Human Bio-Kinematic Parameter Estimation Using Inertial ...dro.deakin.edu.au/eserv/DU:30089358/maddumage-humanbio-2016A.pdf · Human Bio-Kinematic Parameter Estimation Using Inertial

Human Bio-Kinematic Parameter

Estimation Using Inertial Sensors

By

Maddumage Sajeewani Karunarathne

B.Sc.

Submitted in fulfilment of the requirements for the degree of

Doctor of Philosophy

Deakin University

June, 2016

DEAKIN UNIVERSITY

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Human Bio-Kinematic Parameter Estimation Using Inertial Sensors

submitted for the degree of Doctor of Philosophy

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Full Name: Maddumage Sajeewani Karunarathne

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Date: 11.10.2016

DEAKIN UNIVERSITY

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Human Bio-Kinematic Parameter Estimation Using Inertial Sensors

submitted for the degree of Doctor of Philosophy

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the form is correct’

Full Name: Maddumage Sajeewani Karunarathne

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Date: 11.10.2016

Acknowledgements

It is a genuine pleasure to express my deep sense of gratitude to my supervisor, As-

sociate Professor Dr. Pubudu Pathirana. Being an excellent advisor and mentor,

his dedication, keen interest and above all, his immense knowledge mainly sup-

ported me for completing this work. Further, his timely advice, financial supports,

meticulous reviews, scholarly advice and scientific approaches have helped me to a

great extent to complete my dissertation.

Apart from my supervisor, my thank also goes to Dr Samitha Ekanayake. His

ideas and feedbacks inspired me and encouraged me to venturing deeper into this

research field.

I would also like to thank Sabaragamuwa University of Sri Lanka, University

Grants Commission of Sri Lanka and Deakin University for giving me this oppor-

tunity to be a PhD student by supporting through financial support.

Further, I thank Professor Malcolm Horne in the University of Melbourne and

his staff for their help and constructive feedback on clinical trials.

I also thank all the members of the Deakin Network and Sensing Group and

Deakin University staff for sharing me with valuable experience of both study and

life.

Last but not least, I thank my parents for supporting me spiritually and ma-

terially during my study in Australia, as well as throughout my life. At the same

time, I would like to thank my husband who dedicated his time to take care of my

life and cheer me up during highs and lows of my student life. This dissertation is

dedicated to them.

i

Publications

• Published: Saiyi Li, Hai Trieu Pham, Karunarathne M. S., Yee Siong Lee,

SamithaW. Ekanayake, and Pubudu N. Pathirana, “A Mobile Cloud Comput-

ing Framework Integrating Multilevel Encoding for Performance Monitoring

in Telerehabilitation”, Mathematical Problems in Engineering, vol. 2015, pp.

14

• To be submitted: Pathirana P. N., Karunarathne M. S., Nam P. T.,

Hugh Durrant-Whyte, “Robust Estimation of Human Movements from In-

ertial Measurements”

• To be submitted: Karunarathne M. S., Saiyi Li, Ekanayake S. W., Pathi-

rana P. N., “Limb Length Estimation with IMU sensors for Limb Length

Discrepancy”, Journal of Computers in Biology and Medicine, Elsevier Pub-

lication

• Published: Karunarathne M. S., Nguyen N. D., Menikidiwela M. P., Pathi-

rana P. N., “The study to track human arm kinematics applying solutions of

Wahba’s Problem upon inertial/magnetic sensors”, Inclusive Smart Cities and

Digital Health, ICOST 2016, pp. 395-406

• Published: Williams G. L., Karunarathne M. S., Ekanayake S. W., Pathi-

rana P. N., “Ambulatory Energy Expenditure Evaluation for Treadmill Exer-

cises”, Inclusive Smart Cities and e-Health. Springer International Publishing,

2015, pp. 331-336.

• Published: M. S. Karunarathne, S. A. Jones, S. W. Ekanayake and P.

N. Pathirana, “Remote Monitoring System Enabling Cloud Technology upon

Smart Phones and Inertial Sensors for Human Kinematics”, Big Data and

ii

iii

Cloud Computing (BdCloud), 2014 IEEE Fourth International Conference

on, Sydney, NSW, 2014, pp. 137-142.

• Published: M. S. Karunarathne, S. W. Ekanayake and P. N. Pathirana,

“An adaptive complementary filter for inertial sensor based data fusion to

track upper body motion”, Information and Automation for Sustainability

(ICIAfS), 2014 7th International Conference on, Colombo, 2014, pp. 1-5.

• Published: M. S. Karunarathne, S. Li, S. W. Ekanayake and P. N. Pathi-

rana, “A machine-driven process for human limb length estimation using in-

ertial sensors”, 2015 IEEE 10th International Conference on Industrial and

Information Systems (ICIIS), Peradeniya, 2015, pp. 429-433.

• Published: M. S. Karunarathne, S. Li, S. W. Ekanayake and P. N. Pathi-

rana, “An adaptive orientation misalignment calibration method for shoulder

movements using inertial sensors: A feasibility study”, Bioelectronics and

Bioinformatics (ISBB), 2015 International Symposium on, Beijing, 2015, pp.

99-102.

• Accepted: M. S. Karunarathne and P. N. Pathirana, “A Comparison for

Capturing Arm Kinematics using Solutions of Wahbas Problem and Ordi-

nary Data Fusion Mechanisms”, 5th Edition of International Conference on

Wireless Networks and Embedded Systems - WECON 2016

Table of Contents

Acknowledgements i

Publications ii

Table of Contents iv

Abstract viii

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Human kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Musculoskeletal injuries and neurological movement disorders . . . . 7

1.4.1 Musculoskeletal injuries . . . . . . . . . . . . . . . . . . . . 7

1.4.2 Movement disorders . . . . . . . . . . . . . . . . . . . . . . 7

1.5 Sensors in rehabilitation . . . . . . . . . . . . . . . . . . . . . . . . 9

1.5.1 Goniometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.5.2 Passive marker based optical system - VICON and Qualisys

systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.5.3 Kinect c© optical system . . . . . . . . . . . . . . . . . . . . 14

1.5.4 Inertial sensor . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.5.5 Summary and challenges . . . . . . . . . . . . . . . . . . . . 18

1.5.6 Motivation to use inertial sensors . . . . . . . . . . . . . . . 19

1.6 Orientation tracking using inertial sensor measurements . . . . . . . 20

1.6.1 Accelerometer . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.6.2 Magnetometer . . . . . . . . . . . . . . . . . . . . . . . . . . 23

1.6.3 Gyroscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

1.6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

1.7 Wahba’s problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

1.7.1 Applicability of Wahba’s problem for inertial sensor based

orientation estimation . . . . . . . . . . . . . . . . . . . . . 29

1.7.2 Available solutions for Wahba’s problem . . . . . . . . . . . 30

1.8 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

iv

v

1.9 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2 Robust Estimation Of Shoulder Movements 36

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.2 Data fusion techniques and algorithms . . . . . . . . . . . . . . . . 37

2.2.1 Gradient descent algorithm . . . . . . . . . . . . . . . . . . 37

2.2.2 Complementary filter . . . . . . . . . . . . . . . . . . . . . . 39

2.2.3 Adaptive complementary filter . . . . . . . . . . . . . . . . . 40

2.2.4 The algorithms for solving Wahba’s solution . . . . . . . . . 42

2.2.5 Kalman filter . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.2.6 Extended Kalman filter . . . . . . . . . . . . . . . . . . . . . 49

2.2.7 Robust extended Kalman filter . . . . . . . . . . . . . . . . 52

2.2.8 Comparison and summary . . . . . . . . . . . . . . . . . . . 53

2.3 Dynamic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

2.4 Robustness of the non-linear model . . . . . . . . . . . . . . . . . . 60

2.5 Robust optimisation based approach for orientation estimation . . . 62

2.6 Implementation of the orientation estimation . . . . . . . . . . . . . 63

2.6.1 Extended Kalman filter based approach . . . . . . . . . . . . 64

2.6.2 Robust extended Kalman filter approach . . . . . . . . . . . 64

2.6.3 Robust extended Kalman filter with linear

measurements approach . . . . . . . . . . . . . . . . . . . . 64

2.7 Computer simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 66

2.7.1 Model based state estimation techniques compared to uncer-

tainty bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

2.7.2 Model based state estimation techniques compared to noise

variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

2.7.3 Simulation results and discussion . . . . . . . . . . . . . . . 68

2.8 Real-time experiments . . . . . . . . . . . . . . . . . . . . . . . . . 69

2.8.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . 69

2.8.2 Comparison of model based state estimation techniques with

experimental measurements . . . . . . . . . . . . . . . . . . 70

2.8.3 Summary and conclusion . . . . . . . . . . . . . . . . . . . . 76

3 Curvature Estimation In Limb Trajectories Using Inertial Sensors

And Its Applications 77

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.2 Adaptive orientation misalignment calibration mechanism for iner-

tial/magnetic sensors . . . . . . . . . . . . . . . . . . . . . . . . . . 78

3.2.1 Motivation for orientation misalignment calibration . . . . . 78

3.2.2 Geometrical relationship between curvature, misalignment er-

ror and shoulder to limb length . . . . . . . . . . . . . . . . 80

3.2.3 Equations and algorithm formulation . . . . . . . . . . . . . 81

3.2.4 Computer simulations . . . . . . . . . . . . . . . . . . . . . 84

vi

3.2.5 Discussion and conclusion . . . . . . . . . . . . . . . . . . . 88

3.3 Limb length estimation . . . . . . . . . . . . . . . . . . . . . . . . . 88

3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

3.3.2 Proposed approach . . . . . . . . . . . . . . . . . . . . . . . 90

3.3.3 Identification of least noisy threshold (LNT) in noisy data . 92

3.3.4 Real-data experiment and result . . . . . . . . . . . . . . . . 96

3.3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4 Qualitative Analysis Of Human Kinematics With Inertial Sensors102

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.2 Investigation of the thoracic rotational patterns of Parkinson’s pa-

tients using inertial sensors . . . . . . . . . . . . . . . . . . . . . . . 104

4.2.1 Evaluation of physical features of Parkinson’s patients . . . 105

4.2.2 Experiement setup . . . . . . . . . . . . . . . . . . . . . . . 105

4.2.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . 107

4.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

4.3 Ambulatory energy expenditure evaluation for gait exercises . . . . 117

4.3.1 Energy expenditure in activities . . . . . . . . . . . . . . . . 119

4.3.2 Experiment setup . . . . . . . . . . . . . . . . . . . . . . . . 120

4.3.3 Relationship of gyro based proposed energy expenditure with

gold standard metabolic rate . . . . . . . . . . . . . . . . . . 122

4.3.4 Variation of energy expenditure pattern with the subject . . 123

4.3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

5 Mobile - Cloud Based Physical Tele-rehabilitation System - A Pro-

totype 126

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

5.2 Available remote human monitoring system and architectures . . . 127

5.3 System architecture bridging sensor modules, mobile, PC and web

Cloud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

5.3.1 Development of BioKin-Mobi . . . . . . . . . . . . . . . . . 131

5.3.2 Development of web application - BioKin-Cloud . . . . . . . 131

5.3.3 Analysis oriented decision support system . . . . . . . . . . 136

5.3.4 Security service layer . . . . . . . . . . . . . . . . . . . . . . 138

5.4 Multi-Level data encoding technique . . . . . . . . . . . . . . . . . 139

5.4.1 Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

5.4.2 Determine encoding level . . . . . . . . . . . . . . . . . . . . 143

5.4.3 Optimised bio-feedback . . . . . . . . . . . . . . . . . . . . . 145

5.4.4 Results and platform demonstration . . . . . . . . . . . . . . 147

5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

6 Conclusion 153

vii

Bibliography 168

Abstract

This thesis focuses on accurately capturing bio-kinematic parameters for physical

tele-rehabilitation using measurements from inertial sensors. The contributions can

be classified into three categories: accurately capturing human kinematics despite

intrinsic uncertainties omnipresent with human movements, improving the track-

ing accuracy by correcting the sensor misalignment error and assessing rehabilita-

tion exercises quantitatively or qualitatively in a systematic way for evaluating the

progress of people with disabilities.

Firstly, a dynamic model for human kinematics is proposed and different data

fusion algorithms are applied to fuse inertial sensor measurements for obtaining

accurate movement angles. Specifically, a novel robust extended Kalman filter with

linear measurements (REKFLM) is proposed to improve accuracy in estimated an-

gles. Secondly, a sensor misalignment calibration method is proposed. In addition,

a method for estimating the limb’s length for assessing a common musculoskele-

tal disorder called Limb Length Discrepancy is proposed. Importantly, these two

methods are proposed considering the curvature in limb trajectories which has not

previously used in similar problems. Thirdly, the novel REKFLM approach and

other relevant sensor fusion algorithms have successfully been used to assess arm

exercises quantitatively. The qualitative and statistical analyses for trunk move-

ments are conducted to distinguish Parkinson’s patients from healthy subjects.

Finally, these advancements led to a prototype of a mobile cloud-based physical

tele-rehabilitation system for motion capturing and evaluation of patients. This

prototype is developed in the web cloud to facilitate convenient access to patients

using mobile devices. A multi-level encoding scheme is proposed to avoid limitations

of mobile and sensor devices to ensure reliable and efficient rehabilitation services.

viii

Chapter 1

Introduction

1.1 Motivation

Remote health condition monitoring applications are becoming a part of everyday

life due to the rapid increase in the aged population, the people with disabilities

due to various neurological conditions and health care expenditures in across the

world. Stroke which is a severe neurological condition, is considered the leading

cause of disability worldwide. Further, it is considered as the second most common

cause of dementia, and the third leading cause of death [1, 2, 3].

This trend can also be observed in Australia. Based on a study conducted by the

Australian government [4], the aged population (over 65 years) in Australia has

increased by 7% in 1970 and 13% in 2001 which is destined to further increase

next forty years. According to statistical sources in Australia [5], 75% - 80% of

survivors of such neurological conditions (mainly stroke and Parkinson’s disease)

required post rehabilitation therapy [6] which is a heavy burden for Australia in

terms of illness, disability, death and medical care expenditure. The largest cost

component of the total medical budget (around 10700 USD) was allocated for re-

habilitation admissions every year. Moreover, this number is forecasted to increase

over the next decades due to the increasing number of elderly Australians in agree-

ment with the global trends. This naturally raises the need for remote therapy

and tele-rehabilitation. On the other hand, there are motion analysing laboratories

1

Chapter 1. Introduction 2

which are especially designed and augmented by special instruments for kinematic

and kinetic analysis. However, they require expensive specialized instrumentation

and engineering support. Furthermore, bringing survivors to motion analysis labo-

ratories is inconvenient for both patients and caregivers.

Nevertheless, among a dearth of assessment equipment appropriate for home use

[1], few are efficient in terms of cost and usability. Inertial sensors are widely used

for Mo-Cap (Motion-Capturing) systems due to their affordability and usability

for long term monitoring [7]. However, the inertial sensor based systems are gen-

erally deficient of the required accuracy due to noise and so called sensor drift.

Indeed the accuracy improvement of IMU (Inertial Measurement Unit) based esti-

mations will have affordable wearable systems capturing human kinematics vital for

tele-rehabilitation applications. This thesis aims to improve bio-kinematic motion

estimation primarily using model based estimation techniques.

1.2 Background

The advancement in assistive bio-medical applications have drawn researcher’s at-

tention during the last few decades with their remarkable contribution for assisting

people with disabilities in rehabilitation activities. Furthermore, with the rapid

increase of the aged population across the world, the need for such applications is

further increased.

Human monitoring systems with a number of sensors have been already used in

rehabilitation for patients under severe neurological conditions such as Parkinson’s

disease, stroke and cerebral palsy. However, the major challenge of most of these

systems is the substantial cost. On the other hand, some sensor technologies are only

suitable for a laboratory environment. In that scenario, caregivers bring patients

to clinics which waste their time and money. Moreover, it is inconvenient to both

patients and caregivers. On the other hand, the importance of long term monitoring

is emphasised in continuous rehabilitation by clinicians. Hence, systems enabling


long-term monitoring are a significant requirement.

The available sensor technologies in rehabilitation can be categorised into sev-

eral dimensions such as wearable/non-wearable, optical/non-optical, yet each of

these categories have advantages and disadvantages. However, under the aspects of

cost, accuracy, compactness, portability and ability for long-term monitoring, the

inertial sensors have replaced other sensors. IMU included devices are commercially

available such as smart watches and activity tracking bands. Hence the use of IMUs

is very common today for capturing human motions.

Orientation estimation of human body using IMUs is one of the leading research

areas in rehabilitation. One of the first and most influential works in this problem

was a mathematical problem proposed by Wahba in 1965. Over time, the solutions

for this problem have evolved. The deterministic attitude estimators such as TRIAD

method, Davenport’s q method, singular value decomposition method and QUEST

method are well known solutions for Wahba’s problem which has potential to be

applied in quantitative evaluation of human motion tracking.

Nonetheless, the powerful data fusion algorithms such as Kalman filter, parti-

cle filter have been applied to get improved accuracy in attitude estimation using

IMUs. The advantage of applying these algorithms into attitude estimation is that

it enables capturing human movements in real-time. Further, the robustness and

uncertainty could be accounted in some data fusion mechanisms such as robust

extended Kalman filter. All these filters have shown better accuracy in determin-

ing positions and velocity of dynamic objects in fields such as aerial science and

robotics. In the last decade, with the emergence of a new class of attitude esti-

mation techniques, relying on nonlinear observers and accounting uncertainty, has

brought new hopes for more reliable and stable attitude estimation which can be

applied in human motion tracking.

Recently, the advancement of Information Communication Technology (ICT)


and Mobile Cloud Computing (MCC) are commonly used for home-based rehabil-

itation systems. Rehabilitation systems are emerging with easy access to mobile

phone and internet. The mobile phone is one of convenient tool and the cloud based

web services provide unlimited resources for data intensive computations and stor-

age. The combination of the powerful attitude estimators with ICT, has potential

to improve rehabilitation with fast and convenient services.

1.3 Human kinematics

The human upper body can be divided into five segments: trunk, right upper arm,

right forearm, left upper arm and left forearm. The arm segments are connected by

a glenohumeral joint (shoulder joint) and it is a multi-axial synovial ball and socket

joint which has three degrees of freedom (3 DOF). The upper arm and forearm are

connected to each other by elbow joint. It is a synovial hinge joint with 2 DOF.

Human kinematics is defined as a branch of mechanics that describes the motion

without regard to the forces or torques that may produce the motion[8]. Therefore,

human kinematics is essentially the investigation of human body motion ignoring

the cause of the motion such as forces, momentum and torque. Both range of

movement and muscle length is vital for describing human kinematics [9]. Hu-

man kinematics can be categorised in two main groups: Arthorkinematics and Os-

teokinematics. Arthorkinematics refers to actual movement of the joint surfaces in

relation to one another and Osteokinematics refers to the observation of the quality

and degree of motion in the bony lever arm. In this study, Osteokinematics is the

focus.

First, the planes of motion, axes of movement and point of reference should be

identified for better understanding of human motions. The point of reference is an

anatomical position such as shoulder, elbow and neck. The human motion can be

described in three imaginary planes: Sagittal plane as in figure 1.1(a), Frontal plane

as in figure 1.1(b) and Transversal plane as in figure 1.1(c).


(a) Sagittal plane (b) Frontal plane (c) Transversal plane

Figure 1.1: Plane of motion [10]

The Sagittal plane is an imaginary plane which the body divides into right

and left sides around the perpendicular axis. This perpendicular axis is called the

medial-laternal axis. There are two fundamental kinematic movements observed

in this plane which are named Flexion and Extension. Flexion is defined as a

motion when the angle between two bones is decreased [11] and Extension is the

opposite action of flexion as the angle is increased. The Flexion - Extension motion

is demonstrated in figure 1.2.

The Frontal/Coronal plane is also a vertical plane that divides the body into

anterior/front or posterior/back. The main two motions in this plane are abduction

and adduction around the anterior - posterior axis. Abduction is defined as a

movement when a limb is moved away from the midsagittal plane or when the

fingers or toes are moved away from the median longitudinal axis of the hand [11].

Adduction is the opposite action. Adduction happens when a limb is moved toward

or beyond the midsagittal plane or when the fingers or toes are moved towards

median longitudinal axis of the hand or foot[11]. These movements are shown in

figure 1.2.

The last plane is the transverse plane. This is a horizontal plane which divides


the body into upper/superior/cranial and lower/interior/caudal sections. The main

movements in this plane are medial rotation, lateral rotation, pronation and supina-

tion However, all these movements include a rotation around a central axis. This

rotation is defined as a form of movement which a bone moves around a central axis

without undergoing any other displacement. The supination/pronation is shown in

figure 1.2.

Figure 1.2: Osteokinematic motions [10]

Referenced to discussed human kinematics, a human upper arm can perform

three fundamental movements:

1. Abduction and Adduction

2. Flexion and Extension

3. Pronation and Supination

Tables 1.1 and 1.2 show the standard length and constraints of ROM for upper

limbs of healthy subjects.


Table 1.1: Length of upper limb segments

Subject Upper arm (m) Forearm (m) Hand(m)

Adult Male 0.315 0.287 0.105Adult Female 0.272 0.252 0.091

Table 1.2: Angle limits

Angle Min (degrees) Max(degrees)

Shoulder Joint -140 90Elbow Joint 0 145Wrist Joint -70 90

1.4 Musculoskeletal injuries and neurological move-

ment disorders

Movement disorders associated with various injuries and conditions are generally

treated with physical rehabilitation. There are number of causes for abnormal move-

ments, which can be classified into two main categories, including musculoskeletal

injuries and neurological movement disorders. In this section, some examples in

these two categories are briefly discussed.

1.4.1 Musculoskeletal injuries

These injuries are normally observed in joints with certain degree of movements,

such as shoulder, elbow and wrists in upper extremities, hips, knees and ankles in

lower ones, which may eventually lead to abnormal movements or disabilities.

1.4.2 Movement disorders

Movement disorders are generally indicated by various symptoms and signs result-

ing from different neurological disorders and conditions. There are two main types

of symptoms associated with these disorders. In one type, the movements of the pa-

tients are much slower and less magnitude than healthy people, which are classified

as hypokinesias. On the other hand, some patients may experience excessive and


abnormal involuntary movements or hyperkinesias [12]. According to [13], some

common examples of hypokinesias include bradykinesia, freezing, rigidity and stiff

muscles, while those belong to hyperkinesias are chorea, dyskinesia, myoclonus, tics

and tremor.

There are some commonly seen diseases and conditions that are associated with

one or multiple movement disorders, examples of which are discussed as follows.

Firstly, the most common neurological disorder [14] and adult movement disor-

der, essential tremor (ET) is about 20 times prevalent as Parkinson’s disease. Due

to the fact that patients with ET are highly likely to have tremor with 4 to 12 Hz,

their ability to perform tasks in both work and daily living is adversely affected

[15]. Three potential risks that may lead to ET include age, ethnicity and a family

history [14]. As for the pathology of ET, although there are some controversial dis-

cussions, three hypotheses are tested. According to the conclusions made by [16],

some evidence can be found for the neurodegeneration hypotheses. In addition, it

is confirmed that GABAergic tone is reduced in the same location as the change

of neurodegeneration. Lastly, some studies were conducted to test the hypothesis

that there is an oscillating network, rather than one oscillator leading to essential

tremor. A number of medical approaches have been proposed to treat essential

tremor [17], physical rehabilitation methods are also used [18].

The second condition that leads to a number of different movement disorders

is Parkinson’s disease (PD), which is the second most common neurodegenerative

disorder [19]. As for its prevalence, 160 out of 100000 people in Western Europe

with age over 80[20] suffer from the condition. In China, 1.7 % people over 65 years

of age and approximately 1.7 million people over 55[21] years of age are diagnosed

with PD. The potential causes of PD can be generally divided into two categories:

non-genetic (environmental) and genetic risk factors [19]. The former includes but is

not limited to endotoxin (lipopolysaccharide) resulting from Salmonella minnesota

[22] and pesticide[23], while the latter involves causative genes and susceptibility


genes [19]. According to [24], the movement disorders experienced by a PD patient

can be classified into three stages. In the initial stage of PD, the patient may have

forward stooped posture, festinating gait (involuntarily leg movements with short,

accelerating steps with the trunk flexed forward and the legs flexed stiffly at the

hips and knees) and rigidity [25]. Furthermore, during the first ten years of PD,

phenomena such as resting tremor, hypokinesia and micrographic handwriting are

observed. Moreover, in the latter phase, patients may exhibit dyskinesia, akinesia

and postural instability. In terms of treatment, various kinds of medical therapies,

surgical approaches and deep brain stimulation are utilised to control symptoms.

Physical therapies, such as [26] are also considered.

Although the previous two conditions are very common, they are not fatal.

Stroke is one of the most fatal conditions in developed countries[27]. However, the

majority of the stroke suffers lose of some motor functions subsequently [28] after

survival. In [29], it is mentioned that, in 2005, there were 5.7 million death in

low and middle income countries resulted from stroke, which may increase signif-

icantly to 6.5 million and 7.8 million in 2015 and 2030 without intervention. The

risk factors considered for stroke are age, gender, race, ethnicity and heredity [30].

Additionally, hypertension, cardiac disease, diabetes, glucose metabolism, lipids,

cigarette smoking, alcohol, illicit drug use and lifestyle may contribute [30]. The

main pathophysiology of ischemic stroke is tissue necrosis resulted from excito-

toxic, inflammatory and microvascular mechanisms [31]. Similar to PD, a number

of involuntary abnormal movements are associated with stroke. Similar to other

disorders, physiotherapies are also widely utilised to assist stroke patients to regain

some physical functionality [32].

