THE UNIVERSITY OF DANANG
UNIVERSITY OF SCIENCE AND TECHNOLOGY

PHAM DUY DUONG

IMPROVE THE INERTIAL NAVIGATION SYSTEM
TO ENHANCE THE ACCURACY OF WALKING
PARAMETERS ESTIMATION USING IN HEALTH CARE

Major: Control and Automation Engineering
Code: 9 52 02 16

SUMMARY OF DOCTORAL THESIS

Da Nang, 2021


The work was completed at
UNIVERSITY OF SCIENCE AND TECHNOLOGY
- THE UNIVERSITY OF DA NANG

Supervisors 1: PhD. Doan Quang Vinh
Supervisors 2: PhD. Nguyen Anh Duy

Reviewer 1:
Reviewer 2:

The thesis is defensed at the Distinguished Scholar-Doctorate
thesis at University of Science and Technology on the day 17th
month 7, 2021

The dissertation can be found at:
- Learning Resources and Communication Center, University of
Science and Technology
- National Library of Vietnam


PROEM
Rationale of thesis
Human walking parameters depend on the complex interplay of
major parts of the nervous system, skeletal muscle, and cardiovascular
system. The walking parameters will be changed due to the damage in
these systems. Therefore, measuring the walking parameters is very
important to support doctors in diagnosing diseases, evaluate health
status, and the rehabilitation process. Important walking parameters in
health care are walking speed, step length, stride length, foot angle,
step time, step width… The commercial walking parameter
measurement systems are very expensive and limited in working range.
Therefore, they are difficult to widely apply in domestic medical
facilities. In this thesis, we propose low-cost, flexible, and unrestricted
systems in walking parameters measurement using IMUs.
An IMU includes a 3D accelerometer and a 3D gyroscope. The
IMU is attached to body parts to estimate attitude, velocity and
position of body movement using the Inertial Navigation Algorithm
(INA). In which, the attitude in external reference coordinate system
WCS is determined by integrating the angular velocity signal; the
moving acceleration is determined by removing the gravitational
acceleration using the moving attitude; the velocity in WCS is
determined by integrating the moving acceleration; the moving
position is determined by integrating the moving velocity. Thurs, the
walking parameters can be extracted from the attitude, velocity and

position of IMU during moving. A positioning system using IMUs is
known as an Inertial Navigation System (INS).

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The drawback of INA is the estimation error will be increasing
due to integrating the noise of IMUs. Therefore, this thesis improves
the accuracy of moving estimation using IMUs.
Objectives
Research to build systems of walking parameters estimation,
which can be used for walking parameters tests.
Object and scope of the thesis
The Object of the thesis: The object of the thesis is systems for walking
parameters estimation using IMUs.
Scope of the thesis: the scope of the thesis are building hardware and
algorithms of the walking parameters estimation systems. The walking
parameters are walking speed, step/stride length, step time, step
frequency.
Research Methods
Research methodology is a combination of theoretical and
experimental research, research from overview to details, inheriting
research results that have been published in the world, especially the
publication of the thesis author, and partner.
Scientific and practical significance
In science: The thesis is a scientific-technological work in
walking parameters estimation using Kalman Filter (KF) basing on
INS. Contribute to improving the accuracy of motion estimation in
specific cases, creating an accurate and objective information channel
to assist doctors in assessing health status as well as the rehabilitation

process.
In practice: From research and experimental results in building
INA and KF based on INS helps to master the technology of inertial
positioning and then widely deploy INS into practice. From the

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research results of the thesis, it is possible to manufacture equipment
to estimate walking parameters, which can be used in health care and
rehabilitation centers
The new contributions of the thesis
Propose and implement a new system to estimate the walking
parameters using IMU on a foot and on a walker, improving the
system’s accuracy to meet the requirements of medical facilities in
health care.
The general layout of the thesis
This thesis includes the introduction, contents, conclusions,
references and appendices. The content includes 4 chapters. The main
contributions of the thesis are in Chapter 3 and Chapter 4.
Chapter 1: Review of walking parameters estimation in health care
Chapter 2: Research to implement the algorithm of the inertial
navigation system
Chapter 3: Research to build an inertial navigation system on a foot
Chapter 4: Research to build an inertial navigation system on a walker

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CHAPTER 1. REVIEW OF WALKING PARAMETERS

ESTIMATION IN HEALTH CARE
1.1 Concepts about walking paramters
The medically necessary walking parameters are arranged in
order of importance to less important as follows: walking speed,
step/stride length, step frequency, step time, step width, foot angle,
swing time, stance time, distance traveled, ...
1.2 The importance of walking parameter
The walking parameters estimation systems contribute to:
-

Early diagnosis and monitoring of the progression of
diseases related to walking parameters in order to provide
the best treatment plan.

