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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 I

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)

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

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

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,

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

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

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

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

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

CHAPTER 2 RESEARCH TO IMPLEMENT THE

ALGORITHM OF AN INS 2.1 Inertial Measurement Unit

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

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

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=

𝐶𝑏𝑤[𝑎]𝑏 and vice versa [𝑎]𝑏 = 𝐶𝑤𝑏[𝑎]𝑤 In which, 𝐶𝑏𝑤 and 𝐶𝑤𝑏 are rotation matrices and 𝐶𝑏𝑤 = 𝐶𝑇

𝑤 𝑏

∈ 𝑅3×3

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+ 𝑞𝑥𝒊 + 𝑞𝑦𝒋 + 𝑞𝑧𝒌 is defined as a component 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

three-𝑞 presents the rotation in matrix form is

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

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

++

-BỘ LỌC KALMAN

𝑣̂0

[𝑎]𝑤[𝑎] 𝑤

+[𝑔 ] 𝑤

Các tham số

𝑞̂ 𝑣̂ 𝑟̂

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

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

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

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]𝐶𝑇(𝑞)[𝑟𝐷+ 𝑛𝐷𝑑𝐷]𝑏 A measurement equation for height updating can be derived from the condition

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

𝐼𝑛𝑖𝑡

𝑥 0−= 0 15×1

𝑃 0−= 0 15×15

Compute 𝐴 𝑘 (3-7) Compute 𝑄 𝑘 (2 − 29) Update 𝑥𝑘+1− (2-30) Update 𝑃 𝑘+1− (2-31)

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