1.5 Sensors in rehabilitation

The goal of rehabilitation is defined as enabling a person with neurological condi-

tions such as stroke or Parkinson’s disease, to regain the highest possible level of


independence so that they can be as productive as possible [33]. The rehabilita-

tion process engaged dynamic corrective iterations to achieve the desired motions

with resources such as physiotherapy instructions and Mo-Cap equipment. On the

other hand, long-term monitoring of patients is important. With the development

of Mo-Cap systems, different sensor technologies have been considered due to the

complex flexibility of the human body [34]. Human motions are normally captured

with three methods: visual sensors, on-body sensors or a combination of the two.

Figure 1.3 shows the setup for human motion tracking using these methods. The

Figure 1.3: An illustration of available human movement tracking system [34, 35]

overall sensor technologies which apply in human rehabilitation, are characterised

in [34].

The sensor technologies for movement tracking are mainly categorised in three

groups: visual, non-visual and robot aided tracking, as in figure 1.4 [34, 35]. In-

ertial, magnetic, mechanical, acoustic, radio or microwave sensors are considered

under non-visual tracking sensors. Optical sensors and cameras are used under vi-

sual tracking sensor technology. Generally, these visual systems are very accurate

for detecting the positions of a dynamic object. Further, they are grouped as marker

based and marker free visual systems. However, the markers are mounted on body

segments of interest to acquire accurate positions. The marker-free visual based

tracking systems only exploit optical sensors to measure movements of the human

body [34]. The marker free visual systems can avoid the following drawbacks of


markers.

1. Identification of standard bony segments can be unreliable

2. The soft tissue overlying bony parts can move, giving rise to noisy data

3. The marker itself can wobble due to its own inertia

4. The markers can be loose and adrift

However, these marker-free cameras require a million pixel resolution and high speed

to detect tenuous human movements. Indeed, drawbacks such as a sophisticated,

expensive and fixed infrastructure and occlusions are common.

Sensor Technologies for Capturing Human Movements

Visual Sensors Non-Visual Sensors Robot-aided Tracking

Kinect

Leap Motion

Marker BasedMarker Free

VICON

Qualisys

Inertial Magnetic Other

Acoustic

Mechanical

Radio/ Microwave

Glove

Figure 1.4: Classification of human motion tracking using sensor technologies

The following movement tracking technologies will be discussed in detail.

1.5.1 Goniometer

Goniometric measurement is considered as a preliminary method to determine

Range of Motion (ROM) and is considered the gold standard for measuring ROM.

The history of universal goniometers starts from the early 1900s [9]. It was com-

mercially invented in France [10]. Over time, goniometers were developed to include


number of varieties and specializations. The universal goniometers are famous for

measuring the ROM of the upper extremity, lower extremity and spine. The go-

niometers in various sizes and styles are shown in figure 1.5.

Figure 1.5: Various goniometers [10]

However, these goniometers suffer several deficiencies [36]. The main deficiency

is that the presence of goniometers on the limbs to measure ROM may restrict natu-

ral movements. On the other hand, positioning and stability can make measurement

variations. Further, as there is no direct contact with bones, inferring their posi-

tion information from external measurements is inherently subject to measurement

errors. Due to all these problems, the method is considered to be more complicated

and inefficient than other visual estimations [36]. The American Society of Or-

thopaedic Surgeons (ASOS) has suggested that other visual estimations are equal

in performance with goniometric estimations [10] and the inertial sensor based tech-

nologies are considered as a small and light weight replacement of goniometers [37].

1.5.2 Passive marker based optical system - VICON andQualisys systems

Vicon optical systems [38] are often used as the gold standard or benchmark for

human kinematic analysis due to their proven accuracy [39],[34]. The error in the

position of VICON optical system is normally less than 1 mm. This technology is

categorised under visual marker based systems and the markers are usually worn


on the body segments. Figure 1.6 demonstrates the visualization of positions of

markers which are attached to the upper limb using three cameras in order to track

arm kinematics.

Figure 1.6: Demonstration of position tracking using marker based visual trackingsystem: (a) markers attached to the joints; (b - d) marker positions captured bythree cameras [40]

However, VICON system (see figure 1.7(a)) requires a sophisticated laboratory

to setup the system [39] since they are designed to operate in virtual and immersive

environments for measuring kinematics and kinetics. Usually there are eight cam-

eras included in the system and the repeatable dynamic calibration for each camera

is required to track the motion accurately [42]. Unfortunately, these systems are

very costly (approximately 213502 USD). On the other hand, bringing patients

to these clinical laboratories is tedious to both patients and caregivers because it

requires both time and money. Furthermore, these systems are not suitable for

long-term monitoring [43].

(a) An operating VICON system (b) An operating Qualisys system [34]

Figure 1.7: Marker based visual systems


Qualisys (see figure 1.7(b)) system [44] is similar to VICON [34]. It is a Mo-Cap

system consisting of 1 to 16 cameras, each emitting a beam of infrared light. Small

reflective markers are placed on an object to be tracked. Infrared light is flashed

from close to, and then picked up by, the cameras. The system then computes a

3-D position of the reflective target, by combining 2-D data from several cameras.

1.5.3 Kinect c© optical system

Kinect c© optical system implements as non-invasive, portable and affordable visual

motion tracking technologies for the full body motion capturing. Its first version

was released in 2010 with Xbox 360 for gaming and the second version with Xbox

One in 2014. The majority of the applications in Tele-rehabilitation field was with

the first version. The first version of Kinect c© utilised a depth sensor provided by

a company named “PrimeSense” [45]. The appearance and components of this ver-

sion of Kinect c© is shown in Fig. 1.8. The infrared projector and the corresponding

(a) (b)

Figure 1.8: Appearance and components of Kinect c© version 1[46]

camera is shown in figure 1.9. These sensors measure the depth information via

structured light principle, which analyses a pattern of bright spots (infrared light

and unobservable by human eyes) projected to the surface of an object[48]. Two

techniques are used to further process the information to generate depth maps such

as depth from focus and depth from stereo [49]. The principle of the former is that


Figure 1.9: The pinhole camera model of Kinect c© version 1[47].

the further the object is, more blurred it will be [50], while the latter utilised parallax

to estimate the depth information. The second version measures depth information

with time-of-flight (ToF) technique[51], which states that the distance can be mea-

sured by knowing the speed of light and the duration the light used to travel from

the active emitter to the target. As in [51], this version of Kinect c© utilised indi-

rect time-of-flight, which measures the “phase shift between emitted and received

signal”. The depth is computed as

d = cΔφ

4πf, (1.5.1)

where f is the modulation frequency, c is the light speed and Δφ is determined

phase shift.

In general, the accuracy is about 10 cm due to unavoidable factors, such as oc-

clusions. Therefore, the improved skeletonisation algorithms should be investigated

if Kinect c© was used for quantitative estimation. Furthermore, Xu et al. [55] eval-

uated the accuracy of both the first and the second version of Kinect c© for static

postures. Though Kinect c© was initially developed for gaming, it is considered

for use in tele-rehabilitation as a non-invasive and affordable motion capture device

[56], [58]. Even though Kinect c© devices are known as low-cost and non-obstructive

system, they suffer from occlusion, gesture recognition errors and limited sensing

range [59].


1.5.4 Inertial sensor

The inertial sensors contain a multi sensory device called inertial measurement unit

(IMU) which is packed with a three-axial gyroscope, a three axial magnetometer

and a three axial accelerometer. In general, the accelerometer and gyroscope are

used to measure linear acceleration and angular rates [60]. The three-axial magne-

tometer reads the earth’s magnetic field. These sensors are integrated with wireless

communication capabilities enabling them to be used in a multitude of applications

in aerospace, robotics, human motion tracking in health and sport, navigation and

machine interaction.

Inertial sensors have been frequently used in navigation and augmented reality

modelling [61, 62, 63, 64, 65]. This is an easy to use and cost efficient way for full-

body human motion detection [34]. MEMSs (Micro-Electro-Mechanical sensors)

have the capacity to be used in human movement in various environments [37] and

numerous studies on motion tracking and location estimation systems can be found

in the literature. As a combination or individually, accelerometer, gyroscope and

magnetometer readings can be used to estimate the orientation of body segments

[37].

MEMS sensors have their own coordinate system, as shown in figure 1.11.

Throughout this thesis, the superscript S and E denotes the readings with respect

to the sensor coordinate system and the earth coordinate system respectively, as

shown in figure 1.10. Figure 1.10 shows the relative sensor coordinate system when

the leg is moved by an α angle. Initially, the sensor frame S and the earth frame

E are well aligned (see figure 3.1(a)). When the leg is moved by an α angle, the

sensor frame is rotated while the earth frame is the same (see figure 3.1(b)). One

common occurrence of these sensor based Mo-Cap systems is converting orientation

estimation in sensor frame to earth coordinate systems.


ASz

ASx

ASy

AEx

AEz

ASy

(a) Before

ASz

α

AAAAAASαα

ASx

AEx

ASy

ASy

AEz

(b) After

Figure 1.10: Earth and sensor co-ordinate systems

There are various commercially available inertial sensors such as Xsens, micro-

strain, VectorNav, Intersense, PNI and Crossbow [66]. MT9 (newly MTx) is a com-

mercially available digital measurement unit and the accuracy is recorded as 0.058

root-mean-square (RMS) angular resolution; � 1.08 static accuracy; and 38 RMS

dynamic accuracy. However, these inertial sensors undergo the error in accuracy

due to drift caused by continuous integration of gyroscope readings. Even though

gyroscope readings suffer from gyroscopic drift, it can be mitigated with the aid of

acceleration readings or magnetometer readings [37]. The current studies in motion

tracking with the aid of inertial sensors and magnetic sensors have shown good

accuracy [37] and most of them were validated with optical fusion technology such

as VICON systems. Further, theoretically, the accelerometer reads gravity, though

practically, it reads resultant acceleration due to interferences in the environment

[67, 68, 69]. On the other hand, since the magnetic north and geographical north

are different and it highly depends on external magnetic fields in the environment,

a proper calibration is required before measurement[39].


(a) Xsens sensor- MT9 unit [70] (b) BioKin sensor

Figure 1.11: Rotational angles of inertial sensors

1.5.5 Summary and challenges

The existing rehabilitation and motion tracking systems have been comprehensively

summarised in terms of accuracy, compactness, computation, cost and drawbacks

in table 1.3.

Table 1.3: Comparison of sensor technologies use in rehabilitationTechnology Accuracy Compactness Computation Cost Major Drawbacks

Marker based Visualsystem - VICON sys-tem, Qualisys system

High Low High High Occlusion, High spacerequirement, Operatingskill, limited sensingrange, Not suitable forlong term monitoring

Marker based Visualsystem - Kinect Op-tical System

Median Low High Low Occlusion, limited sens-ing range, Not suitablefor long term monitor-ing

Marker-free VisualSystem

High Low High High Occlusion, limited sens-ing range, Not suitablefor long term monitor-ing

Glove High High Low Median Partial and limited pos-ture, Difficult to wear

Inertial Sensors High High Low Low Drift, Resultant accel-eration

Magnetic Sensors Median High Low Low Interference due to Fer-romagnetic materials

In general, these sensor technologies require professionals to perform calibration

and sampling. These systems do not provide patient-oriented therapy, and hence

cannot be directly used in home-based environments, although the advancements


of these technologies are being considered for home use [34].

The second challenge is cost. The affordability of equipment is highly important

for patients, caregivers and medical experts. The cost of Mo-Cap systems is a prime

factor for the uptake of these systems. In certain occasions, the cost is important

than accuracy.

Further, ergonomics based properties such as user friendliness, light weight and

portability of devices are very important. Most people with neurological conditions,

have significant loss of functionality in the attached limbs and therefore need careful

consideration. It has been consistently suggested that the devices need to be quite

user friendly.

Existing rehabilitation systems typically require a large space and specialized

facilities. As a consequence, this prevents people who have less accommodation

space from using these systems to regain their mobility. On the other hand, both

caregivers and patients face difficulties to facilitate patient travel to those clini-

cal laboratories. Further, the clinical environments are not suitable to study their

natural behaviour and sometimes, long term monitoring is required for better un-

derstanding of the underlying condition.

In summary, when one sensor technology is considered for a rehabilitation sys-

tem, number of major issues need to be taken into account: cost, size and weight,

functionality, accuracy, user-friendliness and suitability to dynamic environments.

1.5.6 Motivation to use inertial sensors

In section 1.5.5, the main challenges of the sensor based human motion monitor-

ing and rehabilitation systems were discussed. These challenges entail low cost

healthcare monitoring systems suitable for home use, with remote access for med-

ical professionals and emergency responders. Among these technologies, inertial

sensor based instruments are outperforming than the other methods with respect

to compactness, computation and cost. However, inertial sensor based systems lack


accuracy compared to visual tracking systems. Significant attention has been drawn

to inertial sensor based rehabilitation systems due to ease of use and affordability.

Recently, a number of studies have attempted to increase the accuracy by mitigat-

ing the discussed drawbacks such as gyroscope drift, interferences to accelerometer

and magnetic field applying powerful filtering. Inertial sensor based systems have

the potential to be the most leading technology in rehabilitation, if the accuracy

can be enhanced.

1.6 Orientation tracking using inertial sensor mea-

surements

Inertial sensor contains a multi-sensory device called IMU which is used to measure

the moving object’s angular velocity, gravitational forces with the aid of a three-

axial gyroscope and a three-axial accelerometer. Further, these sensor units are

self-contained with a magnetometer, which is able to measure magnetic field of the

earth. The applications of these sensors spread over multiple disciplines such as

aerospace, robotics, navigation and machine interaction. Recently, these sensors

have been developed with wireless capabilities enabling them to be readily used for

determining human activities [71, 72]. On the other hand, they consume very low

power enabling long term monitoring [73] of human activities.

However, these sensors undergo errors in accuracy due to drift caused by contin-

uous integration of gyroscope readings and interferences to accelerometer measure-

ments due to external forces. Further, since the magnetic north and geographical

north are different and it highly depends on external magnetic fields in the envi-

ronment, the magnetometer readings are noisy.

In this study, BioKin sensors as figure 1.12 are being used to conduct exper-

iments. The BioKin project is aimed at introducing a platform to move gesture

analyses, currently restricted to a suitably equipped clinical environment, into an


ambulatory system possibly aimed at non-clinical settings, which can provide com-

plementary services to communities with limited access to gait laboratories. The

BioKin system consists of several layers: a low-cost wearable wireless motion cap-

ture sensor, data collection and storage engine, motion analysis algorithm and visu-

alization platform. The first layer is implemented in the BioKin-WMS sensor and

the latter layers are distributed among different components of the BioKin soft-

ware suite: BioKin-PC, BioKin-Cloud and BioKin-Mobi. The BioKin sensor is an

inertial sensor providing 140 Hz sampling frequency.

Figure 1.12: BioKin sensor

Each sensory component of inertial sensors will be further investigated in the

following sections.

1.6.1 Accelerometer

A large number of accelerometer based Mo-Cap systems [74, 75, 76, 77, 78] are

present in the literature. In general, the basic mechanism behind the accelerometer

can be described in terms of a Mass–spring system, which operates under the prin-

ciples of Hookes law (F = kx) and Newtons second law of motion (F = ma)[78].

When a massspring system is submitted to a compression or stretching force due to

movement, the spring will generate a restoring force proportional to the amount of

compression or stretch. Given that the mass, and the stiffness of the spring can be

controlled, the resultant acceleration of the mass element can be determined from

the characteristics of its displacement using two equations F = ma and F = kx.


Calibration of accelerometer

There are various types of accelerometers in use and all should undergo a standard

calibration procedure. Usually, there are two calibrations procedures: static cal-

ibration and periodic calibration. Under the static calibration, the accelerometer

readings in a static state will be read. In general, the accelerometer with the global

vertical axis (earth vertical axis) should read gravity which is + or − 9.81ms−2

depending on the direction of vertical axis of the sensor frame. Then a two point

linear calibration is conducted for accelerometer measurements.

Specialised equipment called a shaker is generally used in periodic calibration.

It essentially involves harmonic forcing of the accelerometer to determine the re-

lationship between the known acceleration harmonics and the raw output of the

accelerometer [79]. The accuracy can be enhanced using this method particularly

at a range of amplitudes and frequencies that could be expected under real-world

conditions [79].

Modelling of accelerometer measurements for human activities

The output of an accelerometer worn on the human body originates from several

sources such as 1. Acceleration due to body movements, 2. Gravitational acceler-

ation and 3. External accelerations excluding body movements and accelerations

due to movements of the sensor against other objects or jolting of the sensor on

the body [80]. Hence, the accelerometers read resultant acceleration of all these

acceleration components. Further, accelerometer readings have a constant offset

and a moving bias. The accelerometer readings can be modelled as follows:

at = a+ Ct +Bt +Nt, (1.6.1)

where at, a, Ct, Bt and Nt are the measured accelerometer readings, true arm

rotation, a constant offset or bias, a moving bias and noise at time t respectively

[69].


Orientation determination

Initially, the accelerometer needs to be properly calibrated. The noise in acceler-

ation can be removed using low pass filtering up to a certain extent. The filtered

acceleration can be used to estimate the angle of movement(θa) using (1.6.2) [60].

θa = tan−1 ayaz, (1.6.2)

Challenges

The major challenges of using accelerometers for tracking human body movement

can be listed as follows.

1. The output of accelerometer reading is influenced by motion artefacts and

other noise components discussed in section 1.6.1. Hence, the accuracy of

estimation will be reduced.

2. The gravitational acceleration can be only read in the sagittal and the frontal

plane, but not the transverse plane. Hence, human movement in the trans-

verse plane cannot be tracked accurately with accelerometer readings alone.

1.6.2 Magnetometer

Magnetometers are used to measure the strength of earth’s magnetic field and

determine the heading angle to the earth’s magnetic field. The strength of the

earth’s magnetic field is about 0.5 to 0.6 gauss and has a component parallel to the

earth’s surface that always points toward the magnetic north pole. In the northern

hemisphere, this field points down. At the equator, it points horizontally and in the

southern hemisphere, it points up. This angle between the earths magnetic field

and the horizontal plane is defined as an inclination angle. Another angle between

the earth’s magnetic north and geographic north is defined as a declination angle

in the range of ±20◦ depending on the geographic location [81].

Magnetometer readings suffer accuracy errors due to the following reasons:


1. The accuracy error due to hard-iron interferences with the magnetic field.

This is prevalent in ferromagnetic materials [81]. Investigations into the ef-

fect of magnetic distortions on an orientation sensor’s performance have shown

that substantial errors may be introduced by sources including electrical ap-

pliances, metal furniture and metal structures within a buildings construction

[66]. The hard iron based error can be corrected by conducting proper cali-

brations.

2. The accuracy error due to soft-iron interferences. This error is generated by

internal devices.

3. Scale factor error due to mismatch of the sensitivity of magnetic sensor sensing

axes. This error can be corrected by normalizing magnetometer readings of

each axis with to earth magnetic field.

4. Declination error due to difference of horizontal plane and earth frame. Addi-

tional heading equipment such as calibration table is required to correct this

error.

Calibration of magnetometer

Magnetometer readings can significantly fluctuate across sensors and locations pri-

marily due to soft-iron interferences in each sensor and the strength of hard iron

interferences in the environment. Hence, calibration should be conducted for sensors

and locations separately.

In the calibration process, the sensor is slowly rotated around each axis while

it is being moved in a lemniscate trajectory between ten to twelve minutes as to

measure the maximum value (MAXxS) and minimum value MINx

S in readings of

each axis. Then, each magnetometer reading is normalized with the earth’s max-

imum magnetic field MAXxE and minimum magnetic field MINx

E using equation

1.6.3. The normalized magnetometer readings (MAGx) are usually free from offset

and scaling error.


MAGx =MAXx

E −MINxE

MAXxS −MINx

S

×MAG, (1.6.3)

Eventually, the calibrated sensor readings should be approximately equal to

the actual magnetic readings of the geographical location. In our study, all the

experiments were conducted in Geelong, Victoria, Australia and the magnetometer

readings were as in table 1.4.

Table 1.4: Magnetic fields in Geelong

East Component (nT) North Component (nT) Vertical Component (nT)

4248.95561 21083.6 56226.5

Modelling of magnetometer readings

The calibrated magnetometer readings should be normalised to compensate for tilt.

The normalized magnetometer readings h can be modelled as follows [82].

ht = h+D +Nt, (1.6.4)

where ht, h, D and Nt are normalized magnetometer readings, true earth’s magnetic

field vector, magnetic disturbances and the noise at time t respectively. However, D

can be mitigated by conducting trials at least 60 cm beyond the potential sources

of magnetic disturbances [83], so all the experiments were conducted to mitigate

the magnetic disturbances as in [83].


The heading angle can be calculated based on (1.6.5) where hx and hy are magne-

tometer readings of x axis and y axis respectively.

Heading = arctan(hy

hx), (1.6.5)


Challenges

The major challenges of using magnetometers for tracking human body movements

can be listed as follows.

1. The magnetometer readings are affected by the aforementioned uncertainties

and, hence the estimated movement angles become inaccurate

2. The strength and the direction of the earth’s magnetic field is dependent on

the geographic location and, hence when the heading angle is calculated, more

vertical magnetic directions are susceptible to erroneous deductions

1.6.3 Gyroscope

Gyroscopes are considered for numerous applications [84, 85, 86]. These capture

angular rates in each time stamp. Generally, the angle of rotation is derived by

integrating the angular velocity [84].

Modelling of gyroscope measurements for human activities

When gyroscopes measure the angular rates of each time stamp t, inevitably, it

consists of measurement noise. However, the angular rates are considered to be less

noisy and have a relatively higher accuracy. In order to derive the angle, angular

rates need to be integrated. The integration causes drift which is a major concern.

The measurements of gyroscope can be modelled as (1.6.6).

ωt = ω + Ct +Bt +Nt, (1.6.6)

where ωt ,ω, Ct, Bt and Nt are the measured gyroscope readings, gyroscope readings

for actual arm rotation, a constant offset, a moving bias and a wide band sensor

noise at time t respectively [69].



The gyroscope readings are filtered using a high pass filter. Then, the angular rates

in each t is integrated as (1.6.7) [60].

θω =

∫ t

i=1

f(ωi), (1.6.7)

The gyroscope measurements are always with respect to the sensor frame, hence

it is necessary to convert to the earth frame to estimate the absolute orientation.

For that, the angular rates were integrated and the angle of rotation determined in

each axis with respect to a known reference (initial) position. Rodrigues rotational

formula [87, 39] can be applied to estimate absolute orientation as in (1.6.8) where

vrot is a rotated vector in R3 of the vector �v and K is the unit vector of axis of

rotation.

vrot = �v cos θω + (K × �v) sin θω +K(K.�v)(1− cos θω), (1.6.8)

An alternative approach for this conversion is calculating the quaternion derivative

[88]. Here, the gyroscope readings in the sensor frame ωS at time t is considered as

pure quaternion (1.6.9) and quaternion multiplication (⊗

) is applied for calculating

the derivative as in (1.6.10). Initially, quaternion is considered as[1 0 0 0

]and

then, the quaternion of each time t with respect to the earth frame is calculated as

(1.6.11).

ωSt =

[0 ωS

X ωSY ωS

Z

]t, (1.6.9)

SE qω,t =

1

2SE qt−1

⊗ωSt , (1.6.10)

SEqω,t =

SE qt−1 +

SE qω,tΔt, (1.6.11)

Challenges

Gyroscopic measurement based tracking is associated with the drift which causes

erroneous estimations, therefore mitigating this is essential. It can be mitigated

with a known reference point or direction to a certain extent. However, gyroscope

based tracking is not suitable for longer time frames due to the drift and it should be


reset using a known reference point at regular intervals for comparatively accurate

estimations. This is an inconvenient process for long-term monitoring.

1.6.4 Summary

There are numerous advantages and disadvantages with IMU sensors. However, the

fusion of information from these sensory devices can lead to improved accuracies

resulting in reliable systems for multitude of applications. Later sections will inves-

tigate the available approaches for fusion of each sensory modules to acquire better

accuracy compared to individual estimations.

1.7 Wahba’s problem

The orientation estimation of a dynamic object, based on its observation vectors

in local frame and corresponding global frame’s observations, was approached as

a minimizing loss function problem by Grace Wahba in 1965 [89, 90]. Later, this

problem was generally known as Wahba’s Problem in applied mathematics [91].

Thereupon, the solutions to this problem have been improved and these solutions

have been applied to various applications including aerospace, ship navigation, bio-

medical advancements and multi camera calibration in computer vision [92].

Considering Wahba’s problem, some relevant aspects are as follows.

1. A dynamic object with its own coordinate system and moving in a global

coordinate system

2. The orientation of the object with respect to the global coordinate system is

required to determine using the observation vectors

3. There should be static observation vectors which are common to both local

and global coordinate systems

Under Wahba’s problem, the orthogonal matrix for the corresponding rotation is

found between two coordinate systems from a set of weighted observation vectors


[93, 90]. First, the reference frame coordinate system and local body coordinate

system were abbreviated as RCS and LCS respectively. The unit vectors measured

in LCS are noted as bi and the corresponding vectors in RCI are noted as ri. Here A

and ai are the rotation matrix between two coordinate systems and the non negative

weight respectively.

L(A) ≡ 1

2

∑i

ai|bi − Ari|2, (1.7.1)

As (1.7.1), the Wahba’s problem is basically a minimization problem to determine

least variance of orientation estimation between RCS (ri, i = 1, 2..n) and LCS

(bi, i = 1, 2..n). Here, i from 1 to n is the number of different observation vectors.

This approach was originally used for spacecraft’s attitudes estimation where the

observation vectors are unit vectors of a star or sun [94, 95, 96]. However, each

solutions of Wahba’s problem is attempted to minimise the loss function (1.7.1)

[90]. Later, this equation is simplified to a convenient form as (1.7.2) [90].

L(A) ≡ λ0 − tr(ABT ), (1.7.2)

where B is∑n

i=1 aibirTi . It is clear that the matrix B is maximised when the least

error of estimation L(A) is minimized. each approach in section 1.7.2 was attempted

to find optimal solution based rotation matrix or quaternion presentation from

(1.7.2).