-

Evaluate health status and give advise on assistance,
hospitalization, rehabilitation needs, discharge location, and
the rehabilitation process.

-

Monitoring rehabilitation progress, give good exercise plans
to reduce rehabilitation time.

1.3 The potential of IMU in medical applications
Nowadays, IMU has an increasingly compact size, cheap price,
high accuracy and stability, especially its ability to operate
independently, so it has the most potential in medical applications.
Including artificial respiration support; monitoring activities;

biological response monitoring; detecting patient falls; monitoring the
posture of the patient's bed or patient; monitor the inclination of the
patient's head and neck with the breathing tube and feeding tube to
avoid clogging blood pressure monitoring; used in imaging equipment,
scanners, surgical instruments, prosthetic devices; vibration detection
for Parkinson patients; equipment wear monitoring; remote diagnosis,
rehabilitation,...

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1.4 Overview of research on the application of IMU in walking
parameters estimation
The algorithm using IMUs to estimate walking parameters can
be divided into 3 models: abstraction model, human gait model, the
ơpdirect integration model. In which, direct integration model uses
the integration of acceleration to obtain walking speed. This model
gives high accuracy, is easy to use and does not require training. In
particular, pedestrian navigation using INA is a new direction in this
model. The advantages of this direction are higher accuracy and 3D
parameters to extract more information, which will extend the
application of walking parameters in health care.
Therefore, this thesis uses the INA algorithm in pedestrian
navigation and improves the accuracy of motion estimation.
1.4.1 Abstraction Model
1.4.2 Human Gait Model Some
1.4.3 Direct Integration
1.4.4 Overview of research on walking parameters estimation
using IMUs on a foot
The foot is a great place to attach the IMU due to footsteps

repetition. There are zero velocity intervals (ZVIs) when the foot is on
the floor. Currently, there are many studies published on this issue.
However, each study has its advantages and disadvantages. In which,
the system simplicity in terms of hardware and algorithm, large error
while the high accuracy systems are complex hardware and algorithms,
even limited by the working range and need to pre-install the
environment. Therefore, the proposed system in Chapter 3 is both
simple, accurate and flexible in use.
1.4.5 Overview of research on walking parameters estimation
using IMUs on a walker
The inertial navigation system, placed on the walker, for users
in need of mobility assistance. Currently, there are studies published

Page 5


on this issue. However, most of them apply for a four-wheel walker
(less common type) and estimate basic walking parameters only.
Therefore, the walking parameters estimation system in Chapter 4 is
proposed for the most common types of walkers (two front–wheel
walkers and standard walkers), estimates a lot of walking parameters,
and is flexible in use.
1.4.6 Overview of research in Vietnam
In general, there are not many published studies on INS and
IMU in Vietnam, especially in applications in walking parameters
estimation. The studies on INS and IMU mainly focus on combining
with GPS in positioning problems.
1.5 Conclusion of chapter
In this chapter, the thesis shows the importance of the walking
parameters and the potential of IMU in medical applications. Then,

the overview of research on the application of IMU in the walking
parameters estimation is presented. From the overview of research, the
thesis chooses a research direction suitable to the trend of the world
that is pedestrian navigation using INA. The error of the INA
algorithm is increasing over time, so the thesis proposes methods to
improve the accuracy in two specific cases, namely, the INS placed on
the foot and placed on the walker. This is the main contribution of the
thesis shown in Chapters 3 and 4.
With the INS placed on the foot, the proposed system is both
simple and accurate and flexible in use. With the INS placed on the
walker, the INS placed on the most common types of 2 front-wheels
or standard walkers, estimates a lot of walking parameters, and is
flexible in use.

