Journal of Robotics, Networking and Artificial Life, Vol. 5, No. 2 (September 2018) 83-88___________________________________________________________________________________________________________A Study on High Accuracy Stride Estimation on Smartphone Combining Acceleration Sensor
and Gyro Sensor
Hiroki Tamura1, Keiko Sakurai 2, Koichi Tanno１

1Faculty of Engineering, University of Miyazaki,

1-1,Gakuen-kibanadai-nishi, Miyazaki-shi, Japan
E-mail: htamura@cc.miyazaki-u.ac.jp
2

University of Miyazaki,

1-1,Gakuen-kibanadai-nishi, Miyazaki-shi, Japan
E-mail: ksakurai@cc.miyazaki-u.ac.jp

Abstract
The stride is an important parameter in human motion analysis and has been extensively studied by many researchers.
This paper focuses on smartphones that are popular in the world, regardless of the measurement environment. In
previous research, the stride estimation using the acceleration sensor or the gyro sensor mounted on the smartphone
had been studied. However, the stride estimation accuracy has an error rate of about over 10 %. In this paper, we
propose a highly accurate stride estimation method using stride correction parameter obtained from cross section
movement in addition to conventional sagittal surface stride using acceleration sensor and gyro sensor mounted on asmartphone. Based on the testing results, the error rate of our proposed method with the stride estimated by the Kinect
sensor (RGB-D sensor) as the true value was about 6%. It makes possible to estimate the stride with high accuracy.
Keywords: Locomotive Syndrome, Acceleration sensor, Gyro Sensor, Stride Estimation Method, Smartphone.

1. Introduction

the case of coniferous trees, about 3000 per hectare isstandard [1]. Therefore, in this research, we focus on theestimation of stride width and the estimation of walking
distance by using smartphones widely spread around theworld, regardless of the measurement environment.
Estimation of stride width and walking distance bysmartphone and has been studied so far.
In this paper, we examine the evaluation of walking
motor function using the smartphone. The smartphone is
one of the daily sensors. A wearable device such as asmartphone using an acceleration sensor and/or gyro
sensor has weak accuracy in a specific environment
compared with a motion capture system using the kinect
sensor [2]. Therefore, in this paper, we propose the highly
accurate stride estimation method. We aim to build aWith the progress of information technology in recent
years, informationization is progressing even incomplicated fields such as agriculture and forestry. Since
introduction of information technology is expected tolead to more efficient production fields such as
agriculture and forestry, informationization is necessary.
In the field of forestry, in order to produce trunks withdirect circulation and high circularity, it is necessary togive a space that allows the branches to extend equally inall directions. The planting position is determined by thegrowth and soundness of each tree, the kind of growth
space to be given to those trees, what kind of arrangement
is advantageous from the work efficiency such as
planting, lower cutting, thinning decide. Especially, in

Copyright © 2018, the Authors. Published by Atlantis Press.
This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
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Journal of Robotics, Networking and Artificial Life, Vol. 5, No. 2 (September 2018) 83-88___________________________________________________________________________________________________________

direction of gravity and the angle of the thigh inclinationis θ1 and θ2, then L1 and L3 are given by Eq. (3).

system using smartphones that have accuracy like kinect
sensors.

𝐿

𝐿

𝐿

sin 𝜃

sin 𝜃

(3)

2. Previous Research 1[3]In the previous research, a gyro sensor of a smartphone
is mounted on the thigh. The hip joint angle calculated
from the integrated value of the angular velocity. The
angular velocity calculated by using the X-axis of the
gyro sensor. Assuming that the angular velocity of X-axis
is “gx” and the time when the hip joint angle becomesmaximally is "θmax", the hip joint angle used for stride
estimation is expressed by Eq. (1). The integrationinterval was determined by the slope of the device
calculated by the arc tangent of the gravitational
acceleration of the Y-axis and the Z-axis. When issuingin front of the right foot, the inclination of the device isfrom time to maximize "t0" (right foot rearmost) to theminimum to become time "t1" (landing in front rightmost). Further, if the length of the foot is "Lleg" and thestride is "L", the calculation formula of the stride isexpressed as Eq. (2).

θ

L

𝐿

g

𝑡 𝑑𝑡

(1)

|𝜃

|

(2)

Smartphone

Fig.1. One stride image.

Fig.2. Correction amount by rotation of waist.