1.7.1 Applicability of Wahba’s problem for inertial sensorbased orientation estimation

Considering the applicability of Wahba’s problem for tracking human arm move-

ments, Some similarities can be stated satisfying the above three conditions as

follows.

1. The inertial sensor and earth frame are having two different coordinate sys-

tems

2. The earth magnetic field measurements are static measurement, hence it is

common to both frames


3. When the object is being moved under constant velocity, the resultant accel-

eration is gravity, hence the acceleration vector is common to both frames

Hence, the solutions for Wahba’s problem are applicable tracking human arm move-

ments [97].

The major benefit of applying these techniques is that the use of gyroscope

readings can be avoided. As we know, Even though gyroscope readings are accu-

rate measurements in sensor frame, the integration causes inaccuracies due to drift

[39]. Further, the solutions of Wahba problem have closed form estimation which

are efficient to compute[97, 98]. In addition, this method needs only two measure-

ments to estimate rotation matrix which gives equivalent result in comparison to

the complementary filter.

1.7.2 Available solutions for Wahba’s problem

TRIAD method

TRIAD method is an initial approach to solve this problem [99], which was intro-

duced by Harold Black. He attempted to find an optimal solution through cosine

matrix of two common observation vectors in LCS and RCS. In this approach, the

observation vectors in LCS (b1 and b2) and the corresponding observation vectors

in RCS (r1 and r2) are normalized and the cross product of each vectors were used

to calculate the optimal rotation matrix (A) as (1.7.3).

A =[

R1

‖R1‖ ,R1×R2

‖R1×R2‖ ,R1

‖R1‖ × R1×R2

‖R1×R2‖

] [r1

‖r1‖ ,r1×r2

‖r1×r2‖ ,r1

‖r1‖ × r1×r2‖r1×r2‖

]T, (1.7.3)

Singular value decomposition method

Subsequently, the SVD method was introduced to solve this problem [100, 101].

The significance of this method is that its outstanding performance even with noisy

observation vectors [90, 101]. Under this method, the U and V orthogonal value is

determined using B matrix using (1.7.2). Then, the determinants detU and detV


were obtained. The optimal rotation matrix is estimated using (1.7.4).

L(A) = U

⎡⎢⎢⎣

1 0 0

0 1 0

0 0 (detU)(detV )

⎤⎥⎥⎦V T , (1.7.4)

Davenport’s q method

Davenport introduced this method to determine the attitude of spacecraft [98, 103].

Under the method, trace of ABT in (1.7.2) is written as a homogeneous quadratic

function of quaternion q [90, 98] as (1.7.5).

tr(ABT ) = qTKq (1.7.5)

where K is a symmetric traceless matrix.

K ≡[S − Itr(B) z

zT tr(B)

], (1.7.6)

Here, S is equal to the summation of B and its transpose (B + BT ). z is a 3

by 1 matrix which is equal to the summation of cross product of ri and bi of all

observation vectors. In other words, z =∑n

i=1 aibi × ri (Refer to equations 1.7.1

and equation 1.7.2). Then, the optimal quaternion for the movement is given by

the normalized eigenvector (V ) of K with the largest eigenvalue (D).

Kqopt = λmaxqopt, (1.7.7)

qopt = V < −max(D)), (1.7.8)

QUEST method

The QUaternion ESTimator (QUEST) method was initially introduced in 1979

[90, 104, 105]. Since then, this method is considered as the most applied algorithm

for attitude estimation of spacecraft. Under this method, the fourth order quadratic

method is found λmax in (1.7.7) as follows.

0 = γ[λmax −tr(B)

]− zT

[αI +λmax −tr(B)S +S2

](1.7.9)


where

α = λ2max − [tr(B)]2 + tr(adj[S]),

and

γ = α[λmax + tr(B)] + det(S),

λmax can be found for the optimal quaternion using Newton -Raphson iteration

[91]. When the loss function is very small, λ0 will be close to λmax. in which

case, several iterations are required to obtain the optimal(maximum) λ result. The

advantages and disadvantages of the above four methods in general, are listed in

following table.

Table 1.5: Advantages and disadvantages of solutions to the Wahba’s problemTRIAD Method SVD Method Davenport’s q method QUEST Method

Advantages

Simplest Solution Robust algorithm Fast method since theeigenvalues are used

Always gives one op-timal solution becauseof applying Newton-Raphson iterations

Faster than othermethod

Good performancewith noisy data

Robust algorithm Fast algorithm

Robust algorithm High computationalcost

Since optimal quater-nion is estimated, thesingularity problemsare eliminated

Less computation cost

Since optimal quater-nion is estimated, thesingularity problemsare eliminated

Disad

vantages

Singularity problemoccurs since the resultis rotation matrixwith Euler angles

Singularity problemoccurs since the resultis rotation matrixwith Euler angles

Sometimes, unique so-lution will not befound when two ormore eigenvalues areequal to largest eigen-value

Less Robust algorithm

Three primary approaches to human motion analysis using inertial sensors can

be found [106].

1. Systems that use single module of inertial sensors (either accelerometer or

gyroscope) for analysing qualitative information on human motions


2. Systems that operate on the basis of a combination of accelerometers and

gyroscopes with additional signal processing algorithms

3. Systems that operate on the basis of both inertial sensor types in combination

with additional sensors (usually magnetometers) and data fusion algorithms

Chapter 2 discusses the second and third type of systems for arm kinematics and

chapter 4 investigates the first type of systems for qualitative analyses of upper

body and lower limbs.

1.8 Contributions

This thesis attempts to introduce novel accurate orientation estimator for human

kinematics while delivering four contributions to inertial sensor based rehabilitation

systems. One contribution is introducing novel orientation estimators for monitor-

ing human activity accurately as in [39, 107]. In addition, a novel calibration mech-

anism for correcting sensor misalignment between sensor frame and earth frame has

investigated as in [108]. With these outcomes, the orientation and angle of move-

ment could be estimated accurately facilitating the capture of human movements.

Limb length is a useful assessment criteria for a common anatomical disease

called limb length discrepancy. This condition makes the disorders in human move-

ments specifically gait cycles with presence of leg length discrepancy (LLD). Hence,

the machine driven mechanism [43] to estimate limb length has been investigated

using only an IMU sensor as the second contribution. Importantly, the above cali-

bration mechanism and limb length estimator are developed by applying curvature

and geometrical relationships of limb trajectories.

As the third contribution, a qualitative analyses of human kinematics were inves-

tigated. Under this, analyses were conducted for evaluating the trunk movements

relevant to Parkinson’s disease based on their kinematic features. Further, the

ambulatory energy expenditure evaluation was conducted to investigate the rela-

tionship between energy consumption for gait exercises such as walking and running


as in [109].

Finally, a novel cloud based tele-rehabilitation system based on inertial sensors

was introduced in [110]. This system was then extended to connect other sensory

devices. A multi-level encoding mechanism was introduced in [111] for efficiently

sharing limited resources such as internet bandwidth and mobile phone battery

power while the sensor is transmitting the data to a master server.

1.9 Outline of the thesis

The first chapter is a literature review on human kinematics and available sensor

technologies used for rehabilitation. The principles behind each sensory components

of inertial sensor are comprehensively investigated. In later sections, the histori-

cal attitude determination algorithms are discussed and feasibility for applying in

human motion tracking using inertial sensors is investigated.

The second chapter provides an overview of existing attitude estimators which

are suitable for real time human upper body activity monitoring. Subsequently,

it proposes a novel data fusion algorithm accommodating uncertainty and mea-

surement noise for capturing human motion activities in real-time. Importantly,

the arm kinematics were modelled as a dynamic mathematical model and then,

different data fusion techniques such as extended Kalman filter, robust extended

Kalman filter and introduced novel robust extended Kalman filter with linear mea-

surements are engaged. Further, results are compared with gold standard : VICON

optical system.

In the third chapter, the curvature and geometrical relationships on circular

motions were studied using measurements of inertial sensors. In particular, curva-

ture could be applied in shoulder and hip exercises such as flexion-extension and

abduction-adduction. With the knowledge of these concepts and limb trajectories,

a calibration mechanism for correcting sensor misalignment was introduced. Fur-

ther, a novel approach for estimating limb lengths to assess limb length discrepancy


anatomical condition was discussed.

In the fourth chapter, a qualitative analysis on human upper body movements

was investigated. In this chapter, the single type of sensory module (either ac-

celerometer or gyroscope) are used for the analysis of trunk movements. Trunk

movements were compared between healthy subjects and Parkinson patients to

identify physical features of Parkinson’s disease such as rigidity of trunk, slow move-

ments and inflexibility. Further, for the lower body, gait activities were analysed to

examine the relationship between energy expenditure and gait activities.

With the increasing population of aged and people with disabilities, the need

for innovative solutions supporting accurate and personalized medical diagnosis and

treatments at affordable price is highlighted. Furthermore, carefully monitoring of

patient’s activities and physical features can play a significant role in diagnostic

and rehabilitation processes. This highlights the requirement for a multi-sensor

equipped system to cater to all signals to derive valuable information about a pa-

tient. Hence, the tele-rehabilitation system using different sensory technologies is

implemented using cloud web services and mobile phone. The challenges of such

systems are discussed and multi-level encoding mechanism was introduced for effi-

ciently sharing resources.

Finally, the last chapter presents the conclusion of the discussed work and reveals

future directions for further studies based on the thesis.

Chapter 2

Robust Estimation Of ShoulderMovements

2.1 Introduction

Capturing human posture real time with wearable sensors is useful in many practical

applications ranging from rehabilitation, motion capture for movie industry as well

as activity monitoring in sports. IMU sensors are considered widely for this purpose

as its ability to be used in form of wearable sensors. Indeed, the main challenge

is capturing human movements by estimating the relative attitude of IMU sensors

strategically positioned in different parts of the human body.

Capturing highly flexible human poses with 278 joints combining 308 bones is

challenging albeit approximating the movements of inflexible fibrous joints, rela-

tively flexible cartilaginous joints and highly flexible synovial joints into the joints

with more prominent movements. Usually, the human motion is characterized

through carefully analysing spatial reconstruction, trajectory tracking, joint angle

determination and derivative computation [112].

Using inertial/magnetic sensors for capturing human movement has been al-

ready discussed in sections 1.5.4, 1.6.1, 1.6.2 and 1.6.3. IMU sensors have shown

potentiality due to wearable nature, accuracy and three forms of measurements

facilitating the engagement of sensor fusion ideas. The solutions for Wahba’s prob-

lem which discussed in section 1.7 were enhanced with powerful estimators such

36

Chapter 2. Robust Estimation Of Human Shoulder Movements 37

as Kalman filter and extended Kalman filter(EKF) [113]. However, these studies

are conducted under strong assumptions that the rigid body to which the sensor

is attached is stationary or moving at a constant velocity. In other words, these

algorithms are not suitable for highly dynamic tracking applications. Further, De-

viation from ideal behaviour of the sensors due to noise and external interferences

reduces the accuracy of estimations as well.

In this chapter, four major contributions has been discussed for accurate human

motion tracking using inertial/magnetic sensors. Firstly, an unified quaternion

based model for bio-kinematic state estimation is introduced. Secondly, a theoret-

ical justification is conducted for quaternion normalisation required for recursive

estimators. Thirdly, a converted measurement based approach for the formation

of a quasi-linear state estimation problem is introduced. Finally, the robust ex-

tended Kalman filter based approach to estimate the orientation (attitude) of the

human pose subjected to large uncertainties, is introduced. This novel approach is

validated with computer simulation and in a real-time data with a comprehensive

evaluation of existing sensor fusion approaches in a real time estimation domain.

2.2 Data fusion techniques and algorithms

2.2.1 Gradient descent algorithm

The MARG algorithm in [88] represents orientation as a quaternion minimizing

gyroscope drift accommodating novel algorithm. Under this, an analytically derived

and optimized gradient descent algorithm was introduced by Sebastian et al. in 2011

using IMUs, which is shown in figure 2.1.

In this algorithm, the quaternion representation Sω in (2.2.1) is used for esti-

mating the orientation rather than Euler angles.

Sω =[0 ωx ωy ωz

]. (2.2.1)


Figure 2.1: Block diagram of MARG algorithm implementation [88]

The quaternion derivative is given by SE q in equation (2.2.2) to convert the mea-

surement in sensor frame to earth frame.

q = 12q ⊗ ω. (2.2.2)

Then, the orientation of the earth frame relative to the sensor frame at time t was

calculated by numerically integrating SE q as in equation (2.2.3).

SEqω,t =

SE qest,t−1 +

SE qω,tΔt (2.2.3)

The optimisation problem in [88] was formulated as equation (2.2.4) and the gradi-

ent descent algorithm was used to identify the orientation of the sensor with respect

to the earth coordinate system.

minSE q∈R4

f(SE q,E d,S s), (2.2.4)

where SE q is the estimated orientation of the sensor, E d is the predefined referenced

earth direction such as gravity or magnetic field and S s is the measured field of the


sensor. SE q could be found by MARG algorithm to n iterations with a variable step

size of μ given in equation (2.2.5).

SEqk+1 =

SE qk − μ

Δf(SE qk,E d,S s)

‖Δf(SE qk,E d,S s)‖, k = 0, 1, 2, 3...n (2.2.5)

The error direction of the solution surface was calculated using the objective func-

tion f and its Jacobian, J using equation (2.2.6).

Δf(SE qk,E d,S s) = JT (SE qk,

E d)f(SE qk,E d,S s) (2.2.6)

2.2.2 Complementary filter

The complementary filter was improved by Euston [114] to attitude estimation.

Further, Vasconcelos [115] introduced the time varying complementary filter to

compensate errors due to the drift and Hong [116] proposed a fuzzy logic based

algorithm to correct the error in the gyroscope readings. The traditional comple-

mentary filter is shown in figure 2.2 [60].

Gyro

Low Pass FilterAccelerometer

High Pass Filter

I

A

G

L

H

Figure 2.2: Traditional complementary filter [60]

The rotation angle (θ) can be calculated as in equation (2.2.7) where θω and θa

are angles derived from gyroscope data and acceleration data respectively. K1 and

K2 in equation (2.2.7) are constants and their total value is equal to one.

[θ] = K1× θω +K2× θa (2.2.7)


2.2.3 Adaptive complementary filter

The author have introduced an adaptive complementary filter [39] as an advance-

ment of traditional complementary filter. This filter was created by replacing K1

and K2 constants to variables as in equation (2.2.7). The values for K1 and K2 has

been dynamically bound with a linear relationship to minimize the error of angle

estimation.

When the object is stationary or moving in a relatively low acceleration respect

to gravity, the accelerometer reading can be considered only due to the gravity. At

that time with reference to the gravity, the initial orientation can be found using

acceleration readings. However while the object, potentially the human arm, is

being moved, it reads both gravity and acceleration due to forces generate from

muscles. At this point, acceleration based angles are not accurate since it reads

resultant acceleration. Hence the gyroscope angular rates are used to calculate the

angles in real time. At the final stage, acceleration readings are used to correct the

drift.

The initial gyroscope readings and accelerometer readings are (ω =[ωx ωy ωz

])

and (a =[ax ay az

]) respectively. [Aarm] and [k] are the initial coordination of

the arm and the unit vector. Then, as in figure 2.3, the noise free gyroscope readings

(ω) were obtained by applying a high pass filter to ω and the noise free accelerations

(a) were obtained by applying a low pass filter to accelerations.

ω = fh(ω), a = fl(a), (2.2.8)

The rotated angle (θa) was found using equation (1.6.1) [60]. Further, the same

angle( θω) was found using gyroscope data using equation (1.6.7) [60]. The adaptive

complementary filter is given as follows.

[θ] = Vω × θω + Va × θa, (2.2.9)

where Vω and Va are variables which satisfy the following two conditions.


High Pass Filter =Higgg (h== reFilteFPass F== (( )))

Low Pass Filter = Lo ww (ww == rreFilteFPass F== (( )))

= (== , ((( , ))

Combine rotationand transition

Complementary Filter

Sensor Frame to Global Frame orr FFra laaabme to Glo

Identify Orientation = ( Iddde= ten= ifyf(( ,y Orier nen, ,n, [atatat ]onoiott , [[ ]])])

Sensor Measurements

Figure 2.3: Adaptive complementary filter

1.

Vω + Va = K (2.2.10)

2.

Vω, Va =

{Vω satisfying Vω ∝ ω

Va satisfying Va ∝ a(2.2.11)

In the first condition, it implies that the summation of Vω and Va is equal to a con-

stant. The second condition implies that the value of Vω is changing proportionally

to change of gyroscope readings and the value of Va is changing proportionally to


change of accelerometer readings. The values of Vω in the ith frame were dynami-

cally bound based on following formula.

Vωi =

i∑i=1

[K

ngyro

], (2.2.12)

where ngyro, K and i are the sample size of gyroscope data, a constant and the

index of current frame respectively.

The new orientation of the arm [Aarm] has been found by applying [θ], [k] and

[Aarm] to the Rodrigues rotational formula 1.6.8.

2.2.4 The algorithms for solving Wahba’s solution

The approaches in 1.7 have been investigated with inertial sensor measurements:

accelerometer readings and magnetometer readings as given in figure 2.4. Firstly,

Static Observation Vectors in LCS

Accelerations MagneticOrientations

Low Pass Filtering Calibration

FilteredAccelerations

MagneticOrientations

Optimal Quaternion

Wahba’sSolutions

TRIAD Method

Rotation Matrix

Static Observation Vector in RCS

Earth gravity vectorInitial MagneticOrientation

SVD Method Davenport’s qMethod QUEST Method

Rotation Matrix

Figure 2.4: Orientation estimation using solutions of Wahba’s problem and IMUs

the human arm behaviour was simulated as two scenarios. The first scenario (Ex-

ercise 1) is aimed at simulating shoulder exercises for arm: shoulder to wrist as one


limb. Under this, the exercise abduction/adduction was considered as in section

1.3. The measurements of inertial sensor were simulated as it is worn on the wrist

without bending the elbow. Then, the second scenario (Exercise 2) is aimed to at

simulating the arm bending exercise from the elbow, apparently a day-to-day ac-

tivity:lifting a bottle. In this exercise, the elbow was lifted 45 degrees in Y -Z plane

and the wrist was moved by 153 degrees in same plane. Initially, these scenarios

were simulated without measurement noise. Then, the noise was introduced to each

measurements as equations (1.6.1) and (1.6.4) as decreasing Signal-to-Noise Ratio

(SNR) from 60 dB to 5dB. Later, the optimal estimation of movement angle from

each algorithm with noise was compared with the ideal movement without noise as

in figure 2.5.

5 10 15 20 25 30 35 40 45 50 55 600

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

5 10 15 20 25 30 35 40 45 50 55 60 0

0.2

0.4

0.6

0.8

1

1.2

5 10 15 20 25 30 35 40 45 50 55 60

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

5 10 15 20 25 30 35 40 45 50 55 600

0.2

0.4

0.6

0.8

1

1.2

5 10 15 20 25 30 35 40 45 50 55 60

0.2

0.4

0.6

0.8

1

1.2

5 10 15 20 25 30 35 40 45 50 55 60

(a) (c)(b)

(d) (e) (f)

Root

Mea

n S

quar

e E

rror

in A

ngle

(ra

d)

SNR SNR

SNR SNR SNR

SNR

SVD method / Davenport’s q method TRIAD method QUEST method

Figure 2.5: Simulation Result: (a), (b) and (c) - RMSE of movement angle in X,Y and Z axis for shoulder exercise, (d),(e) and (f) - RMSE of movement angle inrespectively X, Y and Z axis for lifting a bottle exercise

According to the analysis, the angles derived from each approach such as TRIAD

method, Davenport’s q method, SVDmethod and QUESTmethod, were identical in

the absence of noise. However, when the noise was introduced to accelerometer and

magnetometer readings, the estimated angles of each axis were changed. According

to figure 2.5, initially the root mean square error (RMSE) was very small in both

exercises. However, when the Signal-to-noise ratio (SNR) was decreased from 50


dB to 20 dB, the RMSE was increased approximately three times than the rate of

RMSE change from 60 dB to 50 dB. The RMSE was significantly changed when

the noise (lesser than 20 dB) was introduced. The same phenomenon could be seen

in sub figures (d), (e) and (f) for the exercise for day-to-day activity. However,

considering sub figures (a) and (b) for exercise 1 and (d) and (f) for exercise 2, the

QUEST algorithm was outperforming compared to other approaches. The QUEST

algorithm has the least RMSE in all noise levels from 5 dB to 60 dB in those figures.

The second least RMSE could be seen in SVD approach and Davenport’s q method.

Further, both SVD method and Davenport’s q method were performing similarly

and hence the trajectories from each approaches were overlapping in every figure.

The least performing algorithm was the TRIAD method. Although, considering

the subfigures (e) and (f), the QUEST algorithm, SVD method and Davenport’s

q method are equally performing until the SNR level is less than 15 dB. TRIAD

method is outperforming other methods which is a valuable aspect in the TRIAD

method.

Real data experiment

The abduction/adduction and flexion/extension exercises as the section 1.3 were

performed under the real time experiments, in order to compare each approaches for

arm exercises. The experiments to validate the algorithm were conducted with ten

healthy subjects (eight males and two females) without any history of orthopaedic or

intramuscular impairments. The actual exercises were conducted having relatively

low speed compared to gravity or constant velocity in order to closely approximate

the simulated environment. Each exercise was conducted wearing the inertial sen-

sors on the left wrist and elbow. The second exercise was designed as lifting a water

bottle from the front of the body to the mouth. The motion was simultaneously

recorded using the VICON optical motion capture system (VICON T40S System)

equipped with eight cameras sampling at 250 Hz. The angles were derived from

output of the VICON system. During the analysis, VICON data were re-sampled


(a) (b)

(c) (d)

Mov

emen

t an

gle

(in ra

d)M

ovem

ent

angl

e (in

rad)

RM

SE in

mov

emen

t an

gle

(in ra

d)R

MSE

in m

ovem

ent

angl

e (in

rad)

sample time

sample time

sample time

sample time

SVD method / Davenport’s q method TRIAD methodQUEST method VICON Optical System data

0 200 400 600 800 1000 12006

4

2

8

6

4

2

0

2

0 200 400 600 800 1000 12000

1

2

3

4

5

6

7

0 50 100 150 200 250 300 350 400 4500

2

4

6

8

1

2

4

6

0 50 100 150 200 250 300 350 400 4500

1

2

Figure 2.6: Experiment result: (a) - movement angle for abduction exercise, (b) -root mean square error in movement angle for abduction exercise, (c) - movementangle for lifting water bottle exercise and (d) - root mean square error in movementangle for lifting a bottle exercise

at 140Hz for comparison purposes. The movements of the wrist were analysed.

Table 2.1: Root mean square error for flexion-extension exercise

TRIAD method Davenport’s q method SVD method QUEST method

Subject 1 0.287 0.2582 0.2582 0.1267Subject 2 0.0633 0.0713 0.0713 0.0704Subject 3 0.1752 0.0537 0.0537 0.0554Subject 4 0.0717 0.0638 0.0638 0.0691Subject 5 0.0544 0.1138 0.1138 0.0554Subject 6 0.0624 0.0686 0.0686 0.0724Subject 7 0.1205 0.0705 0.0705 0.0403Subject 8 0.0453 0.0204 0.0204 0.0281Subject 9 0.0864 0.0781 0.0781 0.0699Subject 10 0.0813 0.0801 0.0801 0.0634

Overall 0.10475 0.08785 0.08785 0.06511

The root mean square errors of the movement angle for each exercise were anal-

ysed and listed in table 2.1 and 2.2. According to table 2.1 for flexion/extension,

table 2.2 for abduction/adduction and 2.3 for lifting water bottle, in general, the


QUEST algorithm has the least error compared to other methods. The aver-

age RMSE values for all subjects for exercise 1 :abduction/adduction and flex-

ion/extension were respectively 0.0651 radians and 0.0608 radians. Further, the

average RMSE for lifting exercise is 0.0987 radians for QUEST algorithm. The

Davenport’s q method and SVD method performed equally in each of the exer-

cises and they have the second least error. The highest error could be observed in

TRIAD method for three exercises. This result is shown in figure 2.7. Importantly,

the same phenomenon could be observed in simulation for the same exercise.

1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

Subjects

Roo

t Mea

n Sq

uare

d Er

ror (

in ra

dian

s)

1 2 3 4 5 6 7 8 9 100

0.05

0.1

Subjects

Roo

t Mea

n Sq

uare

d Er

ror (

in ra

dian

s)

0.15

(A) Flexion -Extension Exercise (B) Abduction - Adduction Exercise

TRIAD Method Davenport q Method SVD Method QUEST Method

0.3

1 2 3 40

0.05

0.1

0.15

0.2

0.25

0.3

Subjects

Roo

t Mea

n Sq

uare

d Er

ror (

in ra

dian

s)

(C) Lifting a bottle Exercise

0.35

Figure 2.7: Experiment result: (a), (b) and (c) - root mean squared error of move-ment angle for extension/flexion exercise, abduction/adduction exercise and liftinga bottle exercise respectively

Table 2.2: Root mean square error for abduction-adduction exercise


Subject 1 0.0802 0.0841 0.0841 0.0481Subject 2 0.0438 0.0574 0.0574 0.0579Subject 3 0.1008 0.0785 0.0785 0.0793Subject 4 0.1299 0.049 0.049 0.0473Subject 5 0.1424 0.1215 0.1215 0.125Subject 6 0.0703 0.0769 0.0769 0.0674Subject 7 0.0152 0.043 0.043 0.0491Subject 8 0.0283 0.04 0.04 0.0434Subject 9 0.0274 0.0372 0.0372 0.0464Subject 10 0.1116 0.0512 0.0512 0.0438

Overall 0.07499 0.06388 0.06388 0.06077

On the other hand, according to table 2.3 for lifting a bottle exercise, the same

trend could be seen for exercise 1. However, under exercise 1, it rotates through


Table 2.3: Root mean square error for lifting a bottle exercise


Subject 1 0.1593 0.1178 0.1178 0.0681Subject 2 0.1441 0.0817 0.0817 0.0745Subject 3 0.3408 0.2067 0.2067 0.2085Subject 4 0.0611 0.2174 0.2174 0.0438Overall 0.1763 0.1559 0.1559 0.0987

only one joint which is the shoulder joint. The lifting exercise is considered as a

comparatively complex one, because the arm rotates through two joints such as the

shoulder joint and the elbow joint. Further, when the lower arm is being lifted from

the elbow, this exercise is no longer a planar movement like abduction-adduction

because the lower limb is slightly twisting towards the body. The QUEST algo-

rithm was superior to the other methods even with this kinematic complexity as in

the result in table 2.3. This demonstrates the higher robustness of the algorithm

for complex day-to-day exercises. The external accelerations such as force from

arm muscles, will be observed when conducting complicated exercise such as the

lifting exercise. The second least RMSE was observed in Davenport’s q method

and SVD which is 0.1559 radians. Likewise, the highest error was shown in TRIAD

method. However, the accuracy is slightly reduced in the lifting exercise than the

first exercises. Importantly, the impact of external accelerations may affect the es-

timation. However, the QUEST method performed better in real-time environment

in line with our previous observations in a simulated environment. According to

the computer simulation and real time experiments, QUEST algorithm outperforms

than the other algorithms considered for the simple arm exercises such as flexion-

extension and abduction-adduction. However, the accuracy for complicated arm

exercises such as internal/external rotation for day-to-day activities is expected to

be reduced compared to the simple exercises. This implies that the QUEST method

should be improved for complicated exercises to enhance accuracy by integrating

powerful data fusion and optimization mechanisms.