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CHAPTER 2. RESEARCH TO IMPLEMENT THE
ALGORITHM OF AN INS
2.1 Inertial Measurement Unit
2.1.1 Sensor introduction
2.1.2 Inertial sensor IMU
IMU consist of a 3D accelerometer and a 3D. IMU (Strapdown)
types MTi-100 (Chapter 3) and MTi-1 (Chapter 4) of Xsens are used
in this thesis. In this case, the INS is known as Strapdown-INS (SINS).
2.2 Implement inertial navigation system
2.2.1 Navigation systems
2.2.2 Implement the algorithm of SINS
1.1.1.1 Coordinate systems
In this thesis, we apply INS in a very narrow environment, so

we only use two coordinate systems, namely the body coordinate
system (BCS) and the world coordinate system (WCS). The WCS is
the external reference to determine the motion trajectory of the object.
Since an IMU is fixed to the moving object, the origin of BCS
coincides with the physical coordinate system of an IMU. WCS is used
as a local coordinate system. Origin of WCS coincides with the origin
of BCS at the beginning, the 𝑧𝑤 -axis is pointing upward, the 𝑥𝑤 -axis
is in the vertical plane of the 𝑥𝑏 -axis. Symbols [𝑎]𝑏 or [𝑎]𝑤 present a
vector 𝑎 in respect to BCS or WCS.
1.1.1.2 Operation principle of SINS
The measured angular velocity and acceleration signals are in
the BCS coordinate. The attitude of the moving object in the WCS
coordinate is determined by integrating the measured angular velocity
and the initial attitude of the moving object. The attitude is used to
transfer the measured acceleration from the BCS to the WCS and
remove the gravity acceleration. Then, the velocity of moving object
is obtained by integrating the acceleration and initial velocity.
Similary, the position of the moving object is obtained by integrating

Page 7


the velocity and initial position. Coordinate transferation and
integrating implementation are presented in the following subsections.
1.1.1.3 Transfer coordinate systems using quaternion
A vector 𝑎 is transferred from the BCS to the WCS is [𝑎]𝑤 =
𝑤 [𝑎]
𝑤
𝑏
𝑏

𝐶𝑏
𝑏 and vice versa [𝑎]𝑏 = 𝐶𝑤 [𝑎]𝑤 . In which, 𝐶𝑏 and 𝐶𝑤 are
𝑏
rotation matrices and 𝐶𝑏𝑤 = 𝐶 𝑇 𝑤 ∈ 𝑅 3×3 .
A rotation matrix can be obtained by DCM, Euler, and
quaternion methods. In which, the quaternion method is more
advantage is low storage information and low computation load.
A quaternion 𝑞 = 𝑞𝑤 + 𝑞𝑥 𝒊 + 𝑞𝑦 𝒋 + 𝑞𝑧 𝒌 is defined as a threecomponent imaginary complex number used to represent the rotation
from WCS to BCS. When WCS is rotated around a unit vector 𝑢 =
[𝑢𝑥 𝑢𝑦 𝑢𝑧 ] a suitable angle 𝜃 to coincide with BCS, a quaternion
𝑞 presents the rotation in matrix form is
𝑞 = [𝑞𝑤

𝑞𝑥

𝑞𝑦

𝑞𝑧 ] = [cos 𝜃
2

𝜃
sin 𝑢𝑥
2

𝜃
sin 𝑢𝑦
2

𝑇


𝜃
sin 𝑢𝑧 ]
2

(2-6)

A rotation matrix 𝐶𝑤𝑏 can be computed from quaternion 𝑞 as
follows
2 + 𝑞2 ) − 1
2(𝑞𝑤
𝑥

𝐶𝑤𝑏

= 𝐶(𝑞) = [2(𝑞𝑥 𝑞𝑦 − 𝑞𝑤 𝑞𝑧 )
2(𝑞𝑥 𝑞𝑧 + 𝑞𝑤 𝑞𝑦 )

2(𝑞𝑥 𝑞𝑦 + 𝑞𝑤 𝑞𝑧 )

2(𝑞𝑥 𝑞𝑧 − 𝑞𝑤 𝑞𝑦 )

2
2(𝑞𝑤

2(𝑞𝑦 𝑞𝑧 + 𝑞𝑤 𝑞𝑥 )]
2 + 𝑞2 ) − 1
2(𝑞𝑤
𝑧

+


𝑞𝑦2 )

−1

2(𝑞𝑦 𝑞𝑧 − 𝑞𝑤 𝑞𝑥 )

(2-11)

1.1.1.4 Implement integral to determine the attitude, velocity and
position
Integrating to determine attitude 𝑞 ∈ 𝑅 4 , velocity 𝑣 ∈ 𝑅 3 and
position 𝑟 ∈ 𝑅 3 of moving object in WCS can be implemented by
Taylor expansion in third-order for the attitude, first-order for the
velocity and position.
2.3 Implement Kalman Filter MEKF for the INS
The error of integrating will accumulate due to the noise in the
sensor and the approximation. Thus, the values of attitude, velocity,
and position from this integral expansion are called the preliminary

