocity over stride
velocity for seven subjects. The mean is shown bold red,
the quadratic fitting curve dashed black. Additional, the
equation of the fitting curve is given.
Figure 6: Differences between “measured” and estimated
RMS of angular velocity magnitude over their mean. The
mean of differences is shown as red line, the 1σ-
environment as a green and the level of agreement as a
blue line.
To determine the walking speed from the
calculated one-stride-rms of the magnitude of the
angular velocity vector – an inverse model is used:
=0.03
+ 0.2 + 0.049 (2)
On the base on the model (2) an efficient
algorithm to determine gait characteristics from
IMU data (angular velocity) applied to the
metatarsus can be developed. After an online stride
detection, i.e. the phase between two successive gait
events (see e.g. Orlowski, Loose, 2014) the one-
stride-rms of the magnitude of the angular velocity
vector is calculated. Finally the walking speed is
estimated. The walked distance can be determined.
If more strides are included the results should
improve.
4 CONCLUSIONS
The paper dealt with the estimation of gait
parameters based on data acquired by inertial
measurement units (IMU) placed at the middle foot
(metatarsus). The developed method described in
(Loose and Orlowski, 2015) is robust against a wide
spectrum of the gait speed. The gait parameters
(stride duration, length, velocity, distance) are
calculated stride by stride with excellent quality. The
numerical results are comparable with those of
(Sabatini et al., 2005), are extended to the movement
out of the saggital plane and are assessed for the full
range of walking speed (2-8 km/h). This paper is
focused on experimental data acquired by foot
sensors during walking on the treadmill with a
typical speed profile. The experimental setup, the
scenario as well as the cohort were described. The
accurateness and robustness of the method is shown
on a test scenario, where the relative error of the
determined walking distance was < 3%. Then 46
data sets of the treadmill scenario were analyzed.
Statistical evaluation over the whole walking
distance and over all data sets shows excellent
results for essential stride parameters like duration,
length, speed and foot angles as well as good results
for height and width having more natural intra- and
inter-subject variance. The automatically determined
speed levels are evaluated against the adjusted
speeds showing satisfying agreement. The results are
illustrated in Bland-Altman-Plots. The influence of
the walking speed on various physical and statistical
stride parameters is discussed. Based on this
investigation a model to estimate the walking
velocity from measured one-stride-rms of the
magnitude of the angular velocity vector is
proposed. A further evaluation of model and its
parameter using all available data sets it will be
implemented for any IMU attached to the
metatarsus. It is expected that the method can be
applied to sensors placed above the ankle or at the
trunk as well as it can be implemented on smart
phones.
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