2.2.5 Kalman filter

Kalman filter was initially developed by Rudolf Emil Kalman to solve the problem

of estimating the trajectory for the Apollo program in the NASA Ames Research

centre [117, 118]. It is commonly used as a powerful method for sensor data fusion.

Further, it can also be used to estimate the system state at a given time of a

known dynamic model specified control inputs. Kalman filter is commonly used as

an estimation algorithm, because it has proven better accuracy compared to other

non-iterative methods. However, It has several deficiencies such as linear regression

iterations in the Kalman process and demand sampling rates which can exceed the

subject bandwidth [88].

In general, Kalman filter is defined as linear, discrete time, finite dimensional

time-varying system estimating the system state by minimizing mean square error

[119]. It runs through iterative process of filtering and predicting. Each of these

iterations are derived and interpreted as Gaussian probability density functions. A

typical application of Kalman filter is illustrated as in figure 2.8 [119].

Figure 2.8: The Kalman filter [119]


2.2.6 Extended Kalman filter

The conditional probability density functions that provide the minimum mean

square estimation are no longer Gaussian [119], when the state dynamics or ob-

servation dynamics are non-linear. For such circumstances, the extended Kalman

filter: the non-linear version of Kalman filter, is applied. It linearizes about an

estimation of current mean and covariance.

Indeed, the state transition model xk and observation model zk are non-linear

or a differentiable function as equations (2.2.13) and (2.2.14) [119].

xk = f(xk−1, uk−1, wk−1) (2.2.13)

zk = f(xk, vk) (2.2.14)

There are four main steps in the formulation of EKF[120]. x(k|k), u(k), P (k|k) areknown inputs and the new measurement is z(k + 1).

1. State Prediction x(k + 1|k) = F (k)x(k|k) +G(k)u(k)

2. Measurement Prediction z(k + 1|k) = H(k)x(k + 1|k)

3. Measurement Residual v(k + 1) = z(k + 1)− z(k + 1|k)

4. Updated State Estimate: x(k + 1|k + 1) = x(k + 1|k) +W (k + 1)v(k + 1)

W (k + 1) is known as Kalman gain.

Quaternion-based extended Kalman filter

Numerous studies were conducted on 2D and 3D human motion tracking applying

Kalman filter and extended Kalman filter (EKF) such as Azuma and Bizop in 1994

[121, 122], Foxlin et al. in 1996 - 1998 [123, 124], E.R. Bachmann in 2000-2011

[113, 125, 126] and Sebatini et al. in 1995-2013 [127, 128, 129, 130]. The outcomes

of those studies applying EKF for the measurement vectors from inertial/magnetic

sensors has shown better accuracy improvement in obtaining the orientation. Xi-

aoping Yun et al. has introduced quaternion based EKF and the quaternion was


Figure 2.9: Extended Kalman filter [113]

calculated applying QUEST method (refer 1.7.2) using accelerometer measurements

and magnetometer measurements.

The use of quaternion rather than Euler angles has following advantages [113].

1. Quaternion based estimation avoids trigonometric functions, hence it compu-

tationally efficient and easier to implement

2. It avoids the singularities

3. Simple as the rotational complicities can be ignored.

The quaternion derivative SE q is the rate of change of the earth frame relative

to the sensor frame and it was obtained using gyroscope readings as in equation

(2.2.2). In [113], two approaches were presented for calculating the quaternion as

given in figures 2.10 and 2.11.


1. The standard Kalman filter estimation: the quaternion calculated using each

nine observation vectors such as three axes accelerations, three axes gyroscope

readings and three axes magnetometer readings.

Figure 2.10: Block diagram for first approach of implementing Kalman filter [113]

2. Optimal quaternion is estimated applying Kalman filter to three axes gyro-

scope readings and the computed quaternion from QUEST algorithm.

Figure 2.11: Block diagram for second approach of implementing QUEST algorithmand Kalman filter [113]

In the second approach, even though there is an additional computational cost to

develop QUEST algorithm than the first approach, It’s overall computational cost

is low [113]. Even though the calculated quaternion from accelerations and magne-

tometer readings are free from drift, it is not sufficient to estimate the orientation

accurately due to the limitations of accelerometer and magnetometer discussed in

sections 1.6.1 and 1.6.2. The complete algorithm of the second approach is shown

in figure 2.9.


After obtaining the appropriate parameters to initialize EKF, it was simulated

using the observation vectors of MARG sensors. Finally, the real-time quaternion

was produced by EKF, which was visualized using an avatar.

2.2.7 Robust extended Kalman filter

The first appearence of robust Kalman filtering was in 1992 as a potential method

to address the lack of robustness issue which is a significant shortcoming in the state

space control theory [131]. Ian R. Peterson and Andrey V. Savkin has introduced

this improved version of Kalman filter by addressing the issues of robustness against

a large parameter uncertainty in the linear process model. Furthermore, the robust

Kalman filter is available to both linear systems and non-linear systems. The robust

extended Kalman filter (REKF) is the nonlinear form of robust Kalman filter. These

two versions were applied in node localization of mobile robots [132, 133]and missile

guidance [134, 135, 136]. However, these methods are not widely used in human

motion tracking which is our area of interest.

The REKF for a nonlinear uncertain system can be formulated as follows

x = A(x, u) + B2w (2.2.15)

z(t) = K(x, u) (2.2.16)

y = C(x) + v (2.2.17)

where (2.2.15) is the state equation, z(t) in (2.2.16) are uncertainty outputs and

(2.2.17) is the measurement equation. The approximate solutions for the above

problem can be written as equations 2.2.18 and 2.2.19 [133].

˙x(t) = A(x(t), u0) +X−1[ΔxC(x(t))TR(y0 − x(t)) (2.2.18)

+ΔxK(x(t), u0)TK(x(t), u0)], x(t) = x0

X = ΔxA(x(t), u0)TX +XΔxA(x(t), u

0) +XB2Q−1BT

2 X (2.2.19)

−ΔxC(xT )RΔxC(x) + ΔxK(x(t), u0)TΔxK(x(t), u0) = 0


2.2.8 Comparison and summary

The data fusion and filtering mechanisms are categorised into two categories as

model based state estimators and ordinary data fusion techniques. The complemen-

tary filter and adaptive complementary filter are listed under the ordinary filtering

techniques. The Kalman filter, extended Kalman filter, robust Kalman filter and

robust extended Kalman filters are listed under the model based state estimators.

Comparison of filtering mechanisms

Firstly, estimation accuracy of the ordinary data fusion techniques such as high pass

filter, low pass filter, complementary filter and adaptive complementary filter have

been evaluated compared to the VICON system. For that, the author conducted an

action of lifting a bottle discussed in section 2.2.4 as an experiment. Figures 2.12(a)

and 2.12(b) show the exercise procedure and the experiment setup respectively.

(a) The exercise procedure (b) Experimental setup

Figure 2.12: Lifting a bottle: VICON markers and BioKin sensors were attachedto the arm (Left arm).

The elbow joint angle variation of each subject was calculated using the following

methods:


1. High-pass filtered angular rate integration (θω) (To ensure experimental sim-

plicity manually adjusted the initial orientation to match VICON data)

2. Direct orientation estimation from low-pass filtered acceleration measure-

ments (θa)

3. Sensor fusion using the adaptive complementary filter using (2.2.9)

4. Sensor fusion using traditional complementary filter using (2.2.7)

5. Using VICON motion capture data.

For the traditional complementary filter, the constant K1 for gyroscope as in

equation (2.2.7), was 0.98 and the constant K2 was 0.02. The Root Mean Square

Error (RMSE) was used to estimate the error between trajectories (figure 2.13 shows

for subject 1) in which derived from the sensor measurements and the VICON

optical motion capture system as in table 2.4.

0 50 00 2 0−180

−160

−140

−120

−100

−80

−60

−40

−20

0

Time

Ang

le (d

egre

es)

High Pass Filter GyroscopeLow Pass FilterAccelerations

The Ground Truth

Figure 2.13: Elbow angles were calculated with different filtering and sensor fusiontechniques compared to VICON optical motion capture system for subject 1


Table 2.4: The root mean square error comparison of each methods

Method Subject 1 Subject 2 Subject 3 Subject 4

High Pass Filter - Gyroscope 8.918◦ 11.735◦ 6.301◦ 13.779◦

Low Pass Filter - Accelerations 16.484◦ 20.173◦ 31.032◦ 5.522◦

Traditional ComplementaryFilter 8.974◦ 11.853◦ 6.785◦ 13.596◦

Adaptive ComplementaryFilter 7.083◦ 11.270◦ 7.929◦ 8.803◦

As figure 2.13, the plot from the high pass filter on the gyroscope measurements

and the plot from traditional complementary filter were overlapped on each other.

Further, the calculated angles were highly dependent on the accelerations of the

subject’s motion. Subject 4 has shown a better accuracy in the method of low pass

filter compared to others because the particular motion conducted in a very low ac-

celeration. However, this effect has been limited in other three subjects. From table

2.4, the least RMSE of the elbow joint angle and least deviation between minimum

error and maximum error (4.187 degrees) were observed in the adaptive complemen-

tary filter. The deviation in error for other methods: gyroscope based, accelerations

Table 2.5: Advantages and disadvantages of data fusion algorithmsOrdinary filtering techniques Model based state estimators

Complementary filter Adaptive complemen-tary filter

Kalman filter EKF REKF

Advantages Easy to implement

and less computations[39, 137]

Easy to implementand less computations[39, 137]

Noise parameters ofthe measurementsare considered [137]

Noise parameters ofthe measurements areconsidered [137]

Not only noise param-eters but uncertaintyof measurements isalso considered, hencevery robust algorithm

Lower accuracy Average accuracy butbetter than comple-mentary filter [39]

Higher accuracy Higher accuracy Higher accuracy

Simple equations [39,137]

Simple equations [39] Suitable for non-linear systems whichare very common inreal life

Suitable for non-linear systems whichare very common inreal life

Disad

vantages Accuracy is low with

large noise and uncer-tainty

Accuracy is low withlarge noise and uncer-tainty

Complex equationsand calculations



Not consider any sta-tistical description forthe noise corruptingthe signals [137]

Not consider any sta-tistical description forthe noise corruptingthe signals [137]

Not account-ing uncertaintyparameters of mea-surements, henceless robust [132]

Not accounting uncer-tainty parameters ofmeasurements, henceless robust [132]

Not robust Not robust


based and traditional filter are 7.478, 25.5099, 6.811 degrees respectively.

With these experimental results and previous studies in open literature, the

advantages and disadvantages of these data fusion mechanisms are listed in table

2.5.

Model based state estimator implementation relevant to human arm kinematics

is discussed in the next sections of this chapter.

2.3 Dynamic model

General superior performance of dynamic model based estimations inevitably pro-

vides a natural choice for human pose estimation. Identification of a proper dynamic

model facilitating dynamic parameter estimation of rotating and translating frame

is crucial. Indeed the model can be further improved by incorporating full body

human bio-kinematic modelling and here, the author try to keep the overall model

simple to highlight the key contributions of this work. Further, the quaternion

based approach is preferred as it eliminates the issues stated in section 2.2.6. The

nomenclature is included in table 1, Appendix I.

Denoting the orientation quaternion in the earth coordinate frame as q, angular

velocity ω, (2.3.1) is stated as [138],

q = 12q ⊗ ω , (2.3.1)

where, ⊗ denotes the quaternion multiplication with ω = [0 ω1 ω2 ω3]� used as a

pure quaternion. Here vector x is [x1 x2 x3 x4 x5 x6 x7 x8 x9 x10].

Defining the state vector as,

x = [x1 x2 x3 x4 x5 x6 x7 x8 x9 x10]� , (2.3.2)

where,

[x1 x2 x3] = [ω1 ω2 ω3] = ω,

[x4 x5 x6 x7] = [q1 q2 q3 q4] = q,

[x8 x9 x10]� = δ.


ω, q and δ are angular rates, quaternions and gyro drift respectively, the dynamic

model can be stated as,

x = A(x) +Ww,where

A(x) =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

− 1τxx1

− 1τyx2

− 1τzx3

x3x5−x2x6+x1x7

2√

x24+x2

5+x26+x2

7

−x3x4+x1x6+x2x7

2√

x24+x2

5+x26+x2

7

x2x4−x1x5+x3x7

2√

x24+x2

5+x26+x2

7

−x1x4−x2x5−x3x6

2√

x24+x2

5+x26+x2

7

− 1dxx8

− 1dyx9

− 1dzx10

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

∈ R10×1

W =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎣

I3 O3×3

O4×3 O3×3

O3×3 I3

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎦∈ R10×6

w = [Tx, Ty, Tz, B1, B2, B3]� (2.3.3)

Here, Tx, Ty, Tz indicate the torque due to uncertain human movements andB1, B2, B3

indicate the uncertainty in the bias responsible for the Gyroscopic drift. Im and

Om×n denotes identity and zero matrix of indicted sizes. The measurement model

can be stated as follows,

y = C(x) + v, (2.3.4)

where y = [y1 · · · y13]� =[ω1 ω2 ω3 a1 a2 a3 h1 h2 h3 x4 x5 x6 x7

]�, is the IMU

measurement vector with angular rate from gyroscopes, acceleration from accelerom-

eters and orientation of the earth magnetic field from magnetometers. Here, v =

[v1 v2 v3 0 0 0 0 0 0]� is the measurement noise. Further, the time constant for


the motion and variance of continuous white noise is denoted respectively by τ =

[τx τy τz]� and d = [dx dy dz]

� [139].

C(x) =

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

x1 + x8

x2 + x9

x3 + x10

−2‖g‖ (x5x7 − x4x6)

−2‖g‖ (x4x5 + x6x7)

−‖g‖ (x24 − x25 − x26 + x27)

2he2 (x5x6 + x4x7) + 2he3 (x5x7 − x4x6)

he2 (x24 − x25 + x26 − x27) + 2he3 (x6x7 + x4x5)

2he2 (x6x7 − x4x5) + he3 (x24 − x25 − x26 + x27)

x4

x5

x6

x7

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2.3.5)

Let the measurement in the earth frame have g = [0 0 − ‖g‖]� and he =[0 he2 h

e3

]�acceleration and magnetometer readings respectively.

Remark 1. Without the loss of generality, the X axis of the stationary globalco-ordinate frame in a perpendicular direction to the magnetic direction has beenaligned to simplify the resulting expressions.

Considering (2.3.4), an unique solution is given by,

xm =

√Km+

√K2

m+4L2m

2m ∈ {4, 6}

xn =

√−Kn+

√K2

n+4L2n

2n ∈ {5, 7}

where

K4 = K5 =p2 + q3

2, L4 = L5 =

q2−p32,

K6 = K7 =p2 − q3

2, L6 = L7 =

q2+p32


with

p2 =h2‖g‖+a2he

3

he2‖g‖

, p3 =h3‖g‖+ a3h

e3

2he2‖g‖q2 = −a2

2‖g‖ , q3 =−a3‖g‖ . (2.3.6)

Considering the measurement uncertainty, let the measurement model for the con-

verted measurements with respect to magnetometer and accelerometer measure-

ments be:

ai = ai + vai , hej = hej + vej , hj = hj + vhj (2.3.7)

∀i ∈ {1, 2, 3} and j ∈ {2, 3}.

where, ai, hej and hj indicates the accelerometer readings subjected to measure-

ment noise, magnetometer measurement in the earth frame and the mobile frame

respectively. The error bounds are described in the following form:

Assumption 1. The following holds

1 For given constants α and β, let 0 ≤ vai ≤ βai, 0 ≤ vej ≤ αhej and 0 ≤ vhj ≤αhj ∀i ∈ {1, 2, 3} and j ∈ {2, 3}.

In the case of converted measurements, let’s define the following:

μ = (1+α)(1+β)(1−α)(1−β)

, σ = (1−α)(1−β)(1+α)(1+β)

(2.3.8)

λ =√

μ+σ2, φ =

√μ−σ2, (2.3.9)

Now the converted measurement can be stated as,

xi = λxi + ni (2.3.10)

and

‖ni(t)‖ ≤ ‖φxi‖ ∀i ∈ [4, 5, 6, 7] (2.3.11)

Denoting

C =

⎡⎣ I3 O3×4 I3

O4×3 λI4 O4×3

⎤⎦ and

K =

⎡⎣ I3 O3×4 I3

O4×3 φI4 O4×3

⎤⎦


the converted measurement model corresponding to the non-linear measurement

model in equation (2.3.4) can be stated in the following linear form:

yc(t) = Cx(t) + n(t). (2.3.12)

Here yc = [ω1 ω2 ω3 x4 x5 x6 x7]�, n(t) � [n1(t) n2(t) n3(t) n4(t) n5(t) n6(t) n7(t)] .

2.4 Robustness of the non-linear model

Consider nonlinear uncertain systems of the form,

x = A(x, u) +Dw

z = Kx

y = Cx+ n (2.4.1)

defined on [0, T ] with x(t) ∈ Rn (equation (2.3.2)) denoting the state of the system,

y(t) ∈ Rl (equation 2.3.5) the measurements vector. A(x, u) and Cx are defined in

equation (2.3.3) and (2.3.4) respectively. Further, z(t) ∈ Rq, u(t) ∈ R

l, w(t) ∈ Rp

denote the uncertainty output and the uncertainty inputs respectively.

Assumption 2.

(x(0)− x0)�N (x(0)− x0)

+12

∫ T

0

[w(t)�Qw(t) + n(t)�Rn(t)

]dt

≤ d+ 12

∫ T

0z(t)�z(t) (2.4.2)

Introduce the following Riccati Differential Equation(RDE). Here RDE is intro-

duced for calculating the next state,

S +∇xA(x, u)�S + S∇xA(x, u) + SDQ−1D�S

−C�RC +K�K = 0, S(0) = N (2.4.3)

Then, the state propagation by iterating is given by,

˙x(t) = A(x(t), u0)

+ S−1(t)[C�R [yc(t)− Cx(t)] +K�K

],

x(0) = x0. (2.4.4)


The earth frame is oriented with the following assumptions.

1. Accelerations apart from gravity is negligible

2. Earth frame is such that the direction of the magnetic field is perpendicular

to the X axis.

Remark 2. Notice here that the there is a significant component of the earth mag-netic field in the Z direction in Australia and this cannot be neglected unlike in thecase for locations close to the equator.

Robustness of the estimation

The approximate solution for the set of estimated states for the robust set valued

state estimation is :

χs ={x ∈ Rn : 1

2(x− x(s))�X(s) (x− x(s)) ≤ d− φ(s)

}(2.4.5)

where

φ(t) �∫ t

0

[12(y − Cx)�R (y − Cx)− x�K�Kx

]dτ

Therefore, the centroid of the ellipsoidal set is taken as the estimated state. Let

Φ and Θ denote the diagonalising and the resulting diagonal matrix respectively

while ai and aj denote the spectral densities of 1√d−φ(s)

Θ and√d− φ(s) Θ−1 re-

spectively. Taking, δ+ = [0 · · · ai · · · ]� ∈ Rn and δ− = [0 · · · aj · · · ]� ∈ Rn and

noticing Φ�X(s)Φ = Θ, x+ = x(s) + Φδ+ and x− = x(s) + Φδ− indicate the major

axis and the minor axis of the set values state estimation. This provides a measure

of the estimation bounds.


2.5 Robust optimisation based approach for ori-

entation estimation

The x4, x5, x6 and x7 of the state vector denotes the orientation quaternion. With

R+ denoting the set of non-negative real numbers, define,

F (x) = (x4 − P )2 + (x5 −Q)2 + (x6 −R)2 + (x7 − S)2,

G(x) = −2Px4 − 2Qx5 − 2Rx6 − 2Sx7,

x = [x4 x5 x6 x7]T , A1 = [1 0 0 0]T ,

A2 = [0 1 0 0]T , A3 = [0 0 1 0]T , A4 = [0 0 0 1]T ,

Γ =√P 2 +Q2 +R2 + S2, p1 =

1Γ[P Q R S]� ,

p2 =−1Γ[P Q R S]�

Ω = {x ∈ R4+ : x24 + x25 + x26 + x27 = 1},

Λ =

⎧⎪⎪⎨⎪⎪⎩x ∈ R

4+ :

x24 + x25 + x26 + x27 ≤ 1

and

x4 + x5 + x6 + x7 ≥ 1

⎫⎪⎪⎬⎪⎪⎭ ,

∂Λis a boundary ofΛ.

h4 = {x ∈ R4+| x4 = 0}, h5 = {x ∈ R

5+| x5 = 0},

h6 = {x ∈ R4+| x6 = 0}, h7 = {x ∈ R

5+| x7 = 0},

h8 = {x ∈ R4+| x4 + x5 + x6 + x7 = 1},

Λ4 = (∂Λ\Ω)⋂h4,Λ5 = (∂Λ\Ω)⋂h5,Λ6 = (∂Λ\Ω)⋂h6,

Λ7 = (∂Λ\Ω)⋂h7,Λ8 = (∂Λ\Ω)⋂h8Now, the following lemma can be stated as,

Lemma 1. The solution to the following problem of,

minF (x) subjected to x ∈ Ω

can be stated as follows:

1 If P = Q = R = 0 then[12

12

12

12

]�is the optimal solution.

2 if P ≥ 0, Q ≥ 0, R ≥ 0, S ≥ 0 then optimal value of (OP )1 is

min{F (A1), F (A2), F (A3), F (A4), F (p1)}

3 if P ≤ 0, Q ≤ 0, R ≤ 0, S ≤ 0 then optimal value of (OP )1 is

min{F (A1), F (A2), F (A3), F (A4), F (p2)}


4 Else the optimal value of (OP )1 is

min{F (A1), F (A2), F (A3), F (A4)}.

Proof. From lemma 3 and 4 in Appendix I, if x∗ ∈ Ω is an optimal point of problem(OP )3 then it also is an optimal point of problem (OP )1. Therefore, to solveproblem (OP )3, an optimal point x∗ ∈ Ω need to be found for problem (OP )3.

For γ ∈ R, the author denote the γ-level set for linear functional G(x) as follows.

Gγ = {x ∈ R4| G(x) = γ}.

Clearly, Gγ, γ ∈ R are parallel hyperplanes. Therefore, if Gγ0 is a supportinghyperplane of the convex set Λ at x0 ∈ ∂Λ then x0 is an optimal point and G(x0) =γ0 is the optimal value of problem (OP )3. Similar to the proof of lemma 3, if x0

belongs to one of five sets Λi, i = 4, 5, · · · , 8 then one of four points A1, A2, A3,A4 is an optimal point of problem (OP )3. On the other hand, Gγ0 is a supportinghyperplane of the convex set Λ at x0 = [x04 x

05 x

06 x

07]

T ∈ Ω if

x04P

=x05Q

=x06R

=x07R

(2.5.1)

(for case P = 0, Q = 0, R = 0.) In this case, (2.5.1) implies that

(x04)2

P 2=

(x05)2

Q2=

(x06)2

R2=

(x07)2

R2

=(x04)

2 + (x05)2 + (x06)

2 + (x07)2

P 2 +Q2 + 2R2. (2.5.2)

If P > 0, Q > 0, R > 0 then by using (2) there is an unique solution that belongsto Ω of (2.5.1) is p1. If P < 0, Q < 0, R < 0 then by using (2) there is an uniquesolution that belong to Ω of (2.5.1) is p2. Note that if P = 0, Q = 0, P = 0, thenthe author conclude x04 = 0, x05 = 0, x06 = x07 = 0, respectively. Otherwise (2.5.1)has no solution belonging to Ω.

2.6 Implementation of the orientation estimation

The process of pre-filtering is to ensure the frequency bounded noise is filtered

out via simple low pass filtering. Using the empirical knowledge, the bandwidth

of the low pass filters was set. The converted measurements have been used as

raw estimates, standard extended Kalman filtering and also the robust extended

Kalman filtering to evaluate the performance of our approach. Indeed, all these

use the optimisation framework, the author mathematically justified to ensure the


standard quaternions constraint are met. As depicted in figure 2.14, in the first step,

the converted measurement approach is used to compute the quaternion using the

magnetometer (h) and the accelerometer readings (a). The magnetometer readings

suffer scaling error and offset biases. The error are indeed device specific and hence,

the normalised readings were used to calculate the quaternions.