Page 8


value 𝑞̂, 𝑟̂ , 𝑣̂ . The KF filter will estimate their error 𝑞̅ , 𝑟̅ , 𝑣̅ to
compensate for the preliminary values. This is shown in Figure 2.12.
𝑏𝑎
CB
gia tốc

𝑦𝑎


𝑣̂ = 𝑣

Chuyển
sang
WCS

-

+

[𝑎]𝑤

-

𝑞̂ = 𝑞

𝑣̂
𝑞̂0

𝑏𝑔
𝑦𝑔

+

-

𝑟̂ = 𝑟

[𝑎]𝑤


INA

IMU
CB vận
tốc góc

+

𝑣̂0

[𝑔]𝑤

𝜔

𝑟̂0

𝑣̂

𝑞̂

𝜔

𝑞̂ 𝑣̂ 𝑟̂

Các tham số

𝑟̂
𝑞̂


𝑏𝑔

𝑏𝑎

BỘ LỌC
KALMAN

𝑞̅

𝑣̅

HIỆU
CHỈNH
1
𝑞 = 𝑞̂ ⊗ [ ]
𝑞̅

𝑞

𝑣 = 𝑣̂ + 𝑣̅

𝑣

𝑟 = 𝑟̂ + 𝑟̅

𝑟

𝑟̅

Các phép đo


Hình 2.12 INS algorithm using MEKF
Among filters are used for INS, the MEKF filter haves low
computation load and acceptable accuracy. MEKF estimates 𝑞̅ , 𝑣̅ , 𝑟̅
instead of directly estimating 𝑞, 𝑣, 𝑟 is to obtain a linear model. There
is no control signal in MEKF. IMU’s signal and preliminary value
𝑞̂, 𝑟̂ , 𝑣̂ are used to derive parameters of MEKF. Thus, the parameters
of MEKF are time-varying. Data from extra sensors is used to build
measurement updating for the filter. The filter is implemented in
discrete-time including model prediction and measurement equation.
2.4 Conclusion of chapter
In this chapter, the INS system uses a MEKF filter. In which,
INA uses integrals (using Taylor expansion) and coordinates
transform to roughly estimate the preliminary value of attitude,
velocity and position. MEKF both low computation load and
acceptable accuracy to estimate the error of the preliminary values,
thereby compensating for the attitude, velocity and position. MEKF is
linear, has no control input signals, the signals from IMUs as well as

Page 9


the preliminary estimate values used to build the filter parameters, the
values from the auxiliary sensors are used to build the measurement
equation for the filter. MEKF filters will be modified to apply to each
specific system shown in Chapters 3 and 4. This is the main
contribution of the thesis.
CHAPTER 3. RESEARCH TO BUILD AN INS ON A FOOT
3.1 Introduction of chapter
3.2 Propose an INS on a foot

The proposed system consisting of an IMU and a distance
sensor is fixed to a shoe. The parameters of the distance sensor include
the position vector 𝑟𝐷 and direction vector 𝑛𝐷 in BCS.
3.3 Build the model of MEKF filter
The model of the MEKF in Figure 2.12 is modified by adding
the error of position 𝑟̅𝐷 and direction 𝑛̅𝐷 of the distance sensor and
removing the bias of an IMU 𝑏𝑎 , 𝑏𝑔 to reduce the computation load.
So the state vector of the MEKF filter is 𝑥 = [𝑞̅ 𝑟̅ 𝑣̅ 𝑟̅𝐷 𝑛̅𝐷 ]𝑇 ∈
𝑅15. Then the position and direction of distance sensor are updated
𝑟𝐷 = 𝑟̂𝐷 + 𝑟̅𝐷 , 𝑛𝐷 = 𝑛̂𝐷 + 𝑛̅𝐷 . In which, the preliminary values 𝑟̂𝐷 and
𝑛̂𝐷 are measured by rulers.
3.4 Build measurement equations for MEKF filter
3.4.1 Velocity updating ZUPT
There are ZVIs when the foot touching in the floor during
walking. In ZVIs, the velocity and the height of the foot are almost
zero. Measurement equations of the MEKF filter can be derived from
conditions 𝑣 = 03×1 and 𝑟𝑧 = 0.
3.4.2 Measurement updating using distance sensor
Since the floor can be assumpted as a horizontal plane and the
origin of WCS is on the floor, the height of the foot is computed from
the measured value of distance sensor 𝑑𝐷 as [0 0 1]𝑟 =
−[0 0 1]𝐶 𝑇 (𝑞)[𝑟𝐷 + 𝑛𝐷 𝑑𝐷 ]𝑏 . A measurement equation for height
updating can be derived from the condition.
Page 10