3. Proposal method1
Then, L2 is obtained using Eq. (4). The r is representing
the width of the waist.
𝜃𝐿
2𝑟 sin(4)
2

The method we propose aims to estimate steps withhigh precision. Therefore, the calculation of theconventional sagittal plane method is added by themethod for the stride correction parameters obtained
from the cross section movement. To improve the lengthof the step obtained from the sagittal plane, pelvic
rotation motion is measured with a gyro sensor to the hip
joint. It is because the smartphone is fixed to the thigh. In
Fig.1, L1 and L3, we can see that the stride lengths
obtained by the acceleration sensor, and L2 is a correction
amount that takes into consideration the rotation of thelumbar region obtained by the gyro sensor. First, theformula for obtaining the stride length using L1 and L3 isshown in Eq. (3). When the difference between the𝜃𝑔 𝑡 𝑑𝑡(5)

In Fig.2, “θ” is representing an angle due to the rotationin the transverse plane, and it can be calculated using Eq.
(5). The rotation of the cross section is expressed by avalue "gy" of Y-axis gyro sensor. The integration interval
can be determined by the values that form the Y-axis andZ-axis of the acceleration sensor. It is from the momentt0 at which the foot is pulling the most backward until the84Journal of Robotics, Networking and Artificial Life, Vol. 5, No. 2 (September 2018) 83-88___________________________________________________________________________________________________________The smartphone iPhone 4S (iOS 7.0) used for thisresearch has a function capable of detecting gravitational
acceleration. The inclination angle (rad) of the device canbe calculated from the detectable gravitational
acceleration on the Y axis and the Z axis by Eq. (7).

moment t1 when the foot is stepped forward and landed,or from the moment of landing to the moment when thefoot reaches the back. After calculating the rotation angle,
the distance calculated from the rotation of the lumbar
region can be calculated by using the expression for
obtaining the string of the circle. Therefore, if the desired
stride is L, the stride is estimated by Eq. (6). We call the
proposed method 1 about the stride length of Eq. (6).

𝐿

𝐿

𝐿

𝐿

𝜃 ，𝜃

(6)

arctan𝑔𝑟𝑎𝑣𝑖𝑡𝑦 𝑍
𝑔𝑟𝑎𝑣𝑖𝑡𝑦 𝑌(7)

4.2. Walking conditions
Experimental conditions are shown in Fig.4. Before
starting to walk, the subject stands upright with both feetaligned and starts walking from the right foot. Walk threesteps with the subject's right foot as the first step andcalculate the walking distance at the third step. Next,
walking is stopped by aligning the left foot of the fourth
step with the right foot of the third step.

4. How to judge walking
To build a system that calculates the stride from walking
motion, it is necessary to estimate the state that a person
is walking. Therefore, in this section, we describe thewalking judgment method of a person.
4.1. Method of attached the smartphone
In order to determine the walking state, the inclinationof the smartphone is calculated from the value of theacceleration sensor. The inclination of the device can beused directly to track the movement of the thigh. From
this reason, we can capture the periodic movement of thewalking thigh. The smartphone is attached to the thighusing a supporter as shown in Fig.3(a) and the axis
information of the smartphone is shown in Fig.3(b). At
this time, the smartphone should not be turned uprightand must be worn with the display facing in the directionof walking. Although the direction of the device islimited, calibration for determining the axis of the sensor
used for calculating each parameter by this mounting
method becomes unnecessary. Therefore, the subjects
can start walking with free timing.

Fig. 4. Walking conditions.

The example waveform when a person walking can beseen in Fig. 5.

Fig. 5. Device tilt during walking.

(a) Attached location

The periodic waveform indicates walking is occurring,but it may not be determined that the subject is walking.
It is because there are individual differences such as
forward inclination and backward inclination in the
posture. When the inclination angle of the device iswithin ± 10 (degree), it is judged that the subject isstanding. Fig.5 "walking" showed that a positive value
represents a state when the foot is stepping forward anda negative value represents a state when the foot is pulled
backward. Therefore, in this paper, from the positive(b) Smartphone axis information

Fig.3. Position to install smartphone.