2.6.1 Extended Kalman filter based approach

The non-linear dynamic and measurement model described in equations (2.3.3) and

(2.3.4) respectively are used in the standard extended Kalman filter implementation.

E(w�w) =

⎡⎣ Q1I3 O3

O3 Q2I3

⎤⎦ (2.6.1)

The numerical values for Q1 and Q2 are evaluated as given in [138].

2.6.2 Robust extended Kalman filter approach

The non-linear dynamic and measurement model described in equations (2.3.3) and

(2.3.4) respectively are used under the norm bounded uncertainty assumption given

in inequality 2.4.2.

2.6.3 Robust extended Kalman filter with linearmeasurements approach

The non-linear dynamic and measurement model described in equations (2.3.3)

and (2.3.12) respectively are used under the norm bounded uncertainty assumption

given in inequality 2.4.2. The non-linear measurement model given in equation

(2.3.4) is converted to the underlying linear form with the measurement assump-

tions in 2.3.7 resulting in 2.3.12. The quaternions obtained in equation (2.3.6) as

converted measurements is intact considered as time wise observation in the linear

measurement model in equation (2.3.12). Hence, the measurement vector can be

updated as,

y = [y1 · · · y13]� = [ω1 ω2 ω3 a1 a2 a3 h1 h2 h3 x4 x5 x6 x7]� ,


Figure 2.14: Block diagram of the algorithm


0 0.25 0.50 0.75 1 1.25 1.500

0.05

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0.35

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Robust Extended Kalman Filter With Linear MeasurementsExtended Kalman Filter Robust Extended Kalman Filter

RM

SE (r

adia

ns)

Time (seconds)

Figure 2.15: RMSE of the estimated angle

with the angular rates from gyroscopes, accelerations from accelerometers, ori-

entation of the earth magnetic field from magnetometers and the measurement

converted quaternions from equation (2.3.6). Further, the time constants for the

motion and variance of continuous white noise is denoted by τ and d respectively.

2.7 Computer simulation

Two hypothetical scenarios were considered to validate the underlying assertions

by employing torque Tx, Ty, Tz and time constants τx, τy, τz in the respective carte-

sian axes to emulate the relevant kinematics of human arm. The torque gradually

increases while the arm is being lifted and then the torque is kept constant prior

to reducing to the resting state corresponding to the upright position. Gyroscope,

accelerometer and magnetometer readings were captured as the simulated kinemat-

ics using equation (2.3.3), (2.3.4) and (2.3.5). The resulting measurements were

used with different estimators; Extended Kalman filter (EKF), Robust Extended

Kalman Filter (REKF) and Robust Extended Kalman Filter with Linear Measure-

ments (REKFLM) for real time estimation of the arm orientation. Figure 2.15

shows the actual angle variation with time and the estimated angle variation from

each of the algorithms simultaneously for this hypothetical scenario.


2.7.1 Model based state estimation techniques compared touncertainty bias

0

0.5

1

1.5

2

2.5

Roo

t Mea

n Sq

uare

Err

or o

f ang

le (r

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B T B Values

1.73 e 4.33 e 0.0108- Pitch Angle

8.66 e 0.0022

0

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1.73 e 4.33 e 0.0108- Yaw Angle

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B T B Values

1.73 e 4.33 e 0.0108- Yaw Angle

8.66 e 0.0022

Extended Kalman Filter Implementation Robust Extended Kalman Filter Implementation Robust Extended Kalman Filter with Linear Measurement

Figure 2.16: The error in estimated angle with against the uncertainty bias

Under the first simulation scenario, the impact of uncertainty factor is investi-

gated. Notably, the shoulder pitch, yaw and roll angles deduced from the estimated

state is same for each algorithm compared to the simulated actual angles when the

uncertainty is low. However, when the gyroscopic bias uncertainty (√BTB) where

B � [B1 B2 B3]� and B1, B2 and B3 are taken as identical with at 0.00005 incre-

ments from 0.00001. The estimation error is increased significantly as depicted in

figure 2.16.

2.7.2 Model based state estimation techniques compared tonoise variance

Under the second hypothetical scenario, Gaussian noise was introduced to the gen-

erated measurements to validate the robustness of each algorithms in measurement

noise uncertainty. Signal to noise ratio between 60 dB to 20 dB was introduced to

the simulated accelerometer, magnetometer and gyroscope readings with the kine-

matic model parameters of τx,τy and τz set to 0.25 s−1 and[B1 B2 B3

]set to[

0.0001 0.0001 0.0001].

This simulation was extended to investigate the optimisation algorithm dis-

cussed in section 2.5. Here, the estimated quaternion ([X4 X5 X6 X7

]), prior


to using as input to the estimator, is optimised using the proposed algorithm. In-

deed it is the standard practice to normalise the quaternion and here the author

establish a mathematical justification to this process. The model parameters such

as time constant, uncertainty constant are the same as they were for the first sim-

ulation. Gaussian noise (60 dB - 20 dB Signal-to-noise ratios) was introduced to

gyroscope, magnetometer and accelerometer readings as the first simulation.

2.7.3 Simulation results and discussion

The root mean square error (RMSE) was plotted in figure 2.17 for the three esti-

mators considered; EKF, REKF and REKFLM with the subjected (60 dB - 20 dB)

noise levels. Irrespective of engaging optimised quaternion (section 2.5), the RMSE

was less for REKFLM. This is particularly observable when the uncertainties are

significant. Indeed, the filter accuracy in estimating the rotation angle improved

when the noise level reduced from 20dB to 60dB. The error in EKF increased

markedly and the error in REKF was exaggerated compared to the REKFLM. In

all the estimation algorithms considered, quaternion optimisation had a positive yet

lesser impact on lower noise levels(50dB - 60dB) on the angle estimation accuracy

unlike for larger noise levels(20dB - 30dB). Indeed the superior estimation accuracy

in the Robust Extended Kalman Filter with Linear Measurements (REKFLM) is

further enhanced with the use of quaternion optimisation as depicted in figure 2.17.

As shown in figure 2.18, quaternion optimisation resulted in an approximately

30% RMSE improvement in the EKF implementation when the SNR is 20 dB in

addition to a more prominent improvement when the SNR is between 28 dB to

20 dB. Contrastingly, RMSE improvement in the REKF implementation was 42%

when the SNR is 20 dB with noticeable improvements in the 20-30 dB noise range.

The RMSE improvement in REKFLM due to quaternion optimisation is relatively

less in comparison to the other two algorithms; approximately 9% improvement

when the SNR is 20 dB. REKFLM outperforms the other estimators albeit all


Non-Optimized Quaternion Optimized Quaternion

Extended Kalman Filter Implementation

Robust Extended Kalman Filter Implementation

Robust Extended Kalman Filter with Linear Measurement

20 23 25 28 30 50 600

0.2

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1

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Figure 2.17: RMSE subjected to introduced noise

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% Im

prov

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Extended Kalman Filter ImplementationRobust Extended Kalman Filter ImplementationRobust Extended Kalman Filter with Linear Measurement

20 23 25 28 30 50 60

Figure 2.18: Percentage improvement due to quaternion optimisation

approaches proclaim the benefit of quaternion optimisation to varying degrees.

2.8 Real-time experiments

2.8.1 Experimental setup

An inertial measurement sensor in an integrated system with wireless communica-

tion was positioned in the wrist of the subject in order to capture the movement


of the shoulder joint. The validation of the underlying algorithms were conducted

through the data captured from four healthy subjects (two males and two females)

using Kinect c©optical system and ten healthy subjects (eight males and two fe-

males) using VICON optical system without any history of joint or muscle impair-

ments. Each subject was asked to do three simple exercises :

1) Lifting the arm in front of the body by 90o (Forward Flexion-Extension as sub-

figures 2.19-(A) and 2.19-(B))

2) Lifting the arm along the side of the body (Abduction-Adduction as sub-figures

2.19-(A) and 2.19-(C)) and

3) Lifting the arm to the back of the body (Backward Flexion-Extension as sub-

figures 2.19-(A) and 2.19-(D)).

Each exercise was repeated three times approximately over 10 minutes with the

inertial sensor worn at the distal end of lower left arm. The experiment setup is

shown as in Figure 2.19. The exercise routines were simultaneously recorded us-

ing VICON optical motion capture system (VICON T40S System) and a Microsoft

Kinect c© system.

The subject is in the orthostatic position with the sensor frames and earth frames

are approximately aligned initially. In the underlying formulation, the torques are

considered as uncertainty inputs and the time constants are determined inline with

the prior computer simulations discussed in 2.7.

2.8.2 Comparison of model based state estimation tech-niques with experimental measurements

Figure 2.15 shows the RMSE in the estimated shoulder movement angles for the

simple exercise of forward extension, when the movement replicated the execution

in a simulated environment. Here the physical movement is carried out as close as

possible to the simulated movement and the IMU measurements were then used

to estimate the actual angle turned. The arm motion is along a planar trajectory

ensuring minimal system complexity allowing the primary focus on the assessment


(A) – Initial Position (B) - Flexion

(C) – Abduction (D) – Backward Extension

(E) – Biokin Sensor and MOCAP marker

Biokin Sensor

MOCap Marker

(B) - Flexion

VICON Camera

S1

S2

S3

S1 S2 S3

S1 S2 S3

S1

S2

S3

Figure 2.19: Experiment Setup and Procedure: S1, S2 and S3 are sensor and wornmarker positions: distal end of elbow, wrist and palm respectively


of the underlying filtering algorithms. This indeed avoided more complex torques

necessary for generating arbitrary trajectories generally experienced in reality.

Non-Optimized QuaternionR

MSE

(rad

)

Sample time

RM

SE (r

ad)

Optimized Quaternion

0 50 100 150 200 250 3000

0.05

0.1

0.15

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0.25

0.3

Extended Kalman Filter based approachRobust Extended Kalman Filter Implementation


Sample time(a) (b)

0 50 100 150 200 250 3000

0.05

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0.15

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0.25

0.3

Figure 2.20: RMSE in angle estimation for Forward Extension Exercise in compar-ison to VICON optical system

Figure 2.20 shows the estimated angle (roll angle) difference compared to VI-

CON optical system for the same exercise. Here, figure (a) and (b) shows the

RMSE in the corresponding angle differences non-optimised and optimised quater-

nions respectively. Angles derived from REKFLM is similar to the angles measured

from the VICON system irrespective of the engagement of quaternion optimisations

(see figure 2.20). Quaternion optimisation, improved each estimation algorithm

markedly reducing the angle estimation error significantly. The average RMSE for

three exercises: Forward Flexion-Extension, Abduction-Adduction and Backward

Flexion-Extension when IMU measurements were compared to both Kinect c© and

the VICON systems is listed in table 2.6. The bar charts in figures 2.21 and 2.23

show the performance in terms of RMSE of each algorithm over four healthy subjects

with respect to Kinect c© and VICON measurements. The last column indicates

the averaged performance as listed in table 2.6 and each performance improvement

due to quaternion optimisation is provided with each figure concurrently.


Table 2.6: Averaged RMSE Error in angle estimation for arm exercises in compar-ison to Kinect c© and VICON systems based measurements

Averaged RMSE of Non- Optimisation Quaternion Averaged RMSE of Optimized Quaternion

Compared to Kinect c© Optical System Compared to VICON Optical System Compared to Kinect c© Optical System Compared to VICON Optical SystemEKF REKF REKFLM EKF REKF REKFLM EKF REKF REKFLM EKF REKF REKFLM

Forward Flexion-Extension 0.2576 0.1631 0.0712 0.1469 0.0833 0.0491 0.1476 0.0874 0.0613 0.0911 0.0574 0.0393Abduction-Adduction 0.206 0.1242 0.0698 0.1181 0.0933 0.0531 0.1352 0.063 0.0537 0.0924 0.0569 0.0415Abduction-Adduction 0.1622 0.117 0.0527 0.0904 0.058 0.0376 0.1475 0.1004 0.0417 0.0723 0.0438 0.0351

1 2 3 4 Overall0

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Forward Flexion-Extension

Abduction-Deduction

Backward Flexion-Extension




Figure 2.21: RMSE in angle estimation for the upper arm exercises in comparisonto Kinect c© optical System

0

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Subject 1 Subjects 3Subject 2 Subjects 4 Overall

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(b) Abduction - Adduction

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(c) Backward Flexion - ExtensionExtended Kalman Filter Implementation Robust Extended Kalman Filter Implementation

% Im

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Figure 2.22: Percentage improvement due to optimisation of the experiment withKinect c© optical system




Abduction-Deduction

Backward Flexion-Extension




1 2 3 4 5 6 7 8 9 100

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Figure 2.23: Root mean square error of upper arm exercises compared to VICONoptical system


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Extended Kalman Filter Implementation Robust Extended Kalman Filter Implementation Robust Extended Kalman Filter with Linear Measurement

Figure 2.24: Percentage improvement due to optimisation of the experiment withVICON optical system

Similar to computer simulations, the EKF and REKFLM are the least accurate

and most accurate algorithm respectively. The improvement in terms of RMSE

with respect to Kinect c© and VICON measurements due to the engagement of

quaternion optimisation for each filter and subject is depicted in figure 2.22 and

2.24 respectively. As depicted in table 2.6, the averaged RMSE with respect to

Kinect c© when using EKF is reduced by 43%, 34% and 10% for the three ex-

ercises respectively due to quaternion optimisation while the averaged RMSE in

EKF algorithm is reduced by 36%, 21%, and 19% with respect to VICON optical

system. For the case of REKF accuracy improved by 47%, 49% and 14% with re-

spect to Kinect c© system and 30%, 38% and 24% with respect to VICON optical

system across the aforementioned exercises. This result implies that the accuracy

in EKF and REKF methods improved significantly due to quaternion optimisa-

tion yet the accuracy of REKFLM algorithm improved by about 14%, 23% and

21% respectively for the above exercises with the Kinect c© system. Accuracy of the

REKFLM approach is improved by 20%, 21% and 7% for forward Flexion Extension

exercise, Abduction Adduction exercise and Backward Flexion-Extension exercise

respectively compared to VICON optical system when engaged with quaternion

optimisation.

Generally, the observation is that REKFLM algorithm outperforms EKF and REKF.


Further, quaternion optimisation significantly improves the state estimation irre-

spective of the estimator.

2.8.3 Summary and conclusion

Under this chapter, available data fusion techniques both ordinary filters such as low

pass filter, high pass filter, complementary filter and adaptive complementary filter

were investigated, and then, model based state estimators such as Kalman filter,

extended Kalman filter, robust Kalman filter and robust extended Kalman filter to

obtain an accurate estimation using measurements of inertial/magnetic sensors.

Further, the dynamic model for quantify the human kinematics was introduced.

It has been demonstrated that adopting a linear formulation in the measurement

scheme provides improved results for real time human kinematic movement estima-

tion as opposed to the standard approach involving extended Kalman filtering or

even robust version of extended Kalman filtering. Measurement conversion based

linear approach in fact results in improved estimation accuracy. Indeed the Quater-

nion normalisation improved the estimation accuracy of all estimators in general

and the mathematical verification of the process completes the justification of the

current practice in place. Although the improvements due to quaternion estima-

tion is relatively less for the converted measurement Kalman filtering, the proposed

approach still outperforms the traditional approaches. These assertions have been

verified by both computer simulations as well and hardware experimentation.

Chapter 3

Curvature Estimation In LimbTrajectories Using Inertial SensorsAnd Its Applications

3.1 Introduction

In Mathematics, curvature of a curve is defined as the rotating velocity of a tangent

line along the curve with natural parameterization[140]. In other words, curvature

is the deviates from being a flat plane. With respect to the limb trajectories, the

curvature can be calculated and used to investigate the nature of movement [141].

The curvature is a novel concept for inertial sensors which has not been applied

before to the measurements of inertial sensors. The major advantage of applying

curvature for analyses is that it is a frame independent calculation in spatial space.

In this chapter, the main focus is to investigate the curvature calculation based on

inertial sensors. Further, two curvature based applications are discussed such as a

novel misalignment calibration method and limb length estimator.

Quantitative assessment of the progress in physical rehabilitation largely de-

pends on accurate measurement of range of the movements and other kinematic

parameters [142, 143]. Obtaining accurate measurements from wearable sensors

have a significant dependence on the initial orientation calibration and the assump-

tion that the sensor will not slip or move with respect to the attached limb. As one

application of curvature with inertial sensor measurements, this chapter introduces

77

Chapter 3.Curvature Estimation In Limb Trajectories Using InertialSensors And Its Applications 78

a novel calibration algorithm to correct initial orientation misalignment, as well

as to track and correct subsequent alignment errors progressively throughout the

experiment.

Further, limb length is a useful parameter in the assessment of common mus-

culoskeletal disorders such as limb length discrepancy. The measurement variation

among rates is affecting the quantitative aspects in assessments and introduces a

greater subjectivity in the course of treatment. Common practice for measuring

limb length is based on radiography and imaging techniques which are not con-

venient, affordable and requiring professional knowledge. Direct instruments such

as callipers, anthropometers and measuring tapes are difficult to use with patients

due to susceptible to human error in determining rotation joint especially for lower

extremity. As the second application of curvature, the determination of limb length

is automated using a contemporary algorithm to the measurements from a low-cost

and miniaturised inertial sensor which is generally used in rehabilitation. Further-

more, the robustness of the algorithm is optimized with a least noise threshold

model. The proposed estimation technique was validated with real data observed

from eight healthy subjects. The experimental results indicate greater accuracy

compared to manual measurements having low RMSE percentages for arm length

and lower limb lengths. In the rest of this chapter, the novel misalignment calibra-

tion is introduced firstly and then the estimator of human limb length is discussed.

3.2 Adaptive orientation misalignment calibration

mechanism for inertial/magnetic sensors

3.2.1 Motivation for orientation misalignment calibration

The exercises such as flexion - extension, abduction - adduction and internal ro-

tation - external rotation [144], are regularly performed by patients with shoulder

movement disorders in rehabilitation sessions to regain their shoulder functions


[145]. Recently, inertial sensors are pervasively utilised to quantitatively and ob-

jectively track these shoulder exercises in both clinical and in-home environments

[39]. A major assumption in these applications is that the combined structure of

sensor and the limb rotating around the joint, has not misalignment in frames [146].

However, sensor orientation misalignment is unavoidable due to uneven nature and

movements of users’ clothes, muscle or skin, which is highly likely to vary with time

and adversely affects the deviation of limb orientations from sensor measurements

[108]. Nonetheless, a proper calibration phase is required for correcting the initial

IMU orientation misalignment errors before performing the exercises [147].

In literature, the studies in [148, 146, 145, 149, 147] have investigated the initial

misalignment error. Praydi et al. in [148] and Roeternberg et al. in [146] have dis-

cussed the need for orientation calibration (misalignment of sensor frame and joint

coordination system) for human upper limbs in order to track human arm motion

accurately. They have used pre-defined arm poses such as T-pose to calibrate the

frame misalignment and quaternion based calibration method has been introduced

to correct the error. Further, J Favre et al. in [149] has introduced a functional

calibration procedure for 3D knee joint angle by estimating the constant calibra-

tion quaternions for pre-defined postures of lower limbs. According to given passive

movements such as limb flexion, the rotational axes were determined by observed

angular velocities. The rotational quaternion was calculated using angular veloc-

ity. The calculated quaternion was considered as align with the joint coordinate

system as the thigh and shank of lower limbs are collinear. Hence, this algorithm

is limited to human lower limbs. The importance of frame calibration process in

dead-reckoning algorithm has been discussed in [147]. They have used antisymmet-

ric velocity transformation matrix for calibration. However, none of these studies

have discussed the time varying sensor misalignment error for shoulder exercises

which is the case with typical applications of wearable nature.


EZ

EX

EY

SZ

SX

SY

θ

θ

(a) Arm down

EZ θ+α

α

EX

EY

SZ

SX

SY θ+α

(b) Lifting arm

Figure 3.1: The sensor misalignment error in a shoulder abduction exercise

The following sections introduce an innovative algorithm to correct sensor ori-

entation misalignment error for the applications of tracking single plane shoulder

movements for rehabilitation. Importantly, this algorithm takes the arc length of

the motion trajectory into consideration to correct not only initial misalignment

errors, but also, the progressive errors throughout the exercise. The theoretical as-

sertions are validated through controlled experiments with simulated accelerometer

and gyroscope measurements.

3.2.2 Geometrical relationship between curvature, misalign-ment error and shoulder to limb length

Problem formulation

To track shoulder joint exercises, a sensor which captures 3-D gyroscope readings

(ω = [ωx, ωy, ωz]) and 3-D accelerometer readings (As = [asx, asy, a

sz]), is worn on the

distal end of the corresponding upper arm. The three axes of the earth frame and

the sensor frame are denoted by (Ex, Ey, Ez) and (Sx, Sy, Sz) respectively.

Figure 3.1 depicts the misalignment of a sensor in respect to the earth frame

during the shoulder movement. The misalignment error in the sagittal plane is

denoted by θ and the angle change of the arm about Y axis is denoted by α.

Furthermore, the shape of the sensor’s trajectory is an arc with the radius of the

distance between the sensor and the shoulder joint. The roll, pitch and yaw angles


can be calculated using the observed accelerometer and gyroscope reading as in

equations (3.2.1) and (3.2.2) respectively, yet the calculated angles are subject to

misalignment error (θ). It is clear that merely using equations (3.2.1) and (3.2.2)

is insufficient to calculate θ and α because they are identical.

Angroll = θ + α Angyaw = 0 Angpitch = θ + α (3.2.1)

Angroll = 0 Angyaw = θ + α Angpitch = 0 (3.2.2)

Further, the arc length is independent of the sensor orientation which is derived

using accelerometer readings. Therefore, the arc length for the same movement will

be identical in both situations: the error-free situation and the erroneous situation

alike. If the length from the shoulder joint to the sensor is known, the actual

rotated angle in each time interval can be calculated through the arc length as in

the proposed method. With this research, a simulation based feasibility study was

conducted to correct sensor orientation misalignment.

3.2.3 Equations and algorithm formulation

The flow chart in figure 3.2 shows the determination of the sensor and the earth

frame misalignment for shoulder planar movement. Here, the author assume the

sensor attached to the arm is subject to a circular motion about the Y axis without

noise and drift. Then, the assumption is that the arm is moved exactly through a

plane under a low speed with static initialisation. The distance between the sensor

and the shoulder joint (R) is directly measured. In addition, actual rotation angle

of the arm, misalignment error and calculated angle with the misalignment error are

denoted as α, θ and β of positive angles in clockwise rotations respectively. Since

this is a non-uniform circular motion, the object is subjected to radial acceleration

(ar) towards the centre of the circular trajectory and tangent acceleration (aT )

towards the direction of the motion.

It is necessary to consider the linear acceleration with respect to the earth frame

AE = [AEx , A

Ey , A

Ez ] without the gravity component for calculating the length L.


Sensor Data

Angular Rates Accelerometer Data

Quaternion Propagationgravity

Estimated Quaternion Quaternion Rotation

Kinematic Acceleration

Kinematic Acceleration

Length from Arbitrary origin to sensor

Measured Arm Length

Sensor is not Aligned

Arc Length Calculation Actual Movement Calculation

Figure 3.2: Proposed algorithm


Since the movement starts from static position, the mean of accelerometer readings

while the arm is stationary, is considered as gravity. The linear acceleration with

respect to the earth frame can be written as equations 3.2.3, 3.2.4 and 3.2.5 which

is same as gravity compensated sensor readings obtained from equation AEt − g in

figure 3.2.

aEx = aT cosα− ar sinα = Lα cosα− Lα2 sinα (3.2.3)

aEy = 0 (3.2.4)

aEz = aT sinα + ar cosα = Lα sinα + Lα2 cosα, (3.2.5)

where α and α are the angular velocity and the angular acceleration.

Furthermore, the three orthogonally mounted gyroscopes read only Y axial an-

gular velocity with the absence of drift, noise and misalignment error, because the

motion is across the Sx−Sz plane. The sensor orientation in each temporal interval

(Δt) can be calculated by quaternion propagation shown in figure 3.2. It is well

α

α+θE

Z

EX

SZ

SY

αθ

α+θ

EY

SX

SZ

S

R

o

�

L

L

Figure 3.3: The geometrical relationships between error-θ and arm movement-α

known that the arc length L can be calculated as

Lt+1t = θt+1

t L, (3.2.6)

where Lt+1t and θt+1

t are the arc-length of the trajectory and rotation angle of the

limb from time t to t + 1 with temporal interval Δt → 0. Since the recommended


frequency range for navigation systems with accelerometer is between 100 Hz to 400

Hz [150], the rotated angle between two frames can be considered as small enough

to meet the requirement in equation (3.2.6). Furthermore, the calculated length

(L in figure 3.2) should be equal to the measured length (R), unless the sensor is

misaligned (In section 3.3 , the machine-driven process for estimating limb length

is investigated). If the sensor is misaligned, the origin (O) and R will vary from

desired values as in figure 3.3. The length from the arbitrary origin (O) to the

sensor can be calculated using equations (3.2.3), (3.2.4) and (3.2.5). Therefore, the

change of α can be computed as

α =β × L

R, (3.2.7)

where β is the erroneous rotated angle.

3.2.4 Computer simulations

Simulation for calculating length from shoulder to sensor

The first simulation is designed to validate the equations derived for calculating

the length with the absence of noise, drift and misalignment. This validation was

conducted for a non-uniform circular motion with a constant angular acceleration.

The sensor moved along a circular trajectory with radius of 0.315 meter which is

the average length of an upper arm according to [151]. The radius derived from the

proposed algorithm and the actual one were same.

Then, the accelerometer readings and gyroscope readings were simulated as

equations 1.6.1 and 1.6.6 respectively. The noise with various signal-to-noise ratios

(SNR) were introduced and one dimensional median smoother with order 10 was

applied to both the erroneous accelerometer data and the gyroscope data to reduce

the noise. According to following sections, the direct correlation between the mis-

alignment and noise could be observed. This observation is due to the fact that the

curvature is very sensitive to noise. Therefore, the relationship between curvature

and noise was thoroughly investigated.