Besides, from the condition of the unit vector, we have ‖𝑛𝐷 ‖ =
1. Another measurement equation for the MEKF filter can be derived
from the condition.
3.5 Implement MEKF filter for this system

MEKF filter implementation procedures for the system are
described in detail in Figure 3.2.
Begin
T: True

F: False

𝐼𝑛𝑖𝑡
𝑥0− = 015×1
𝑃0− = 015×15

F
ZVI=1
T
𝐶𝑜𝑚𝑝𝑢𝑡𝑒
𝐻𝑘 , 𝑅𝑘 (3-11)

Compute 𝐾𝑘 (2-33)
Update 𝑥𝑘 (2-34)
Update 𝑃𝑘 (2-35)

F
𝑑𝐷 > 0

T
𝐶𝑜𝑚𝑝𝑢𝑡𝑒
𝐻𝑘 (3-25)
𝑅𝑘 (3-26)

Compute 𝐴𝑘 (3-7)

Compute 𝑄𝑘 (2 − 29)
−
Update 𝑥𝑘+1
(2-30)
−
Update 𝑃𝑘+1
(2-31)

End

Hình 3.2 MEKF filter implementation procedures
3.6 Extract walking parameters from the position of the foot
The algorithm of INS using the MEKF filter estimates attitude,
velocity and position of the foot during walking. The walking
parameters (such as walking speed, step length, step time,...) can be
easily computed basing on ZVIs. Since the IMU is fixed to a foot only,
the stride cycle is the interval between the middle of 𝑖-th ZVI and the
middle of 𝑖 + 1-th ZVI.

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3.7 Experiments for system validation and results analysis
An experimental system to verify the accuracy of the proposed
system is implemented as in Figure. 3.3. In which, an IMU (Mti-100,
Xsens, Netherlands) and two distance sensors (VL6180) are attached
to a shoe. In the experimental system, we set up two distance sensors
instead of one distance sensor to evaluate the effect of the position and
number of the distance sensor. There are markers fixed in the
experimental system to track the motion of the foot using a reference

camera system (OptiTrack Six Flex 13).

Hạt phản quang

Cảm biến
khoảng cách 2

Cảm biến
khoảng cách 1

Cảm biến
quán tính

Figure 3.3 Experimental system on a foot
3.7.1 Experiment with the OptiTrack system
An experiment is implemented 4 times with a three-stride
walking under the tracking of the OptiTrack system. The purpose of
this experiment is to analyze the 3D position of the foot in each step
and evaluate the role of KF and measurement updating. Figure 3.10
shows the 3D estimated position and the error of the 3D estimated
position. In which, the left figure shows the estimated position in the
blue line and the reference position in the red-dash line tracked by the
OptiTrack system. The right figure shows the error of the estimated
position. As can be seen, the estimated position is close to the
reference position with respect to all axes.

Page 12


Hình 3.10 Estimated position of the foot using the proposed system

In quantity, the error evaluation criteria including the maximum
axial error, the average error on the axes, position error, relative
distance error are extracted in the following cases: using INA only,
using KF uses ZUPT update, uses ZUPT update to incorporate the
height at ZVI intervals and the proposed system uses distance sensor.
After only 3 strides, the error in the estimated distance was 1216%
when using INS without the MEKF filter. When using ZUPT velocity
update at ZVI intervals, the error of the distance decreased from 1216%
to 0.51% compared with the preliminary estimate without using KF.
When using the height update at the ZVI intervals, the maximum
vertical error decreased from about 5 cm to about 4 cm and the average
vertical error decreased from 1.48 cm to 1.01 cm compared to the case
only use the ZUPT velocity update. Although the error of estimating
the vertical foot position is eliminated after each step, the height error
during moving is not updated. The distance sensor is now used to
update foot height. When using information from the distance sensor,
Page 13


the maximum of estimated vertical error significantly reduces from
3.96 cm to 2.15 cm and the mean of error reduces from 1.01 cm to
0.56 cm. The estimated position error of 2.2 cm in 3 strides
corresponds to an error of about 3.5 mm per step. This is a very small
error in the step length estimation application.
Walking parameters of the 4-times experiment with 3-strides of
users are shown in Table 3.3. Besides, the parameters of a step can be
computed from the parameters of a stride.
Basing on the experimental results, the position of the distance
sensor does not affect to estimated parameters. Using more distance
sensors gives slightly better results than the case of using one distance

sensor but the number of state variables to be estimated must be
increased, so it was not suitable for real-time processing.
Bảng 3.3 Estimated walking parameters of 3-strides walking
Stride parameters
Moving time (s)

