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

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

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.

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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