Roll

Angle

(in r

adia

n)

0

0.5

1

1.5

2

2.5

Ideal Angles without Alignment Error

Angles with Sensor Alignment Error

Sensor Alignment Error

Pit

ch A

ngle

(in r

adia

n)

-0.1

-0.05

0

0.05

0.1

Yaw

An

gle

(in r

adia

n)

0

0.5

1

1.5

2

2.5

Time (sec)1000 20 40 60 80

Figure 3.4: Simulation results

Impact of noisy accelerometer measurements for curvature

With the increase of the SNR, RMSE of the estimated curvature reduces as in table

3.1. For example, when the SNR raises from 1 dB to 60 dB in acceleration, RMSE

of the curvature dropped from 0.436 to 0.017 (refer to the last column in table 3.1).

When noise was introduced to acceleration, initially the radius was highly varied

and later (after approximately 30 seconds), the variance narrowed and the radius

converged to the expected value.

Impact of noisy gyroscope measurements for curvature

With the increase of the SNR, RMSE of the estimated curvature reduces as in table

3.2. However, the radius changed significantly, when the ample noise was included

to angular rates as in figure 3.5.


Table 3.1: The results of curvature after introducing noise to accelerometer readingsSNR RMSE in Curvature

1-10 sample 10-20 sample 20-30 sample 30-60 sample 60-100 sample 1-100 sample

1 1.292 0.404 0.117 0.113 0.071 0.4362 1.301 0.503 0.187 0.09 0.044 0.4495 0.659 0.307 0.078 0.053 0.042 0.23410 0.166 0.045 0.045 0.027 0.024 0.06120 0.124 0.014 0.014 0.007 0.009 0.0430 0.08 0.007 0.007 0.003 0.003 0.02540 0.057 0.006 0.006 0.001 0.001 0.01850 0.057 0.001 0.001 0 0 0.01860 0.053 0 0 0 0 0.017

Table 3.2: The results of curvature after introducing noise to gyroscope readingsSNR RMSE in Curvature

1-10 sample 10-20 sample 20 -30 sample 30-60 sample 60-100 sample 1-100 sample

1 0.315 0.316 0.315 0.315 0.315 0.3152 0.315 0.314 0.315 0.315 0.315 0.3155 0.316 0.316 0.313 0.315 0.313 0.31410 0.322 0.319 0.315 0.317 0.315 0.31720 0.318 0.328 0.323 0.306 0.315 0.31530 0.336 0.291 0.233 0.279 0.297 0.28840 0.181 0.121 0.209 0.223 0.311 0.24050 0.052 0.080 0.052 0.041 0.059 0.05560 0.019 0.008 0.009 0.010 0.014 0.012

Err

or

in C

urv

atu

re

(m )

0

0.5

1

1.5

2

-1

0 20 40 60 80 1000

0.2

0.4

0.6

Time (sec)

10

20

30

40

50

60

Err

or

in C

urv

atu

re

(m )-1

Figure 3.5: The error of estimated curvature with noisy data. The top figure showsthe errors when noise was introduced to acceleration while the lower one illustratesthe errors when noise was added to angular rates. The colour bar is the amount ofnoise in the form of signal-to-noise ratio with unit of dB.


Simulation for frame calibration

Initially, the simulation was designed to identify the time varying sensor misalign-

ment without noise and drift. The arm was rotated with constant angular acceler-

ation about Y axis. The sensor was simulated with misalignment error varied with

time while rotating around the same arm rotation axis under different angular ac-

celerations. The actual arm rotation and misalignment error were calculated using

pre-determined length. The simulation results showing in figure 3.4 were identical

as expected demonstrating the potential to apply the proposed algorithm for given

calibration. Then, noise with 60 dB, 50dB and 40 dB signal-to-noise ratios (SNR)

were introduced to accelerations and angular rates to validate the robustness of the

algorithm.

Length

(m

)

0

0.1

0.2

0.3 Without Noise

With Noise

Actu

al

Rota

tion

(radia

n)

0

1

2

3

Time (1/150 s)

0 20 40 60 80 100

Ori

enta

tion M

isali

gnm

ent

(radia

n)

0

0.2

0.4

0.6

0.8

1

Figure 3.6: Visualization of impact of noise to estimation


3.2.5 Discussion and conclusion

As in figure 3.6, when the accelerometer readings and gyroscope measurements were

subject to noise, the length from sensor to origin was varied with actual length. As

a result of that, the calculated actual arm rotation after introducing noise and the

simulated arm rotation without noise were different with 0.2023 radians root mean

square error. Then, RMSE between calculated orientation misalignment error and

introduced alignment error is 0.0246 radians when the SNR is 60 dB in both accel-

erations and angular rates. Furthermore, the root mean square error in actual arm

rotation angle was increased to 1.4491 radians and 3.0665 radians, when the signal-

to-noise ratio is respectively 50 dB and 40 dB. At that time, the root mean square

error in orientation misalignment was increased to respectively 0.0441 radians and

0.1834 radians. Hence it is required to minimise drift of gyroscope readings and

filter the noise from accelerometer readings in order to apply this algorithm.

3.3 Limb length estimation

3.3.1 Introduction

Limb length discrepancy or anisomelia, is defined as an anatomical condition in

which paired limbs are noticeably unequal [152, 153, 154]. The possible causes

for this condition are infections, paralysis, tumors and consequences of surgical

procedures [152]. The most common form of the discrepancy can be seen in lower

extremity which is called Leg Length Discrepancy (LLD) [152]. The outcomes of this

condition are the muscle tightens or weakens, joint tightness and difficulties in hip

abduction/adduction due to tightens[152]. According to the studies in [155, 156],

LLD is consider as a common condition which can be seen between 40% - 70% of

population. Statistically, one out of a thousand people are suffering from LLD of

greater than 20 mm, a condition that can develop either from childhood or later in

life.

The consequences such as low back pain (LBP), osteoarthritis (OA) of the hip,


stress fractures, aseptic loosening of hip prostheses, standing imbalance, running

and walking difficulties are associated with LLD. The affected limb length discrep-

ancy can range between 9 mm to 60mm [152] and the severity of LLD is determined

based on limb length inequalities. According to [157], the treatments are defined

as 1. mild (0-20 mm) - insignificant to treat, 2. moderate (20-60 mm) should be

treated by using shoe lifts, epiphysiodesis, or shortening and 3. severe (60-200 mm)

should be treated by combined surgical procedures with prosthetic fitting. However,

quantifying the magnitude of LLD for treatments are very subjective and accurate

detection of limb lengths plays a vital role in determining the appropriate course of

action [152, 154].

A number of sensor technologies are used to estimate the limb lengths. Radio-

graphic technology is considered as the gold standard which enables to measure the

leg length between markers: femur/pelvic to ankle [152]. There are basically three

commonly used radiographic techniques; orthoroentgenogram, scanogram and com-

puterized digital radio-graph. These technologies have shortcomings, such as distor-

tion by parallax error, radiation exposure, cost and the requirement of dedicated lab-

oratory facilities restricting any use in non-clinical settings. Some investigators have

used direct measurements, such as measuring limb lengths using instruments such

as anthropometric callipers and measuring tapes [158, 159, 160, 161, 162, 163, 39].

However they are cumbersome to use and susceptible to human error especially

when determining the pelvic bone of DDL patients [152]. However, the develop-

ment of reliable, accurate, affordable and easy to use limb length measurement

technique is a necessity especially for DDL patients [154].

With the advancement in MEMS sensors, miniaturised and low cost sensors

that can be packaged as wearable devices are decorously considered for human

motion capture. However, usage of MEMS sensors for limb length estimation has

not been considered. Further, if this process could be automated by using MEMS

sensors, it will not only results in improved accuracy, but also measurements in


the absence of specialised personnel enhancing the use in non-clinical settings and

tele-rehabilitation. This application is aimed at providing a novel and systematic

approach to estimate limb length using MEMS sensors especially for applications

such as the treatment of LLD. Further, only one IMU sensor is required to facilitate

the measurement of limb length.

3.3.2 Proposed approach

The underlying approach is based on the following assumptions.

Assumption 3. The limbs’ movement originates from a stationary posture. Theacceleration for initiating the movement is negligible with respect to gravity andaccelerating time period is insignificant compared to the overall motion time.

Assumption 4. The sensor frame is aligned with the joint coordinate frame

Assumption 5. The limb is rotated in a single plane (either in sagittal, coronal oraxial plane) as a rigid body between the rotation joint and the sensor

Assumption 6. The sensor is attached at the distal end of the limb, distance (L)away from the rotating joint

The accelerometer measurements and gyroscope measurements of the inertial

device are fed into the algorithm for limb length estimation. Furthermore, the

quaternion (qt) is required to transform the accelerometer reading in the sensor

frame, to the earth frame at time t. Hence the quaternion derivative qt is calculated

as in equation 2.2.2. The quaternion qt at time t is calculated using the quaternion

propagation equation 2.2.3 [164, 66]. The initial quaternion q0 is considered as

[1, 0, 0, 0].

Further, AE is used to calculate the curvature of the motion trajectory as section

3.2.3. Here, a different approach was applied to compensate gravity compared to

section 3.2.3. In this approach, the mean value of the accelerometer readings were

used during the static state as the gravitational acceleration g =[gx gy gz

]. Due

to static conditions, the measurements are entirely based on gravitational force.

According to assumption 4, the gravity readings from sensor gS is with respect to

the earth coordination system. In other words, gS = gE. When the arm is moved,


Sensor Data

Angular Rates Accelerometer Data

Figure 3.7: Algorithm of limb length estimator


the sensor frame and earth frame are different. Hence the accelerometer readings

in the sensor frame at time t is transformed to the earth frame as given in equation

3.3.1.

AEt = qtA

St q

−1t . (3.3.1)

Since the accelerometer readings AEt is the resultant acceleration of both kinematic

acceleration AEt and g, the kinematic acceleration is calculated using the relationship

AEt = AE

t − g.

As the limb is stationary at the outset, linear velocity (V E1 = [vx, vy, vz]

E1 ) is

zero and at each time stamp it is calculated by integrating kinematic accelerations

and the curvature of the trajectory is calculated using the equation 5.4.1 [141].

Kt =

∥∥∥V Et × AE

t

∥∥∥∥∥∥V Et

∥∥∥3 (3.3.2)

The curvature is constant and equal to reciprocal of radius in a circular motion.

Hence, the limb length is calculated as follows,

L =

∑Tt=1

1Kt

T. (3.3.3)

The accelerometer readings were used for calculating curvature instead of deriving

angular velocity from gyroscope since the accelerometer measures the linear accel-

eration directly respect to the earth frame instead of the local frame. The mean of

L is considered as limb length.

The technique is illustrated in figure 3.7. However, with the noisy measurements,

the accuracy of curvature calculation is significantly affected [43]. Following section

describes the Least Noise Threshold (LNT) approach for computationally remove

noisy measurements from curvature calculation.

3.3.3 Identification of least noisy threshold (LNT) in noisydata

The accelerometer readings become noisy and irregular with the presence of noise

[67, 68, 69]. The noise can mostly be seen in beginning of the movements due to


the instantaneous acceleration to start the limb movement from a static status, as

well as the ending portion of the measurements due to decelerating force on the arm

to cease the motion. On the other hand, the resultant acceleration is affected by

white noise [69]. However accelerometer readings are successfully used for physical

activity identification based on thresholds [165]. In this study, noisy portions of

acceleration readings are excluded from curvature calculation for estimating limb

length accurately. The exclusion of noisy data as in [43] can be conducted by

manual observation for initial and terminal phases for exclusion of the uncertainty

regions which can time consuming and requires technical know-how. Therefore, a

systematic method is required to exclude noisy data to facilitate the overall imple-

mentation in a user friendly manner.

Sample entropy (SampEn) is a technique used for determining the regularity of

data in complex systems [166, 167]. SampEn produces more consistent outcomes

than other entropy related techniques [168]. In this paper, SampEn is applied on

each segment of curvature Kj with j = 1, 2, · · · , J and the window size WSampEn

to determine the LNT. Here j is the index of curvature segments and J is the total

number of segments. The value of sampling entropy Hj is calculated with Kj as

follow:

Hj = SampEn(dim, r,Kj) (3.3.4)

where dim is the embedded dimension, r is the tolerance used to determine the

regularity of two subsets. The least entropy thresholds (ζ to η) are determined by

applying SampEn as pseudocode Algorithm 1: Determining the mean length.

In the pseudocode, the variables: entropy as an array, average adult’s limb

length and the estimated optimal length are denoted as H [·], L and L. Repetitive

section A is aimed at capturing ζ to η the global minimum and most likely avoiding

locals minimum recursively; based on a condition that the L should be varied within

±10cm of L. L is the corresponding average limb segment length of healthy adults

in [151, 169]. The start index, end index and middle index of local minimum H are


Algorithm 1 Determining the mean length

Input: H[], LOutput: L1: Call Repetitive Section A:FindLocalMinimumH

2: L =(Σ

η×WSampEn

i=ζ×WSampEnLi

)/ ((η − ζ)×WSampEn)

3: if L � L : ±0.1 then4: L = L5: break6: else7: H1 = H.SubArray(η, length(H)), H2 = H.SubArray(1, ζ)8: Repetitive Section A:FindLocalMinimumH1 || Repetitive Section

A:FindLocalMinimumH2

9: function Repetitive Section A: FindLocalMinimum(H)10: for i = 2, length(H) do11: if (H[i] ≤ H[i− 1])&&(H[i] ≥ H[i+ 1]) then12: H[V al, J ].add(H[i], i)13: break

14: ˆH[V al, j] = Sort(H, ASC)15: for i =← H.getJIndex(1),−1 : 1 do � search start index16: S = i17: if (H[i] > H.getV alue(2)) then18: break

19: for i =← H.getJIndex(1),+1 : H.getJIndex(2) do � search end index20: E = i21: if (H[i] > H.getV alue(2)) then22: break

23: H ← H[S,E], ζ ← S, η ← E24: if length(H) > 6 then � Narrow down the local minimum25: M ← S+E

2, ζ ←M − 3, η ←M + 3, H ← H[M − 3,M + 3]

26: break27: return H

denoted as S, E, M respectively. If the above condition is not satisfied in current

local minimum, the next local minimum H will be considered.


Sample time

Sam

ple

Ent

ropy

( A II )

(A I )

(A III )

Gravtity compensated linear acceleration around X axis

Gravtity compensated linear acceleration around Z axisGravtity compensated linear acceleration around Y axis

0 50 100 150 200-0.5

0

0.5

1

0 5 10 15 200.02

0.06

0.1

0.14

0.18

0 50 100 150 2000

0.51

1.52

2.53

0 50 150 250 350-4

-2

0

2

4

6

0 5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

0 50 150 250 3500

4

8

12

16

Simulated linear acceleration around X axisSimulated linear acceleration around Y axisSimulated linear acceleration around Z axis

0 200 400 600 800 1000 1200-3-2-101234

0 10 20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

0 200 400 600 800 1000 12000

4

8

12

16

0 100 200 300 400 500-3-2-1012345

0 10 20 30 40 5000.10.20.30.40.50.60.7

0 100 200 300 400 5000

20

40

60

80

100

120

( B II )

(B I )

(B III )

( C II )

(C I )

(C III )

( D II )

(D I )

(D III )

Sam

ple

Entro

py A

ccel

erat

ion

(ms

)-2

Cur

vatu

re (m

)-1

(A ) Hip to Ankle Limb Segment (B ) Hip to Knee Limb Segment

(C ) Shoulder to Wrist Limb Segment (D ) Shoulder to Elbow Limb Segment

Sample time

Sample time Sample time

Kin

emat

ic A

ccel

erat

ion

(ms

)-2

Kin

emat

icC

urva

ture

(m )-1

Figure 3.8: Experimentally Determined LNT


In figure 3.8, sub figures (A) to (D) depicts the determined LNT results for

limb segments: hip to ankle, hip to knee, shoulder to wrist and shoulder to elbow

respectively. For each limb segment, there are three subfigures (I to III) showing the

sample entropy, kinematic acceleration and trajectory curvature respectively. In II

plots, the simulated linear accelerations without the presence of noise are shown

as a dotted line. According to the protocol, the lower limbs were lifted around

34◦- 40◦ degrees within 20-30 seconds and the upper limbs were moved around

80◦- 100◦ degrees within 60-80 seconds. The least entropy thresholds (ζ and η)

were determined by applying the algorithm 1. The examples of the least entropy

thresholds for various body segments are shown in figure 3.8. In this approach, the

segment with the least entropies for hip to ankle, hip to knee, shoulder to wrist and

shoulder to elbow are 9 to 12, 14 to 16, 17 to 21 and 45 to 60 respectively.

The reasoning behind considering trajectory curvature to determine the sample

entropy, but not linear acceleration or linear velocity, is that the curvature is inde-

pendent from linear acceleration and linear velocity, even though the curvature can

be calculated using them.

3.3.4 Real-data experiment and result

Real-data experiment setup

Experimental evidence validated the optimized algorithm using LNT, which con-

sisted eight healthy subjects (six males and two females) without any history of

orthopaedic or intramuscular impairments. These subjects participated in the ex-

periment after gaining ethics clearance from Deakin University. BioKin [170] wire-

less inertial sensors were used in the experiment to collect data. According to the

experimental protocol, two sensors were attached to two distinct positions in the up-

per and lower limbs (refer to figure 3.9). Subsequently, the corresponding distance

from rotation joint to the sensors were manually measured using an anthropometer.


InertialSensors

(a) Armdown

InertialSensors

(b) Lifting arm

InertialSensors

(c) Legdown

InertialSensors

(d) Lifting leg

Figure 3.9: Experimental setup. (a) and (b) - Lifting the arm: inertial sensors wereattached close to elbow and wrist on the left arm, (c) and (d) - Lifting the leg:inertial sensors were attached close to knee and ankle on the right leg

As for the limb movement, each subject was asked to perform limb extension

exercises as indicated in figure 3.9. They were asked to stretch the upper limb as

much as they can and then slowly move in the sagittal plane to their front as figure

3.9(b) from the initial static position (refer to figure 3.9(a)). Then, the subject

was asked to slowly lift the lower limb wearing two sensors from the initial position

depicted in figure 3.9(c) to their front in the sagittal plane shown as figure 3.9(d).

Real-data experiment result

Four limb sections: shoulder to elbow, shoulder to wrist, hip to knee and hip to

ankle were considered for validating the proposed estimator. These four segments

are refered as target limbs in the remaining discussion. The corresponding time

duration for least entropy matching for target limb was determined. The limb

lengths were estimated with the measurements bounded by the thresholds (δ and

ε) determined using LNT technique. The estimated lengths of the target limbs

were then compared to the corresponding measured limb lengths. As evident from

figure 3.10, a higher degree of correlation can be observed between the measured

and the calculated limb lengths. The information in figure 3.10, can be represented


1 2 3 4 5 6 7 80

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

SubjectsLe

ngth

of t

he L

imb

Elem

ent (

m)

(A) Shoulder Joint to Elbow Joint

1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

Subjects

Leng

th o

f the

Lim

b El

emen

t (m

)

(B) Shoulder Joint to Wrist Joint

1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

Subjects

Leng

th o

f the

Lim

b El

emen

t (m

)

(C) H Joint to Knee Joint

1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Leng

th o

f the

Lim

b El

emen

t (m

)

Subjects(D) H p Joint to Ankle Joint

Measured Length Calculated Length

Figure 3.10: Comparison between measured length and calculated length for thetargeted limbs (A) to (D): (A) - Shoulder joint to elbow , (B) - Shoulder joint towrist, (C) - Hip joint to knee, (D) - Hip joint to ankle

Table 3.3: RMSEs, error percentages with respect to the actual lengths and meanlength of measure and estimated target limb elements

Limb Element RMSE Error Percentage Mean of measured limb length Mean of estimated limb length

Shoulder to Elbow 0.061 27 % 0.2644 m 0.2991 mShoulder to Wrist 0.048 9.96% 0.4963 m 0.4806 m

Hip to Knee 0.058 14.4% 0.4369 m 0.4743 mHip to Ankle 0.067 8.6% 0.7888 m 0.8316 m

in terms of limb lengths as shown in table 3.3. In this analysis, two types of errors

were calculated for each target limb to illustrate the performance of the proposed

estimator. Firstly, RMSE between the estimated and actual length of a target

limb were calculated. Secondly, in order to compensate for the varying lengths of

the target limbs impacting the error, normalised error percentage is calculated as

follows.

P =

√∑Nn=1(

Ln−Ln

Ln)2

N× 100% (3.3.5)

Considering table 3.3, it is noticeable that the automated approach can achieve

very close result to the manual method, especially for the limb with longer lengths,


such as shoulder to wrist and hip to ankle.

1 2 3 40.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Limb elements

Mea

n Le

ngth

(m

)

Calculated lengthMeasured length

Figure 3.11: The mean value between measured length and calculated length: xaxis indicates the target limbs such as 1 - Shoulder to wrist, 2 - Shoulder to elbow,3 - Hip to ankle and 4 - Hip to knee

From table 3.3, shoulder to wrist was the most accurately estimated with RMSE

of 0.048 m and least percentage error could be observed in hip to knee target limb.

However, shoulder to elbow limb has the highest average percentage error (27%),

almost doubled compared to hip to knee, although the percentage error for the other

two limb segments were below 10%. This is mainly due to comparatively shorter

limb lengths considered. For an example, the average measured length of shoulder

to elbow is 0.2644 m and the estimated length is 0.2991 m. Though the absolute

error is only 0.0327 m, the percentage error reaches 23%. In comparison, though

the absolute error for hip to ankle is 0.0428 m, because the limb length is 0.7888

m, the percentage error is only 5.4%.

Considering RMSEs for each target limbs, the proposed approach with LNT

gives significantly accurate result with a low RMSE (approximately 0.06 m). How-

ever, a lesser percentage error (less than 15%) could be obtained for the longer limb

component such as hip to knee, hip to ankle and shoulder to wrist. Furthermore, the

mean length and standard deviation of each target limb segments were calculated

for the second analysis as shown in figure 3.10. The box plot shown in figure 3.11


compares the average measured limb length to the estimated one of all subjects.

According to the statistical distribution shown in figure 3.11, the distributions of

measured and estimated limb lengths are similar for each target limb. On the other

hand, the estimated and measured values are quite close for the mean limb length.

According to figure 3.11 and table 3.3, lesser deviation can be observed for the limb

from shoulder to wrist. The difference in mean values of measured and estimated

shoulder to wrist length is 1.57 cm. The differences in the mean values of measured

and estimated limb lengths for shoulder to elbow, hip to knee and hip to ankle

are 3.47 cm, 3.74 cm and 4.28 cm respectively. From these results, the automated

approach could achieve very close result to the manual method, especially for the

limb with longer lengths, such as shoulder to wrist and hip to ankle.

3.3.5 Conclusion

A novel method was introduced to estimate the limb lengths using measurements

from inertial sensors. Furthermore, a curvature based approach is used in the

algorithm which is not presented in the open literature. In addition, the Least

Noise Threshold was applied to noisy measurements for systematically determining

the curvature providing an optimised result. The proposed algorithm along with

LNT method was evaluated by comparing the estimated limb length with that

measured manually. The low RMSEs and error percentages confirmed the excellent

performance of the approach. As a result, the proposed algorithm has the potential

to automate the measuring process of individuals’ limb lengths, which is important

in assessing limb length discrepancy.

3.4 Summary

In this chapter, a novel calibration mechanism was discussed and subsequently, the

sample entropy based limb length estimator was introduced. Importantly, these

two methods were deduced by applying curvature and geometrical relationships


of circular movements. Further, the inaccuracy due to misalignment of sensors

has been corrected which results improved accuracy for quantitative analyses using

inertial sensors.

Chapter 4

Qualitative Analysis Of HumanKinematics With Inertial Sensors

4.1 Introduction

In literature, computational methodologies for analysing human kinematics are ba-

sically divided into two categories [171] as follows.

1. Algorithms which partition the human kinematics through thresholds based

on experimental observations of sensor data [172, 173, 174]

2. Machine-learning schemes which extract patterns from large sensor datasets

based on certain assumptions [175, 176]

In the first category, several sensors are fused to derive deterministic information

(threshold) about human kinematics such as movement angle and limb length. In

the second category, the machine learning and statistical tests are applied to obtain

a qualitative information under a certain confidence level. Both of these analyses

are essential particularly for evaluating patients with certain neurological conditions

such as stroke and Parkinson’s disease. However, qualitative analysis is not univer-

sal as quantitative analysis, because the analysis usually depends on a number of

impact factors. As an example, the severity of a Parkinson’s patient is subjectively

determined based on several physical features such as slow movements, less flexi-

bility and rigidness. In such cases, the qualitative analyses are usually conducted

102

Chapter 4.Qualitative Analysis Of Human Kinematics With Inertialsensors 103

for determining severity of the disease. The observations are analysed applying

statistical and machine learning techniques to evaluate how well the given activities

are performed.

In this chapter, two major objectives were attempted to achieve using qualitative

analyses about human movements. the first objective is to investigate the feasibility

of statistically distinguishing the Parkinson’s patients and healthy subjects based on

sensor observations while conducting trunk movements. The main focus is analysing

three physical features of Parkinson’s patients such as slow movements, rigidness

and less flexibility of trunk based on thoracic movement and trunk rotation with

leg displacements. In this study, the thoracic rotation is referred the spine rotation

without leg displacements.

As the second objective, the relationship between energy consumption and gait

activities is investigated. The main challenge with this analysis is that the metabolic

relationship with energy and exercise level has number of influencing factors, such

as age, height, weight, fitness of the body and the nature of the exercise. Hence,

the derivation of the relationship between energy and a particular influencing fac-

tor is difficult. Furthermore, medical standard equipment for determining energy

consumption such as V O2 machines, evaluate overall energy consumption of the

complete human body rather than particular body movements such as gaits. Hence,

identifying the metabolic equation of energy consumption for gait exercises is chal-

lenging with this equipment. Additionally, they are not easy to use nor cost effective

and only suitable for laboratory environments [177].