Time 1
0.8833

Time 2
0.87

Time 3
0.8667

Time 4
0.9033

Average
0.8808

Stance time (s)

0.37

0.28

0.4

0.34


0.3475

Cycle (s)

12,533

1.15

12,667

12,433

12,283

Length (m)

0.929

0.9942

0.8659

0.9424

0.9329

Height (m)

0.0453


0.0759

0.0481

0.0743

0.0609

Speed (m/s)

0.7412

0.8645

0.6836

0.7579

0.7618

Frequency (stride/s)

0.6834

0.7194

0.6818

0.6834


0.692

3.7.2

An experiment of walking along a corridor 30 m
The experiment was implemented with 5 users walking 30 m

along the corridor, 3 times for each user. The average error of the
estimated distance is 0.43 m over a total of 30 m travel. The error is
very small (1.4%) in the application of walking parameters estimation.
The average error is less than 1 cm in each step. This is a very small
error on foot length of 71 cm in this experiment.

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3.8 Evaluate the performance of the proposed system
The proposed system has simple hardware and algorithms,
small errors and flexible use. The system has overcome the limitations
of related studies
3.9 Conclusion of chapter
In this chapter, an INS on a foot is proposed to estimate walking
parameters using a distance sensor. The distance sensor is pointing to
the floor during walking to update the height of the foot in order to
improve the accuracy of walking parameters estimation.
The new contribution of the thesis in this chapter is to propose
and implement a new system to estimate the walking parameters using
the IMU sensor placed on the foot to achieve advantages such as small
error, simple hardware, simple algorithm and flexibility in use. In

particular, the specific new contributions are as follows:
-

Propose hardware of the INS system consisting of an IMU and a
distance sensor. The distance sensor is pointing to the floor to
correct the foot’s trajectory, especially the height of the foot
during walking.

-

Propose a model of the Kalman filter for the INS system. In which,
two state variables (𝑟̅𝐷 và 𝑛̅𝐷 ) of the distance sensor are added to
accurately estimate the position 𝑟𝐷 and direction 𝑛𝐷 of the
distance sensor. The measured distance is used to build updating
equations for the INS system.

-

Propose the updating equations of the Kalman filter for the INS
system using the measured distance to improve the accuracy of
the height of the foot during moving.

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CHAPTER 4. RESEARCH TO BUILD AN INS ON A WALK
4.1 Introduction of chapter
In this chapter, an INS on a walker (2 front-wheel and standard
type) is proposed to estimate the walking parameters for users in need
of mobility assistance. In which, an IMU is fixed to the frame of a

walker and two encoders are used to monitor the rotation of the
walker’s wheels.
4.2 Propose an INS on a walker
4.2.1 System overview
The proposed system, consists of an IMU fixed to the frame of
a walker and two encoders to monitor the rotation of wheels. WCS,
BCS and ICS are used for this system as in Figure 4.2. In which, ICS
takes the role of BCS shown in Chapters 2 and 3. BCS is set on the
walker’s frame.

Figure 4.2 Coordinate systems
4.2.2 Hardware connection and data synchronization
4.2.3 Estimate the relationship between ICS and BCS
Let 𝑇𝑏𝐼 ∈ 𝑅 3 and 𝐶𝑏𝐼 ∈ 𝑅 3×3 are translation vector and rotation
matrix to convert a vector in BCS to ICS. In this case, 𝑇𝑏𝐼 is the
position of an IMU in BCS and can be measured by rulers. The 𝑧𝑏 axis at the beginning time coincide with the direction of gravity
acceleration measured by IMU. The 𝑥𝑏 -axis coincides with the

Page 16


moving direction of the walker in an experiment with continuous
rolling 1 meter forward. We have 𝐶𝑏𝐼 = [[𝑥𝑏 ]𝐼 [𝑧𝑏 ]𝐼 × [𝑥𝑏 ]𝐼 [𝑧𝑏 ]𝐼 ].
4.3 Algorithm for movement detection and classification
4.3.1 Movement definition of a walker
The movement of a two front-wheel walker can be classified by:
continuous rolling, step-by-step rolling, two back-tip lifting, complete
lifting and rotating.
4.3.2 Algorithm for movement detection
An interval is considered a moving interval if the number of

encoder pulses obtained during the sampling time is greater than a
threshold for a sufficiently large time (about 0.3 s). When the angle of
rotation in the 𝑦𝑏 direction is sufficiently larger than a threshold in a
sufficiently large period (about 0.3 s), that interval is also considered
a moving interval.
4.3.3 Algorithm for movement classification
Begin