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Journal of Robotics, Networking and Artificial Life, Vol. 5, No. 2 (September 2018) 83-88___________________________________________________________________________________________________________

peak to the positive peak or from the negative peak to thenegative peak is taken as the stride length (1 step).

device tracking the movement of the foot with the YZ
acceleration in Fig.8. First, when the inclination of thedevice is near from the peak of the downward convex, itmeans YZ acceleration enters the third quadrant. Whenthe tilt of the device is negative, the foot is in the state ofbeing pulled to the back most, and that state can be said
to capture the acceleration of the kicking leg. Next, theYZ acceleration takes the fourth quadrant. It means thatthe fourth quadrant is oriented mainly in the direction ofwalking, which shows that it captures the movement in
the process of stepping forward. Next, take the first
quadrant. It can be seen in Fig.8 that the first quadrantmeans upward when steps are taken. It means that theforce in the direction of walking weakened. Then, after
the first quadrant, move the foot in the third quadrant
direction representing the lower part of the thigh. Thismeans the moment of landing. After the third quadrant,
which means landing, the waveform is slightly disturbed,
but the device vibrates after landing.
Therefore, the landing assessment is performed using
the first peak of the third quadrant that occurs temporarily
because the slope of the device is 10 (degree) or more(shown in Fig. 9). The value of 10 (degree) is to prevent
peak misrecognition.

5. Method of judging landing
The Y-axis value and the Z-axis acceleration sensor areused to determine the landing (hereinafter "acceleration
YZ"). The YZ acceleration value is not the accelerationof gravity used in the determination of the subject
acceleration produced by the subject. As shown in
Fig.3(a), when the smartphone is installed on the thighs,
the magnitude of the acceleration YZ represents theacceleration in the sagittal plane. Fig. 6 shows that theslope of the smartphone and YZ acceleration during
walking.

Fig.6. Changes in the magnitude of YZ acceleration

Fig.6 shows that it is quite difficult to find features when
landing. However, by disassembling into each quadrantas shown in Fig.7, the feature amount at landing can bemeasured.

Fig.9. YZ acceleration in the third quadrant only

6. Experimental Results
In this section, we show the result of stride estimation.
We experimented with simultaneous measurements
between kinect and smartphone sensors. The number ofsubjects is 54 (Men: 12, Women: 42) at the age of 20 to
60. The proposed method 2 is a hybrid with the previous
research 1 and proposed method 1. If the waist rotation
exceeds 12cm, we used the proposed method 1, else usedprevious research 1. This is based on the results
calculated from preliminary experiments, when the waist
rotation amount exceeds 12 cm, the stride had a tendency
to decrease error.
Fig. 10 can be seen that the proposed method 2 is better
than in previous research 1 and proposed method 1. From
this fact, it is assumed that the method of combining thesagittal and transverse fields more accurately captures
motion rather than a method that only focuses on thesagittal plane.

Fig.7. Device axis and quadrant as seen from sagittal plane

Fig. 8 shows that the waveform of YZ acceleration
when Fig.6 is divided into four quadrants.

Fig.8. Quadrant decomposition of the magnitude
of YZ acceleration

In order to see what type of YZ acceleration is occurringin what kind of motion, it can compare the tilt of the86Journal of Robotics, Networking and Artificial Life, Vol. 5, No. 2 (September 2018) 83-88

Error Rate___________________________________________________________________________________________________________

judge that the first peak in the third quadrant is thelanding timing. From this result, we considered that it isdifficult to make landing determination by the same
method. Therefore, using the method of the previous
study, the landing determination was made to judge that"the time when the device is the most inclined is thelanding".

20%
18%
16%
14%
12%
10%
8%
6%
4%
2%
0%

Previous
Research 1
Average Error Rate
8.95%
Max Error Rate
18.42%

Proposal
Method 1
7.50%
16.40%

Proposal
Method 2
6.20%
13.90%

Fig. 10. Estimation accuracy of each strides estimation
method.

7. Experimental Results 2
In this section, by using the proposed method 2, weinvestigated the problem which occurs at the time ofwalking uphill and the sensor showing the characteristics
of ascending slope walking.
For climbing experiments, we use the experimental hill
climbing model as shown in Fig.11. The hill-climbing
model is designed to secure a walking distance of 2 m
with 0 degree, 10 degrees, 20 degrees and 30 degrees. By
using the model and determining the walking condition,
it becomes possible for the subject to carry out theexperiment smoothly.

Fig. 12. Landing determination timing method.