The rest of this chapter is organized as follows: section 4.2.1 discusses the analy-

sis for trunk movements using inertial sensors. In this section, statistical techniques

have been applied to distinguish the Parkinson’s patient and healthy subjects based

on the underlined physical features. Section 4.3 introduces ambulatory energy ex-

penditure evaluation for several level of treadmill exercises from walking to running

with the aid of inertial sensors. Section 4.4 concludes the chapter.


4.2 Investigation of the thoracic rotational pat-

terns of Parkinson’s patients using inertial

sensors

Parkinson’s disease (PD) is a chronic, progressive and degenerative disorder of the

central nervous system [178] as discussed in section 1.4. A high percentage (52-62%)

of people with Parkinson’s disease have difficulty when turning [179], which is often

associated with falling and freezing of gait [180, 181]. This indicates a significant

negative effect on their quality of life [181]. Hence, it is important to analyse key

elements such as maximum span of turning, duration for turning and turning quality

in order to evaluate a Parkinson’s patients. In addition, if these assessments can be

carried out at home, this would be an affordable and cost saving solution than the

current practice which requires patients to attend clinics.

Some of the key clinical features of Parkinson’s patients are described as bradyki-

nesia, rigidity, tremor and postural instability. As a result, a patient’s movement

may slightly differ compared to a healthy person, particularly during standing, lo-

comotion and trunk movements [182]. Parkinsonian gait has various typical charac-

teristics such as a low walking velocity, small stride length, propulsion, retropulsion,

shuffling steps, reduced or absent arm swing and rigidity in trunk movements [182].

The Parkinson’s patients usually show difficulties while performing multi axial body

rotations. One such critical movement is trunk rotation, which changes the trunk

from the sagittal to transverse axis during locomotion [182].

According to Richard et al. 1999 [183], systematic manipulation of velocity

can be used to identify the coordination deficits and rigidity in trunk movement of

Parkinsons patients. This is believed to be a sensitive measure for early diagnosis

of Parkinson’s patients in pharmacological therapy [183]. According to studies of

Van Emmerik et al. in 1993, Wagenaar et al. in 1994 and Pei-Yi Chou et al.

in 2013, difficulties in trunk movement of Parkinson’s patients has been shown in

gait initiation and switching gaits. Knuttson at al. 1972, and Murray et al. 1978


recognised two major characteristics of a Parkinson’s patient such as lower velocity

during movement and rigidity of the trunk.

MEMS sensors are more accurate and less noisy for movements having low ac-

celerations and velocity. Usually Parkinson’s patients have slow movements. Hence

these sensors can be used to capture and monitor kinematics of Parkinson’s patients

especially to identify trunk moving patterns compared to healthy people. However,

tremor is a natural property of Parkinson disease which cannot be avoided or reset.

G Buzsaki et al. [184] has suggested that the tremor of Parkinson’s disease has

a systematic rhythm and this systematic rhythm can be removed. Hence, this is

unlike to have any substantial impact in the analysis on their natural movement

patterns.

4.2.1 Evaluation of physical features of Parkinson’s patients

In this section, two movement disorders of Parkinson’s patients are investigated.

4.2.2 Experiement setup

In the clinical study, a specifically designed jacket as shown in figure 4.1 is used.

Initially, the jacket was designed with 13 pockets to accommodate BioKin inertial

sensors. A stretchable fabric was used to ensure the tightness between the fabric

and body surface.

Two following exercises were conducted while wearing the jacket.

1. Turning the body with leg displacements (Refer figure 4.2 (a) and (c))

2. The trunk rotation (Refer figure 4.2 (a) and (b))

In the turning body exercise with leg displacements, sensor 5 and 9 were used

to analyse kinematics of the spine. Firstly, three healthy subjects were asked to

turn their body by 90 degrees, as shown in figures 4.2(a) and 4.2(c) without foot

displacements and secondly, to turn their body by 90 degrees having steps imitating

the Parkinson’s patient as figures 4.2(a) and 4.2(b).


Sensor 1 Sensor 2

Sensor 3 Sensor 4

Sensor 5

Sensor 6 Sensor 7

Sensor 8

Sensor 9

Sensor 10

Sensor 11

Sensor 12

Sensor 13

Figure 4.1: Sensor suite having 13 sensor positions

(a) (b) (c)

Figure 4.2: Exercise 1: (a) and (b) are the initial posture and end posture of thoracicrotation, (a) and (c) are the initial posture and end posture of body rotation withleg displacements

The second exercise is designed to evaluate the trunk movements while perform-

ing a pointing test as shown in figure 4.3. Four sensors (Sensor 1, Sensor 2, Sensor 3

and Sensor 4 of the jacket) were used to make it more convenient to patients (refer

to figure 4.1). This analysis was conducted with eight healthy controls and sev-

enteen Parkinson’s patients. All the subjects were between 40-60 years old. Each

subject was positioned in the centre of a room and the two markers were attached

on both sides (left and right) of the wall. The subject was then asked to point to


(a) Start (b) End

Figure 4.3: Pointing exercise

each marker alternatively with thoracic rotation but without leg displacement.

4.2.3 Results and discussion

Distinguishing upper body kinematics: Thoracic rotation with and with-out leg displacements

The gyroscope rates were analysed for two scenarios: 1. Thoracic rotation (Refer

figure 4.4 ) and 2. Body rotation with leg displacements (Refer figure 4.5).

Figure 4.4: Angular rates for thoracic rotation

From figures 4.4 and 4.5, The moving pattern was clearly observed that can be

used to differentiate the thoracic rotation and the body rotation having leg dis-

placements. Fast Fourier Transform (FFT) technique was applied to both datasets


Figure 4.5: Angular rates for rotation with steps

to distinguish thoracic rotation from the body rotation with leg displacements. Fre-

quency spectrums were obtained from the FFT analyses of angular rates observed

in two scenarios. Several peaks could be observed in the frequency spectrum of the

body rotation with leg displacements as shown in figure 4.6(b). For the thoracic

rotation without leg displacements, these peaks were not evident in the frequency

spectrum, as shown in figure 4.6(a).

(a) Thoracic rotation (b) Turning body havingleg displacements

Figure 4.6: Frequency spectrum after applying FFT technique

Additionally, the gradient based statistical method was applied to differentiate

the kinematic artefacts of the two exercise scenarios. These two activities could

be distinguished by calculating the gradient of the movement angle at each sample


time. The gradient derived from the integrated angle of the thoracic movement,

was negative at each sample time, as shown in figure 4.7(a). Time varying sign of

gradient for the rotation with leg displacement could be observed as shown in figure

4.7(b).

(a) Thoracic rotation (b) Turning body having leg displace-ments

Figure 4.7: Gradient analyses of angular rates

According to the experimental results of the FFT technique and gradient based

method, the thoracic movement was successfully distinguished from the turning

the body with leg movements. Additionally, according to the frequency spectrums

generated by FFT, these two activities belong to different frequency domains.

Upper trunk movement without leg displacements

Trunk movements were further investigated based on the pointing exercise, as shown

in figure 4.3. The angular rates acquired from sensor 2 and sensor 4 (refer to figure

4.1) were processed in following forms.

1. Average maximum magnitude in angular rates acquired from sensor 2 and

sensor 4

2. Relative difference of magnitude in angular rates between sensors worn on

upper and lower body of trunk on the same side

3. Average maximum span (movement angle) of the hip


4. Relative difference of maximum span (movement angle) between sensors worn

on upper and lower body of trunk on the same side

A similar pattern in the above forms of data series could be seen in both healthy

subjects and Parkinson’s patients as shown in figure 4.8.

0 5 10 15 20 25 30

0

50

100

Time/(s)

w/(d

eg/s

)0 5 10 15 20 25 30

0

50

100

Time/(s)w/

(deg

/s)

Parkinson PatientHealthy Subject

0 5 10 15 20 25 30

0

10

20

30

50

/(deg

/s)

Time/(s)

w

0 5 10 15 20 25 30

0

20

Time/(s)

q/(de

g)

0 5 10 15 20 25 30

01020

Time/(s)

q/(de

g)

0 5 10 15

0

50

100

(A) Angular rates in Sensor 2Time/(s)

w/(d

eg/s

)

0 5 10 15

0

50

100

Time/(s)

w/(d

eg/s

)

0 5 10 15

0

20

100

/(deg

/s)

w

Time/(s)

0 5 10 15

020

(D) Movement Angle in Sensor 2Time/(s)

q/(de

g)

0 5 10 15

0

50

Time/(s)

q/(de

g)

(F) Angular rates in Sensor 2

(G) Movement Angle in Sensor 2

Figure 4.8: Comparison of healthy subjects and Parkinson’s patients

In order to distinguish the healthy subject and Parkinson’s patients, these data

series measured from gyroscope were further investigated based on two physical


features. The first physical feature under the consideration was execution speed

of movements. For this, the average cycle time and average magnitude in angular

rates for each pointing cycle were calculated. Figure 4.9 shows the statistical result

of analysing average relative magnitude. The averaged relative magnitude values

for eight controls and seventeen Parkinson’s patients are shown as in figure 4.9(a).

In general, the higher mean value is for healthy subjects than the patients, but the

variance for heathy subjects and patients are very similar according to table 4.1.

Figure 4.9(b) shows the variance of each subject as a box plot.

Table 4.1: The result of averaged relative magnitude in angular rates

Mean Standard Deviation

Healthy Subjects 67.08 degs−1 20.71 degs−1

Parkinson’s Patients 45.91 degs−1 20.8 degs−1

10

20

30

40

50

60

70

80

90

100

51 432 106 987 11 141312 15 16 191817 20 21 242322 25

Normal Patient

Rel

ativ

e A

ngul

ar ra

tes

(deg

/s)

Varia

nce

of H

ealth

y Su

bjec

t

Varia

nce

of P

atie

nts

(a) Magnitude in angular rates

0

20

40

60

80

100

120

Rel

ativ

e A

ngul

ar ra

tes

(deg

/s)

51 432 106 987 11 141312 1516 191817 20 21 242322 25

Normal Patient

Varia

nce

of H

ealth

y Su

bjec

t

Varia

nce

of P

atie

nts

(b) Variance in angular rates

Figure 4.9: Magnitude in relative movement based on angular rates of a cycle

Figure 4.10 shows the results of analysing cycle time in the pointing exercise.

The cycle time is referred to as the time for pointing from one marker to another and

pointing back to previous marker. According to figure 4.10(a), the mean value of

cycle time for Parkinson’s patients is higher than healthy subjects. This means that

healthy subjects finish the pointing cycle in a shorter time duration than patients.

However, the variance of patients is approximately three times higher than healthy

subjects according to table 4.2. Figure 4.10(b) shows the variance of each subject

in a box plot.


Table 4.2: The result of averaged cycle time of pointing cycle

Mean Standard Deviation

Healthy Subjects 2.67 seconds 0.38 secondsParkinson’s Patients 3.41 seconds 1.38 seconds

1.5

2

3

4

5

6

Cyc

le T

ime

(s)

51 432 106 987 11 141312 15 16 191817 20 21 242322 25

Normal Patient

Var

ianc

e of

Hea

lthy

Subj

ect

Varia

nce

of P

atie

nts

(a) Cycle time

1

2

3

4

5

6

7

Cyc

le T

ime

(s)

51 432 106 987 11 141312 1516 191817 20 21 242322 25

Normal Patient

Varia

nce

of H

ealth

y Su

bjec

t

Varia

nce

of P

atie

nts

(b) Variance in cycle time

Figure 4.10: Cycle time of a pointing cycle

The second physical feature is the relative maximum span between the upper

trunk and the lower trunk. The eight healthy subjects and twenty patients par-

ticipated in this analysis. The integrated movement angles for each pointing cycle

were calculated using gyroscope readings acquired from two sensors worn on upper

trunk and lower trunk of left side of the trunk. Then, the difference in movement

angles between upper trunk and lower trunk is the relative maximum span for the

cycle. To avoid the impact of gyroscope drift, the averaged relative maximum span

for all cycles is considered. Figure 4.11 shows the averaged relative maximum span

for all subjects.

Table 4.3: The result of averaged relative maximum span

Healthy subject Parkinson’s Patient

Average maximum span of upper trunk 49.50 degrees 41 degreesAverage maximum span of lower trunk 48 seconds 27.88 seconds

Relative average maximum span 28.66 degrees 16.67 degreesStandard deviation of relative span 17.89 degrees 18.61 degrees

According to the experimental results as shown in table 4.3, the healthy subject

has a larger span for both upper body and lower body compared to Parkinson’s


Rel

ativ

e A

ngle

(deg

)

5432 6 987 242322 25 2726 28

Normal Patient

Varia

nce

of H

ealth

y Su

bjec

t

Varia

nce

of P

atie

nts

Figure 4.11: Comparison of relative orientation between upper trunk and lowertrunk

patients. Similarly, the relative average maximum span between upper body and

lower body is relatively higher for a healthy subject than a Parkinson’s patient. The

relative span for a healthy subject is approximately twice compared to a Parkinson’s

patient. This implies that the Parkinson’s patient has less flexibility in the trunk

compared to a healthy person. The standard deviation in both healthy subjects’

and patients’ relative span are approximately similar.

According to above analyses, the author can conclude that Parkinson’s patient

has less flexibility to move both upper trunk and lower trunk independently because

they have less relative span than a healthy subject. Further, Parkinson’s patients

move slower than healthy subjects since the patients’ cycle time is approximately

21% less than a healthy person’s cycle time.

Analysis combining multiple features

In this section, each patient is investigated based on two of above identified physical

features in the pointing exercise. The combinations of physical features are as

follows.

1. Cycle time and relative averaged maximum span of a cycle

2. Cycle time and relative average maximum magnitude in angular rates of a

cycle


3. Cycle time and averaged movement angle of hip in a cycle

4. Cycle time and average maximum magnitude in angular rates of hip sensor

Initially, seventeen Parkinson’s patients and eight healthy subjects were consid-

ered. Each combination was plotted as a scatter diagram as figure 4.12. Here, the

y axis always denotes cycle time.

0 20 40 60 80 1000

1

2

3

4

5

6

7

Relative Anglular rate (deg/s)

Cyc

le T

ime

(s)

Averaged Maximum Span in Hip (deg)

Cyc

le T

ime

(s)

Average Magnitude in angular rates

Cyc

le T

ime

(s)

worn on hip (deg/s)(D)(C)

(B)

0 10 20 30 40 50 60 70 80 901.52

2.53

3.54

4.55

5.56

Relative Angle (deg)

Cyc

le T

ime

(s)

PatientNormal Subject


40 60 80 100 120 140 160 180 200 2201. 5

22. 5

33. 54

4. 55

5. 56

6. 5


0 20 40 60 80 100 1201. 52

2. 53

3. 54

4. 55

5. 56

6. 5


Figure 4.12: Scatter diagrams: (A)- Cycle time and relative averaged maximumspan of a cycle, (B) - Cycle time and relative average maximum magnitude inangular rates of a cycle, (C) - Cycle time and averaged movement angle of hip in acycle and (D) - Cycle time and average maximum magnitude in angular rates of acycle

Further, the mean and standard deviation for all Parkinson’s patients and

healthy subjects were calculated separately. Two ellipses were drawn for Parkin-

son’s patients and healthy subjects in each diagrams in figure 4.12. The radius of


ellipse was the standard deviation in corresponding axes. The centre of the ellipse

is the coordinations of the mean value of Parkinson’s patients or healthy subjects.

With this representation as shown in figure 4.13, the patients and healthy subjects

could be classified.

CycleTime(secon

ds)

Relative Angle (deg)CycleTime(secon

ds)

Relative Magnitude in Angular rates (deg/s)

CycleTime(secon

ds)

Average Maximum Span in Hip (deg)

(A) (B)

(C)

CycleTime(secon

ds)

Average MaximumMagnitude in Angular Rates worn on Hip (deg/s)(D)

Figure 4.13: Classification between healthy subjects and patients: (A)- Cycle timeand relative averaged maximum span of a cycle, (B) - Cycle time and relative aver-age maximum magnitude in angular rates of a cycle, (C) - Cycle time and averagedmovement angle of hip in a cycle and (D) - Cycle time and average maximummagnitude in angular rates of a cycle

According to the result as in figures 4.13, figure 4.13 (B) has classified patients

(red region) and healthy subjects (green region) with least overlapping of two re-

gions. The second least overlapped representation is figure 4.13 (D). This implies

that angular rates without processing gives a more accurate classification than other

process factors such as integrated angle.


Figures (C) and (D) of 4.13 are processed based on angular rates measured from

sensors worn on the hip. Here, the possibility to reduce sensor usage is investigated

in these tests in order to make it more convenient for the patients. According to

results, figure (D) has less overlapped regions than figure (A), which means that

the angular rates from a sensor worn on hip is represented in two groups than the

processed relative angle using two sensors.

4.2.4 Summary

The qualitative analyses can be used evidently to distinguish the Parkinson’s pa-

tients from healthy subjects based on upper body kinematics. In this study, three

important physical features of Parkinson’s patient such as rigidness, reduced flex-

ibility and slower movements could be qualitatively distinguished using gyroscope

readings from the IMU that was attached on the back of the trunk.

However, one of challenges associated with these analyses is the larger variance

which makes it difficult to separate the two groups as Parkinson’s disease affected

and non-affected. The reason behind this difficulty is the level of Parkinson’s dis-

ease severity of each patients and healthy subjects with back pains (not due to

Parkinson’s disease). Some of patients are close to healthy subject in functionality

aspects. Hence, further investigations should be conducted to obtain more accurate

classification of patients from healthy subjects on their physical features.

Subjects were evaluated based on several mutual physical features to classify

the Parkinson’s patients and healthy subjects. Under these analyses, this approach

could be statistically distinguished that Parkinson’s patients and healthy subjects

based on cycle time and relative average maximum magnitude in angular rates of

a cycle.


4.3 Ambulatory energy expenditure evaluation for

gait exercises

Walking and running are identified as two crucial exercises in human locomotion,

hence numerous studies were conducted under these two categories typically using

a treadmill, such as Andriacchi et al. in 1977, Larsson et al. in 1980, Wagenaar

and Beek in 1992 and Emmerik and Wagenaar in 1996. Parallel to treadmill based

research, a number of studies were conducted to suggest transition in the frequency

relations between the arms and the legs in the bipedal walking mode, such as Craik

et al. in 1976, Wagenaar and Van Emmerik in 1994. A number of studies also

used inertial sensors for analysing gait patterns. Seven T. Moore et al. in 2006,

Benoit Mariani et al. in 2010, Rahimi F. in 2011 and Weijun Tao et al. in 2012

investigated gaits patterns and switching gaits using body worn sensors. Inertial

sensors have been used to obtain the main gait characteristics such as stride length

and gait cycle time [185]. In sports science, the measurement of how much energy

someone has expended through exercise is recognized as a hard problem to solve.

A common form of exercise that would involve energy estimation is walking.

This enabled an easy scenario for capturing the gyroscope data from the movement

of legs using IMU. Knowing this, the experiment performed with healthy subjects

between the ages of 20 to 45 and were on a treadmill at various speeds for some

time for each speed. The BioKin system, and an oxygen intake measurement device

were used to measure limb movement and oxygen consumption levels. Using the

data collected, a correlation was sought and a linear model derived so that energy

estimation for running or similar activities could be measured accurately using an

angular speed ratio based device in place of a bulk oxygen consumption system.

The rate of energy expenditure of a person who is moving (e.g. walking or

running) is linearly proportional to their velocity [186]. Inertial data acquisition

is prone to errors but as a first step to gaining energy expenditure information

[187], the system utilizes a single tri-axial accelerometer and is called the Move II


sensor. In the experiment, which comprised three different walk speeds on a tread

mill, the step cycle or two consecutive steps were interpreted and converted the

signal to a feature vector using weight and height as parameters to influence energy

expenditure measurement. One restriction is that it is indoor based and does not

have any GPS based sensors to measure outside movements. Steps using a sensor

placed on the chest in [188] utilized a full angular speed ratio unit that comprised of

accelerometer, gyroscope and magnetometer (although the former two were used).

The same issue was raised in [189] where a sensor using an angular speed ratio, albeit

a different model from [187], was placed on the hip. [189, 190, 191, 192, 193] found

that utilising acceleration and rotation data as well as using a V O2 breath sensor

apparatus to confirm energy measurement was accurate in some combinations but

not others. Vathsangam et al. investigated this further, using statistical analysis

to gain a better understanding of the results. Specifically, it was found that the

combination of both acceleration and gyroscope data yielded the least amount of

error.

It was evident from the paper that a different implementation of energy mea-

surement capture was presented. A new approach was looked at in [194] and [195],

where the angle of the knee was taken by using gyroscopes on two sensors on the

leg, where one would be on the knee and other positioned on the lower leg, and

the results were then used to estimate energy levels. In both papers, the aim is to

verify that using knee angle measurements is reliable, not to observe energy expen-

diture. It should be noted that all of the papers surveyed looked at indoor walking

whilst [189] also considered outdoor walking using a GPS system. Walking can be

considered a common enough activity that should be used for the purposes of gait

analysis and energy expenditure measurement and is easy to model.

In [189, 190, 191, 192, 193], the authors constantly used Bayesian Linear Re-

gression and Gaussian Process Regression throughout their experiments as well as

coupling both gyroscopic and acceleration measurements. In [189], the authors used


Hierarchical Linear Models. This was used to supplement the energy expenditure

estimation model by looking at the variations from user to user. It includes the

user’s height, weight, and age as parameters for the model as inputs. From this, a

gap in the literature covered was found, and taking the experiment from [194] and

[195] and instead of using the knees - it was found that using the angular velocity

of the legs could be used to measure energy expenditure.

4.3.1 Energy expenditure in activities

The gold standard in evaluating the energy expenditure in a human body is by

means of a metabolic measurements system [196]. A metabolic measurement system

measures the consumption of Oxygen through a breathing mask attachment, as

illustrated in figure 4.14. Energy expenditure from the rate of oxygen consumption

data is calculated using(4.3.1) [197]:

Em =vo × 20900

60(4.3.1)

where vo represents the oxygen consumption during the activity in l/min and en-

ergy rate that is being measured Em is in watts. The energy calculation from IMU

does not have a direct relationship with energy expenditure via a rate of change of

limb angles. The major disadvantage in such a system is the inability to measure

energy or activity level while the subject is at rest or performing non-mobile exer-

cises whereas the metabolic measurement systems can measure energy expenditure

during any activity. Therefore, this study is focused on measuring energy expendi-

ture in walking and running based activities where the subject’s activity level has

a close relationship with the movement intensities of body segments.

In this study, angular rates of the lower limb has been used to estimate the

energy expenditure during the activity as follows:

Er =k

T

∑(‖ω‖2) . (4.3.2)

Here T is the duration of the activity in seconds, energy rate of the activity

level Er is in watts, ω = [ ωx ωy ωz ] represents the raw gyroscope measurements


around the respective local coordinate axis from the ankle mounted sensor (see

figure 4.14(b)) and k is a scalar function to transform the angular rates into the

energy. This equation assumes a linear relationship between mean of ‖ω‖2 and the

actual energy expenditure, which will be confirmed later.

Another method to evaluate energy in walking or running based exercises is

based on the assumption that the energy consumption is linearly proportionl to

the speed of walking or running [186]. The following empirical formula has been

employed in calculating energy using speed of motion,

Es =(vL ×m)

1000, (4.3.3)

where vL represents the linear velocity of motion (i.e. the treadmill speed),

energy rate of the activity level Es is in watts and m represents the weight of the

subject in kilograms. This provides the Es in the rate of oxygen consumption which

can be used with equation (4.3.1) to calculate the actual energy consumption inW .

4.3.2 Experiment setup

The experiment was conducted in a laboratory environment with a speed regulated

treadmill for precise control of the activity intensity. The experiment was performed

with six subjects (five males and one female) without any history of orthopaedic

or intramuscular impairments. All subjects were non athletes and recruited from

general population within the age bracket of 20 to 45 years.

The oxygen intake measurement system was the Metamax 3B unit developed

by Cortex-Medical. Time-stamped metabolic information was stored in the device

and was later transferred to a computer for analysis.

Inertial measurements, in particular the angular speed of the limb which is of

interest to this study, were recorded using BioKin sensor attached to ankle of the

subject as shown in figure 4.14(b).

The activity level of the experiment was controlled by means of the speed of

the treadmill the subject is walking/running. Before the exercises, the subject’s


(a) Experimental setup (b) Sensor worn Leg

Figure 4.14: (a)- Experimental Setup: Metamax metabolic measurement systemwas attached to the subject while performing the treadmill based exercises. (b) -Capturing inertial data: BioKin-WMS inertial measurement sensor was attachedto the subject’s ankle while performing the treadmill based exercises.

metabolic rate was measured for the resting state. This parameter was used to

calibrate the Metamax system as well as to obtain a baseline measurement for the

subject. However, in the inertial measurement system, the resting state does not

provide any valuable information, hence this was normalized by means of normal-

izing against the first activity level, as explained in the next section.

Each subject was asked to perform walking/running activities for five activity

levels at treadmill speeds 3, 5, 7, 9 and 11km/h with each activity lasting for 2 min-

utes. The length of time is comparatively short compared to [191] but the duration

is long enough to get valid sets of data for each speed section (see [197]). The

V O2 measurements were taken in the final minute of recording. In addition to the

logging of gyroscope, accelerometer and rate of oxygen consumption measurements,

height and weight were measured in order to use older models/equations to roughly

estimate their energy expenditure.