Movement detection:
- Using encoders
- Around y-axis using IMU
- Around z-axis using IMU
T: True
Đ

Movement using
encoder

Movement
around y-axis

Movement
around y-axis

S

Đ

Movement interval
> T step (Tb)

S

Đ

Continuous
rolling

Step-by-step
rolling

F: False
S

S

Movement
around y-axis
Đ

S

Đ

Two backtips lifting

Movement
around z-axis

Complete
lifting


Đ

Rotation

S

Not moving

End

Figure 4.4 Algorithm for movement classification

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4.4 Estimate the trajectory of the walker
Walker’s movement estimation using IMU is performed by the
INS algorithm using KF (type MEKF) shown in Chapter 2 with the
input state variables 𝑥 = [𝑞̅ 𝑏𝑔 𝑟̅ 𝑣̅ 𝑏𝑎 ]𝑇 . At ZVI intervals, the
ZUPT update is used to update the velocity and the height of the
walker.
4.4.1 Measurement equation for quaternion using vertical
direction
In the rolling case, the 𝑧𝑏 -axis of the walker is pointing upward
and coincides with the 𝑧𝑤 -axis, which can be determined by the
acceleration 𝑦𝑎 measured by an IMU at the beginning time. A
measurement equation is derived using this information.
4.4.2 Measurement equation for quaternion using yaw angle
In the rolling case, the yaw angle can be computed by encoders

and can be used to derive a measurement equation for KF.
4.4.3 Measurement equation for position using encoders
In the rolling case, the position of the walker can be computed
using two encoders. The computed position is used to update the
position of KF.
4.4.4 Combine the estimated trajectory using IMU and estimated
trajectory using encoders
The second method of estimating the movement of the walker
is a combination of the estimated trajectory using IMU in lifting
intervals and the estimated trajectory using encoders in rolling
intervals.
4.5 Walking parameters extraction
A new BCS coordinate system (BCSN) is defined. In which, the
origin is in the middle of two back tips of the walker and axes of
BCSN coincide with the axes of BCS. During walking the origin of
BCSN coincide with the heel of the user. Thurs, the walking
parameters can be extracted using the trajectory of BCSN. The results

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of walking parameters extraction during walking 20 times along a
corridor 20 m long using four different walking styles are shown in
Table 4.3.
Furthermore, it is also possible to access the movement
trajectory and posture of the walker during walking. This is quite
useful for physicians or experts in assessing the user's ability to walk
and health conditions.
Bảng 4.3 Walking parameters of an user walk 20 m using walker
Walking

style

Time

1
2
Step-by3
step rolling
4
5
1
2
Continuous
3
rolling
4
5
1
2
2 back-tip
3
lifting
4
5
1
2
Complete
3
lifting
4

5
Average of error

Distance
(m)
19,95
19,94
19,89
19,9
19,99
19,78
19,85
19,81
19,63
19,85
20,42
19,84
20,03
20,26
19,66
20,32
20,26
20,04
20,23
20,62
1%

Number
of step
(step)

42
41
46
48
48
32
35
34
33
33
38
38
39
39
39
35
35
34
33
34

Walking
time (s)
146,54
148,9
146,84
152,76
168,38
22,76
27,17

26,06
26,54
25,19
136,12
130,6
138,94
138,57
132,1
136,78
135,58
138,31
135,1
140,76

Step
length
(mm)
476,71
489,08
435,41
417,77
418,16
620,72
575,15
589,86
587,94
614,45
539,05
523,94
514,93

521,12
506,13
582,06
581,12
591,25
615,19
608,57

Step
cycle (s)
3,49
3,63
3,19
3,18
3,51
0,71
0,78
0,77
0,8
0,76
3,58
3,44
3,56
3,55
3,39
3,91
3,87
4,07
4,09
4,14


Walking
speed
(mm/s)
136,92
135,01
136,7
131,09
119,28
933,58
776,97
797,96
798,23
837,86
150,63
152,67
144,68
146,7
149,71
150,19
151,33
146,12
151,16
147,67

4.6 Experiments for algorithm analyzation
4.6.1 Experimental system
4.6.2 Experiment description
4.6.3 Analysis of the combination the estimated trajectory using
IMU and estimated trajectory using encoders

The first experiment is implemented by five users of the
proposed walker system along a 20-m corridor. In which, the

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continuous rolling is used in the first 5 m, the step-by-step rolling is
used in the second 5 m, the two back-tip lifting is used in the third 5
m and the complete lifting is used in the last 5 m. The average error of
the estimated distance is 0.8% of 20 m traveling distance. So, the
average error is about 0,42 cm in each step. This is an acceptable error
in the application of walking parameters measurement.