7.2. The correction formula using the value ofgravity acceleration Y-axis
Next, we will describe the sensor value. Fig.13 showsthat the peak value in the positive direction of thegravitational acceleration Y axis increases as theinclination angle increases. This indicates that the swingup motion of the thigh is getting bigger when walking
uphill. From the experimental results, we confirmed thatthe error between the measured value and the true value
also increased as the inclination angle became larger in
the ascending slope walking. The verification results on
this relationship will be described in detail in theexperimental result of section 7.3.
[rad]30 degrees

Fig. 11. Experimental climbing model.
20 degrees

7.1. Changing method of landing determination
Fig.12 shows the difference in landing timing. The
vertical axis is the of the device, and the horizontal axis
is the number of data. Also, peak 1 is the proposed
method 1, and peak 2 is the determination by "the time
when the device is the most inclined is the landing".
When peak 1 and peak 2 are value of 1, it means that it isjudged as "landing". The value of acceleration changes
from the difference in walking motion due to theinclination. As a result of the experiment, we found thatthe landing determination by the YZ acceleration cannot

10 degrees

0 degreeFig. 13. The value of gravity acceleration Y axis.

87Journal of Robotics, Networking and Artificial Life, Vol. 5, No. 2 (September 2018) 83-88___________________________________________________________________________________________________________

7.3. The correction formula using the value ofgravity acceleration Y-axis

8. Conclusions
In this paper, the movement of the sagittal during
walking motion that focuses on the movement of thecross-section, a method for estimating the step with highaccuracy studied.
The results of proposed method 1 have the improvement
rate of about 1.5% as an average error rate and theimprovement rate of about 2.0% as a maximum error ratefrom previous research 1. The stride estimation methodof proposed method 1 is more significant than theprevious research 1.
Furthermore, the results of proposed method 2 have theimprovement rate of about 2.8% as an average error rate
and the improvement rate of about 4.5% as a maximum
error rate from previous research 1.
By classifying walking based on the amount of rotationof the lumbar region, it was possible to estimate
according to individual differences, and improvement of
versatility was confirmed. From these results, the error
rate of our proposed method 2 with the stride estimatedby Kinect sensor (RGB-D sensor [2]) as the true value
was about 6.2%, making it possible to estimate the stride
with high accuracy.
In the case of ascending slope walking, we confirmedthat the error between the measured value and the true
value increases as the inclination angle increases. From
the result, as a result of calculating the error by thecorrection formula using the value of the gravitational
acceleration Y axis, 86.7% at 30 degrees, 54.6% at 20
degrees, 14.5% at 10 degrees, 13.9% at 0 degrees were
improved.

In this section, the calculation result of the correction
equation will be described. The results are shown in
Fig.14, and the horizontal axis represents thegravitational acceleration Y axis, and the vertical axis
represents the error between the true value and thecalculation result. In Fig.14, × indicates 0 degrees, ▲indicates 10 degrees, ■ indicates 20 degrees, and ◆indicates 30 degrees. Experiment method andenvironment are the same as in section 4, and there are 3
subjects. Table 1 shows the average of the error rates
according to each slope when this correction formula is
not used and the average of the error rates when using thecorrection formula.
As a result, by using the correction formula calculated
from all the subjects, 86.7% in the case of 30 degrees,
54.6% in the case of 20 degrees, 14.5% in the case of 10
degrees, and 13.9% in the case of 0 degrees were
improved. In addition, the error rate as a whole was
12.6%. However, since the average error of 0 degree
walking in the proposed method 2 was 7.5%, it was 3.5%
worse in walking distance estimation at 0 degree. As afactor of worsening, it may be thought that the landing
determination method was changed so as to be able torespond to the measurement of the ascent slope walking.

References
1. National Federation of Forest Owners' Co-operative
Associations
http://www.nw-mori.or.jp/(accessed 2018-1-8)
2. Kouta Momose, etc.， Basic study on evaluation method
for patient with locomotive syndrome using a RGB-D
sensor ， IEICE Technical Rep ， vol.113, no. 486,
NLP2013-182, March, 2014, pp. 103-106, (Japanese)
3. Hiroki Tamura, Yoshinobu Furukawa, “Estimation of
Locomotive Syndrome using Smartphone”, Symposium ofJapanese Society for Medical and Biological Engineering,
1P-2-7, September, 2016,(Japanese)

Fig. 14. Calculation result of correction equation.
Table. 1. Average error ratio before and after correction.

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