Figure 4.12 The results of movement detection and classification
4.6.4 Analysis of the measurement updating using encoder
The second experiment is implemented with five users. In
which, each user walks along a 20 m corridor 20 times (five times for
each walking style) using the walker. The average error is 1.47% in
the estimated distance, respectively of 0.77 cm for each step with 0,53
m average step length. This is an acceptable error in the application of
walking parameters measurement.
4.6.5 Analyze and evaluate the effect of measurement updatings
using encoders
The measurement updatings take an important role in
continuous rolling cases (the average error reduces from 9.337 m to
0.327 m). However, the measurement updatings have little effect in
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step-by-step rolling cases (the average error reduces from 0. 445 m to

0.059 m). In which, the measurement equation for position using
encoders gives the best result.
The measurement updating is ineffective in the lifting case. In
this case, the ZUPT for the velocity and the height of the walker has
been updated to improve the accuracy of estimated walking
parameters.
4.6.6 Accuracy analysis using OptiTrack system

Hình 4.13 Estimated a reference trajectory of the walker
The accuracy of the proposed system is also verified by the
OptiTrack system through the third experiment. In which, two markers
are fixed on feet and a marker is fixed to the origin of BCS to obtain
the reference trajectory of the walker. The estimated trajectory (the
blue line in the left figure), reference trajectory (the dash-red line in
the left figure) and the error of estimated trajectory (the blue line in
the right figure) are shown in Figure 4.13. In which, the error of the
final position is less than 1 cm and the average error is 7.3 mm in each
step. This is an acceptable error in the application of walking
parameters measurement.

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Figure 4.15 Step point detection using OptiTrack system
4.6.7 Evaluate the role of the KF in the INS system
To evaluate the role of the KF in the INS system, the results of
the experiment with the OptiTrack system are estimated without the
KF. The error of the estimated final position is over 60 m. This error
is too large compared to the travel distance of 2 m. Hence INS must
be used with filters, in this case, the KF.

4.6.8 Evaluate the accuracy in rotation movement
Average results are 0.638 𝑚 in 40 𝑚 traveling (1,6%) with an
1800 rotation and 0.712 𝑚 in 48 𝑚 traveling with 7-time 900 rotation
(1,4%).
4.6.9 Experiment with the patients
An experiment is implemented at the department of
physiotherapy and rehabilitation – C17 Military Hospital at Danang
City from 25/12/2020 to 2/1/2021. The experiment was carried out
with 10 patients who have difficulty walking, due to diseases such as
ligament rupture, cerebral hemorrhage and left tibial plateau rupture,
and are undergoing rehabilitation treatment.

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Extracted walking parameters are the number of steps, the
length of step, the time of step, walking speed, frequency of step and
walking style using a walker.
The distance error is 1,38%. This is a small error in the
application of walking parameters measurement. Thus, the proposed
system is used to collect data and extract walking parameters of
patients who are recovering walking function at the hospital.
4.7 Evaluate the performance of the proposed system
The proposed system has small errors and used for standard
walker and two front-while walker. The system has overcome the
limitations of related studies
4.8 Conclusion of chapter
The new contribution of the thesis in this chapter is to propose
and implement a new system to estimate the walking parameters using
an IMU placed on the walker, to obtain the small error, flexible in use,

using for 2-wheel or non-wheel walker. In particular, the specific new
contributions are as follows:
- Proposed hardware system including an IMU placed on the
walker combined with two encoders attached to two wheels.
- Propose a method to calibrate the relationship between the IMU
and the walker.
- Propose an algorithm to detect and classify the walker's
movement.
- Propose updating equations for the INS system using information
from encoders to improve accuracy in the time intervals of
walkers being pushed on the ground when the basic INS system
cannot estimate exactly.
- Propose an algorithm to detect the event that the foot is on the
ground in case the walker is pushed continuously on the ground.

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