In this study, the author aimed at develop a relationship between the energy

expenditure from a gold standard metabolic measurement system and the proposed

energy expenditure system introduced in equation (4.3.2). The system uses angular

rate measurements recorded by an IMU sensor worn on the ankle. The subject

was investigated based variation of the energy expenditure relationships estimated


0 1 2 3 4 50

1

2

3

4

5

Limb angular rate based energy ratio (ψr)M

etab

olic

rate

bas

ed e

nerg

y ra

tio (ψ

m)

Mean data for five subjectsLeast Square LineEvaluation data for the sixth subject

Figure 4.15: Variation of treadmill speed derived, normalized energy expenditure(ψr) with activity levels for all test subjects

with different methods. An additional energy expenditure estimation method was

employed using speed of walking or running as introduced in equation (4.3.3). Note

that during the treadmill based exercises, some subjects could not perform the full

set of activity levels due to physical fitness level of the individual.

4.3.3 Relationship of gyro based proposed energy expendi-ture with gold standard metabolic rate

In this section, the proposed energy expenditure technique was compared as (4.3.2)

with the gold standard oxygen consumption based system. In order to maintain gen-

erality and comparability between two energy expenditure calculation techniques,

the normalized energy expenditure compared to the first level of activities, i.e.

3km/h walking was used in this study. The normalized energy at ith activity level

is calculated as,

ψi =Ei

E1

. (4.3.4)

Here, E1 is the energy for the base activity level of 3km/h walk and Ei is the

estimated energy at ith activity level. The mean energy across five subjects for

each activity level was calculated and figure 4.15 illustrates the comparison of this

approach with gold standard. A linear regression line was generated using least-

square approximation of the data points and the linear relationship was evaluated


using the sixth subject data. The evaluation data set demonstrated a mean error

of −0.0959 with a standard deviation of 0.2306. The proposed hypothesis in this

study to explain such high standard deviation is the subject specific variation of

the energy expenditure calculation from each method. In order to evaluate this

hypothesis, the data for each subject was analysed to derive a pattern, as shown in

the next section.

4.3.4 Variation of energy expenditure pattern with the sub-ject

The variations in the normalized energy-activity level relationship within each sub-

ject were investigated. The energy expenditure calculated from each method were

evaluated in section 4.3.1 and are shown in Fig. 4.16(a), 4.16(b) and 4.16(c).The

normalized energy-activity level is represented as a ratio ψi with ψr being the ratio

of limb based movements, ψm is V O2 based Energy Expenditure and ψs is running

or walking speed. The idea of using a ratio is useful as it allows us to see these

variations from an objective viewpoint and allows the observation of abnormalities

from what happens in the individual ψs, ψm and ψr readings in a unitless context.

Essentially, the walking/running speed based energy estimation ratio ψs does not

demonstrate any difference among the subjects due to the fact that ψs only de-

pends on the speed and does not take any physical parameter of the subject into

the equation. However, metabolic rate and lower-limb angular rate based energy

estimation techniques demonstrates a clear variation between the subjects. This

variation could be from the varying weight and height of each subject, with Body

Mass Index (BMI) seemingly affecting the V O2 Max of those who run/walk as ob-

served in [198]. Therefore, further study will need to be performed with more test

subjects in order to confirm if these two variables can be attributed to be an influ-

ence on the final results and then possibly define the relationship between energy

estimation and a person’s BMI.

It should be noted that subject 4 and 5 did not complete the run, with subject


(a) (b)

(c)

Figure 4.16: (a)- Variation of rate gyro derived, normalized energy expenditure (ψr)with activity levels for all test subjects, (b)- Variation of metabolic measurementbased, normalized energy expenditure (ψm) with activity levels for all test subjects,(c)- Variation of treadmill speed derived, normalized energy expenditure (ψs) withactivity levels for all test subjects

4’s V O2 result was not recorded in the final activity level. Subject 5 found the

ambulation at the intensity level was too uncomfortable and had to discontinue

that part of the experiment.

4.3.5 Summary

In this study, the feasibility of employing a single inertial sensor based energy

expenditure estimation technique were investigated for treadmill based exercises.


Although the author have limited the study to treadmill based exercises, to main-

tain a controlled experimental setup the same technique could be used in out-door

walking and running based exercises. The proposed energy estimation method was

evaluated with the industry standard Metamax metabolic rate measurement sys-

tem, which is the gold standard form of measurement in human energy expenditure.

4.4 Conclusion

The investigation of human movements are usually conducted as two types of anal-

yses: deterministic and qualitative analyses. The use of inertial sensors for deter-

ministic analyses was investigated in chapter 2 and chapter 3. In this chapter, the

main focus was to investigate the possibility to use inertial sensors in qualitative

analyses which are very important for qualitative evaluations of human movements.

The trunk movements and gait analyses were investigated under this form of ap-

proaches. The feasibility of separating Parkinson’s patients and healthy patients

were investigated based on three physical features such as rigidness, flexibility and

execution speed of movements based on trunk movements using gyroscope readings.

Further, the relationship between energy expenditure for ambulatory exercises was

analysed using angular rates and accelerometer readings. The author confirmed a

linear relationship with energy and activity levels in line with common understand-

ing in literature. All these analyses demonstrates that the IMU sensors can be used

to perform qualitative analyses of human movements.

Chapter 5

Mobile - Cloud Based PhysicalTele-rehabilitation System - APrototype

5.1 Introduction

The severe challenges in rehabilitation such as skyrocketing healthcare expenditure

and increasing aged population highlight the need for innovative solutions sup-

porting more accurate, affordable, flexible and personalized medical diagnosis and

treatments [199]. This implies that the unnecessary cost components should be

avoided while providing convenient and more facilities to patients. As in [199], the

critical and costly part of current healthcare systems is the frequently monitoring of

patients signs and other physiological signals, which can be mitigated with the aid

of long-term, off-site or in-home care health systems. Through in-home care [199],

it is possible to save time and money for both caregivers and patients, providing

greater convenience to patients at the same time.

Furthermore, mobile phone based, domestic medication is popular due to easy

access and higher availability. Recent advances in wireless body sensors and mobile

technologies have promoted the use of mobile-based health monitoring and alert

systems (usually referred as mHealth) [199]. However the usage of mobile phone,

in-home based medications is limited due to its inherent constraints such as less

126

Chapter 5.Mobile - Cloud Based Physical Tele-rehabilitation System -A Prototypes 127

memory, limited processing power, battery power and screen size [200]. Still, mo-

bile phones are popular for medical monitoring and recently, mobile-based medical

monitoring devices have been developed with the ability to process a wide variety

of classes of physiological signals [199, 201, 202].

This chapter attempts to propose a novel cloud based architecture of a biomed-

ical system for a wearable motion kinematic analysis system using IMU devices

which mitigates the above mentioned deficiencies of mobile devices. Furthermore,

novel multilevel data encoding scheme is proposed satisfying the limitations in mo-

bile cloud computing devices such as battery power and computational cost. An-

other advantage of this scheme is that different sensory devices can be connected

together for deriving better information. the introducing platform is usable not

only for patients to experience tele-rehabilitation services but also for therapists to

acquire essential support from analysis oriented decision support system (AODSS)

for making decisions on treatments after conducting extensive analyses. Further,

the safety issues and solutions are addressed in underlined tele-rehabilitation system

for reliable service.

5.2 Available remote human monitoring system

and architectures

Cloud and mobile technologies are widely used in various fields such as bio-medical

[199, 203] and sport activity monitoring [199, 203]. The studies in [199, 203] pre-

sented a mobile phone based system, which was enabled with features to acquire

various physiological signals from a set of ambient body sensors. The system per-

formed the regular lightweight and on-site diagnostic tasks using cloud technology

by executing heavy algorithms on diverse devices such as smart phones, laptops,

tablets, hospital servers and video conferencing tools. Importantly, their architec-

ture is fully reliant on a cloud service. It has monitored the abnormalities of patients

and capable of raising diagnostic alarms for medical staffs when necessary.


The Mobile Cloud Computing(MCC) is an emerging technology in computing.

The one advantage using MCC model in medical domain is that the data intensive

analyses from the medical applications can be executed in one system rather than

number of dedicated analysing systems [73]. The second advantage is that the

data acquired from medical systems can be stored in a private or hybrid database

servers according to privacy needs. Third advantage is that the most of cloud

services provides relational database management services (RDBMS) as their web

service, since most of developers are familiar with RDBMS. Additionally, the fast,

flexible and comprehensive analyses can be performed by extracting the appropriate

datasets from systems using pre-processed MATLAB scripts and stored the results

in different formats such as PDF and JSON.

The case study in [204] presented a biometric evaluation system on the cloud

server. A common dataset named HumanID was utilized in the system and it

allowed the user to submit the algorithm as a source code or Linux x-86 executable

in a pre-defined standard format. The main advantage of this system is that the

researcher does not need to acquire a local copy of huge dataset. In addition,

this system is more suitable for comparing and bench marking algorithms in the

experiment stage. Once the evaluation is completed, the results are available in the

form of a Receiver Operating Characteristic (ROC) curve and a Cumulative Match

Curve (CMC). In future, this system has been suggested to deploy in the Amazon

web service.

Even though the numerically intensive and power hungry operations are suitable

to execute in a cloud server, it suffers several limitations such as imbalance of loads

on the server and network traffic[199]. However, most of the cloud service providers

has given an in-built services to manage the load on the server and network traffic

through their elasticity policy. Hence, It is easy to get rid of these limitations

without externally written programs on the cloud. The smart phone only works

as an intermediary tool to process and visualize data under this model. The cloud


data model is used as a supervised training data model to diagnose diseases, based

on several pattern recognition methods including Neural Networks and Fuzzy Logic.

5.3 System architecture bridging sensor modules,

mobile, PC and web Cloud

BioKin system

The BioKin system consists of several layers: a low-cost wearable wireless mo-

tion capturing MEMS sensors, data collection and storage engine, motion analysis

algorithm and visualization platform. The first layer is implemented in the BioKin-

WMS sensor and the latter layers are distributed among different components of

the BioKin software suite: BioKin-PC, BioKin-Cloud and BioKin-Mobi.

Cloud technology And MCC Model

With the aid of recent developments in Cloud technology, the most dominant con-

straints of mobile phones in memory and processing power aspects can now be

shrunk. Recently, fast growing cloud computing technology has led to a novel com-

puting paradigm: MCC model which allows users to access unlimited computing

power and storage space online [199]. According to the National Institute of Stan-

dards and Technology of the United States, cloud technology is defined as a model

for enabling ubiquitous, convenient, on - demand network access to a shared pool

of configurable computing resources (networks, servers, storage, applications, and

services) that can be rapidly provisioned and released with minimal management

effort or service provider interaction [205]. By definition, it is required to fulfil essen-

tial characteristics such as on demand self-service, broad network access, resource

pooling, rapid elasticity and measured services. Hence, cloud technology can be

used to mitigate resource constraints of a mobile phone. Hybrid technology align-

ing mobile phones and cloud technology, is emerging nowadays because of elasticity

in resources and processing power which are limitations of a mobile phone.

Cloud technology is attractive in quick start ups and research projects since it is


Web application

Sense IMUdataTransmitdatawirelessly

Transmitdata file tocloudReceivedata filefrom cloudVisualizeoutput

Web Application Database (RDS) Process dataMaintainrecord forchronicdiseases

Storeprocesseddata

Update

BioKin BioKin Mobi BioKin Cloud

Figure 5.1: Proposed architecture bridging BioKin, BioKin Mobi and BioKin Cloud

a low cost, viable computer platform which makes easy to test and prove potential

concepts [205]. There are basically three types of cloud architectures; public cloud,

private cloud and hybrid cloud. A public cloud is a model which allows users to

access to the cloud via interfaces using mainstream web browsers. It is typically

based on a pay-per-use model [205]. The key advantage of cloud computing is that

the user can lease only the required amount of software and/or hardware for the

desired duration without incurring capital and maintenance expenses. Further, it

is able to dynamically scale resources if needed [206, 204].

Accurate clinical decision making in medical monitoring mainly depends on the

strategic fusion of multi- parameter physiological signals and a large database set

[207]. Thus, the focus is developing a web based application (BioKin-Cloud app)

and a mobile application (BioKin-Mobi) to manipulate signals which are sent from

BioKin sensors to the cloud application. The system was deployed in a public cloud

under the Amazon web service provider. The architecture of the system is shown

in figure 5.1.


(a) Standing (b) Push off a gait

Figure 5.2: 3D skeletal visualization of human posture

5.3.1 Development of BioKin-Mobi

BioKin-Mobi utilizes WiFi hotspot feature of modern smart phones to connect mul-

tiple BioKin wireless sensors communicating using IEEE 802.11b/g/n and storing

collected data in a local storage, until it is transferred to the BioKin-Cloud system.

The BioKin device is only used to gather data on motion which it will transmit to

the mobile phone. Once the data for an entire motion is gathered, the phone will

create a text based file and send it to the web server. Due to computational limita-

tions of the mobile phones, the mobile software does not provide motion analysis.

Instead, BioKin-Mobi can request a pre-analysed motion history from the cloud

application. The mobile software supports 3D playback visualization of such pre-

analysed data. Figure 5.2 shows screen captures of BioKin-Mobi in an Android

mobile phone, illustrating the 3D playback feature.

5.3.2 Development of web application - BioKin-Cloud

The web application was initially developed in a local machine under the Eclipse

Integrated Development Environment (IDE). Infrastructure as a Service (IaaS) was


used which offered by Amazon Web Services (AWS) [208]. The Amazon cloud

service provides the tool for Eclipse with access to web services and web resources,

hence it mitigates the development cost. Further, it is easy to access available web

services and resources for the account through the AWS Explorer window.

Figure 5.3: The patients and therapists interaction scenario

Furthermore, the web application listens for the appearance of the data files

and updates relevant records in the relational database according to the head of

the files. A relational database service named Amazon RDS was used for the cloud

application to maintain the data intensive tasks. The Amazon Relational Database

Service (RDS) [209] is a web service that makes it easy to setup, operate and scale

a relational database in the cloud. Figure 5.2 demonstrates the scenario of how a

patient and a therapist interact with those three parts of the system: BioKinWMS,

BioKin-Mobi and BioKin-Cloud. Figure 5.4 displays a snapshot of the home page

in the cloud based web system for BioKin.

There are three main components in the tele-rehabilitation platform: therapist

side, server side and patient side. Except for the server side, there is only one


Figure 5.4: Home page of the web system

Figure 5.5: The overview of the tele-rehabilitation system

instance of the other two components in figure, which can actually be multiple

simultaneous instances, representing a number of therapists and patients accessing

the tele-rehabilitation services at the same time.

• Therapist side

Primary focus of this side is on the inclusion of patient profile management,

building exercise models and visual (on-line or off-line) review of the exercise

data and analysis result collected from various sensors and ADOSS (refer to

section 5.3.3). Exercise models built in this side have two major aims. First

of all, the models can be downloaded by patients and utilised as a guidance in

performing tele-rehabilitation exercises. Secondly, models built by therapists


can be used as references for tele-rehabilitation exercise performance evalua-

tion. As for the data flow, except for life streaming, which is introduced in

the patient side.

Process Request

Patient Profile Database

WCF Channel

Create& Update Patient Profile

Delete& Search Patient Profile

Model Motion Capture

Off-line Review

Show Confirmation

WCF Channel

Signal Processing

Generate Response

Patient Exercise Database

Model Motion Database

Encode Decode

EncodeReview Data Presentation

Decode

Figure 5.6: Data flow model in therapist side (except for online review)

Figure 5.6 shows the data flow between the cloud (server side) and the ther-

apist side. Symbols in the graph with different colours indicate the data

and requests from various sources and their corresponding responses. Here,

squares and downward triangles are the encoded version (refer to section 5.4)

of data represented by circles, while upward triangles and diamonds repre-

sent database operations without storing new data. Additionally, as for the

responses, there are two methods to display information. One is showing a

confirmation statement to notify the therapists whether or not the requested

operation was successful. The second approach is visually displaying informa-

tion obtained from the cloud, such as histograms. In addition, the data flow

of off-line review (with green symbols) in figure 5.6 is an abstract process and

detailed information is discussed in section. 5.3.3.

• Patient side

The patient side of the platform provides interactive tele-rehabilitation ser-

vices and passive exercise monitoring capabilities. The data flow is shown in


WCF Channel

WCF Channel

Request Model Motion

Exercise Capture

Process Request

Patient Profile Database

Patient Exercise Database

Model Motion Database

Signal Processing

Generate Response

Generate BioFeedback

Display Model Motion

Present BioFeedback

Channel SelectionWCF ChannelDisplay

Exercise Data

Encode Decode

EncodeDecode

Decode Encode

Local Database

M

Figure 5.7: Data flow model in patient side (with online review for therapists)

figure 5.7. For interactive tele-rehabilitation, first of all, the patient requires

the exercise model created by his/her therapist from the cloud (shown with

blue symbols), which is later utilised in the rehabilitation exercises as refer-

ences and streamed to the patient’s mobile devices (with purple symbols).

After that, the performed exercise motions of the patient are recorded and

sent to the cloud (with red symbols). It is noteworthy to send encoded data

which produced by this system, instead of sending video or audio data like

typical tele-rehabilitation systems.

When the cloud (server side) receives the recorded exercise information, signal

processing techniques are applied to filter out the noise and also to extract

relevant features. The data is stored in patient exercise database for off-line

review and also used to provide corresponding bio-feedback, particularly for

performance measurement and assessment through the comparison between

patients’ acts and therapist model. The bio-feedback is denoted with blue

triangles and presented in various forms (refer to section 5.4.3). Finally, if a

therapist has enough bandwidth and choose to review the patient’s exercise


online, he/she just has to register a channel, through which the processed

motion information is forwarded by the cloud to the therapist. As for the

passive exercise monitoring, the data follow the path indicated by red symbols.

In order to solve the disconnection issue in mobile terminals, a small local

database is maintained in the patient side to store the most recently used

model motion information and the patient’s exercise motion data. Therefore,

even when the patient is unable to connect to the Internet temporarily, he/she

is still able to use the tele-rehabilitation system. When the connection is

established again, the patient’s motion data can be synchronised to the main

database in the server side for further analysis. Indeed when the Internet is

not available, the patient is unable to receive bio-feedback and performance

measurement updates if the computational power in their mobile device is

insufficient.

5.3.3 Analysis oriented decision support system

In this subsection, the concept of analysis oriented decision support system (AODSS)

is discussed, which is a combination of the concepts of the service-oriented decision

support system (SODSS) [210] and the clinical decision support system (CDSS)

[211]. Since AODSS is integrated in the MCC-based tele-rehabilitation platform, it

contributes to the establishment of mobile CDSS mentioned in [211], which is con-

sidered as a research challenge in CDSS. The contribution of this study to AODSS

is that data is analysed with different granularities, which can be collected from

various types of sensors and stored in various databases in the cloud. This method

is embedded into the data flow (with green symbols) shown in figure 5.6.

The concept of AODSS is illustrated in figure 5.8. The first column shows the

source of data, which is not included in the data flow of information query and re-

sponse between the therapist side and the sever side. Data from the sensor is stored

in single or multiple databases in the cloud which is highly likely to be distributed


BioKinSensor

OtherSensors

HardwareArchitecture

UploadData

MySQLDatabaseInstance

Amazon RDSservice

NoSQLDatabase inApache

Cassandra

Amazon RDSservice

Data Layer

ETL

Data ManagementTool

DataManagement

Layer

Analytics

DataAnalysisLayer

Data Mining andPattern Recognition

ClassificationData

ClusteringRegression

AnomalyDetectionAttributeImportance

Simulation

Automated DecisionSupport Systems

Gait Analysis

Upper BodyAnalysis

Hand Analysis

Long Termmonitoring

Data As A Service Information As A ServiceAnalytics As A Service

User Layer

Figure 5.8: The conceptual architecture for analysis oriented decision support sys-tem

into different servers to maintain the response speed with a large number of queries.

After raising a query from the therapist side (user layer), the data extraction tool

retrieves related data from the data layer, which is further processed by using var-

ious integrated data mining tools (in data analysis layer) and mining algorithms,

such as clustering, classification, regression, attribute importance, anomaly detec-

tion, association and feature extraction. Eventually, the data is visually presented

to the therapist to assist him/her to make further decisions.

The main contribution of this AODSS is its ability to analyse a huge amount

of data collected from IMU devices (i.e. BioKin sensors) and provide supportive

information in various granularities to therapists based on the encoding levels of

data sources.

stroke tele-rehabilitation is used as an example for this. Since the kinematic

performance of a post-stroke patient can be assessed through the movement of limbs,

AODSS first retrieves related data from the database. Due to the fact that data used

by AODSS is encoded with various encoding schemes, AODSS is able to provide

results in various granularities. For instance, AODSS can provide a histogram


showing the change in performance (computed by the performance measurement

algorithms mentioned in section 5.4.1) of a patient in tele-rehabilitation sessions

during a day, a month or even longer period. After receiving the analysis results,

the therapist will have a general idea about the effectiveness of the therapy and the

progress of the patient. If the therapist wants to know the movement patterns of the

patient in each session, AODSS is also able to analyse the encoded data at motion

trajectory, elbow points or shape model level and generate a report to show the

details in each session. These information assists the therapist to investigate why

is the patient under-progressing or improving. Thus, the therapists can re-evaluate

the exercise components in the session to suit the patient’s capabilities to achieve

better rehabilitative outcomes or have the confidence to encourage the patient to

stick with the therapy.

5.3.4 Security service layer

As mentioned previously, security and privacy are some of the challenges faced in

CDSS. Therefore, AODSS is inevitably impacted by this challenge. Security service

layer (SSL) introduced in this subsection is a concept that has the potential to solve

this challenge in the proposed AODSS, as well as the MCC-based tele-rehabilitation

platform.

Since many parties such as patients, clinicians, health-care administrators, in-

surers, and researchers are involved, an End-to-End security control will be applied

to enhance the protection of data. The security associations is managed by a Se-

curity Association Manager to coordinate the communication groups [212]. The

Security Association Manager includes a Security Policy Collections, Security As-

sociation Flows, and Distributed Logs. The Security Policies Collections specifies

which security level and which rules need to be used in associations with the types of

parties. The Security Association Flows contains routing algorithms, keys, encryp-

tion schemes, protocol modes, and flow-level lifetime. The distributed logs store


the logs of both end points in order to avoid fragmentation of logs stored in dif-

ferent repository. The Security Association Manager can collaborate with external

Certificate Authority [213] to enhance authorization processes. This collaboration

allows a patient or the service provider to rely on their service provider to provide

other e-Healthcare providers with only the specific data necessary to complete the

transaction.

An example would be the security enhancements defining work roles in order to

ensure security to data and avoid unauthorized and unauthenticated access. Each

role of this system, including software engineers and database administrators are

created as a project group and their scope of access is predefined. Each role can only

access the system using their credentials. Further, any modifications to the system

can be done only by accessing the cloud server and this requires three security

certificate files including key pairs, security keys and X.509 certificates to make

any modifications. This is an in-built requirement of the cloud service provider.

Further, the text file which is sent from the smart phone to the cloud application, is

encrypted, hence it mitigates disclosing data to unauthorized people. Additionally,

the database instance is configured to get a snapshot of the database automatically

once a day. Those undertakings mitigate concerns of security and data loss.

5.4 Multi-Level data encoding technique

This section is dedicated to solving one of the limitation, namely limited power

for computing and data transferring, in applying mobile cloud computing in tele-

rehabilitation field by utilising the characteristics of biomedical data collected from

various types of sensors.

5.4.1 Protocol

Due to the limited battery resources in a mobile device, how to reduce the power

consumption is an open question in MCC field. In this study, a multi-level data


encoding scheme is proposed so that the data can be encoded differently to reduce

the quantity and time during transfer, thereby reducing the power utilized to trans-

fer data. However, different encoding schemes require varying computational times.

Generally speaking, if the amount of data after encoding is smaller, the time utilised

to encode the original data is longer. Therefore, it is crucial to find an approach to

determine which level of encoding should be utilised.

Motion Trajectory

Shape Model

Elbow Points

Performance Measurement

Level 1

Level 2

Level 3

Level 4

Figure 5.9: Multi-level exercise data encoding scheme

Figure 5.9 shows the data encoding schemes for motion rehabilitation. The en-

coding scheme in the higher position indicates that the data amount after encoding

is smaller than approaches in lower levels. For instance, in human motion capturing,

the details of each encoding scheme are introduced as follows.

• 3D Motion Trajectory

In the majority of the motion capture devices, human motions are analysed

with joint positions in the forms of Γn(t) = [xn(t), yn(t), zn(t)]�, where xn(t),

yn(t) and zn(t) are 3D positions of nth joint (n = 1, 2, · · · , N) on the X, Y

and Z axes at time t in the traditional Cartesian coordinate system. each

point of data in an axis requires 8 bytes, hence for three axis points, 3 × 8


bytes (24 bytes) is required. Hence, a frame of 3D trajectories for N joints is

24×N bytes.

• Elbow point technique

In a motion trajectory, each point has its own importance and its contribution

to the shape of trajectory is different from others. An array of points lying on

a straight line can be represented by only two points at the two end-point of

the line. Therefore, points at the middle of the straight line can be removed

to reduce the computational cost and data storage. Points lying on a curve

are called “elbow points” which are essential points to form the shape of the

trajectory [214]. Differentiation of “straight points” and “elbow points” can

be based on curvature. Curvature at a point Γn(t) is defined as:

κn(t) =‖vn(t)× an(t)‖

v3n(t), (5.4.1)

where

vn(t) =

[(∂xn(t)

∂t

)2

+

(∂yn(t)

∂t

)2

+

(∂zn(t)

∂t

)2] 1

2

. (5.4.2)

A point is marked as an “elbow point” when its curvature is larger than a

specific threshold ε. Conversely, a point is marked as a “straight point” if its

curvature is larger than or equal to zero and less than the specific threshold

ε. In elbow method, points with curvature κ < ε will be removed from the

trajectory. The original trajectory can be approximately reconstructed from

the new trajectory if the coordinates of the elbow points and their sequential

orders can be determined. The new trajectory which includes only elbow

points obviously requires less computational cost than the original trajectory.

this technique is illustrated in figure 5.10 for the 2D case. The technique

can be applied in 3D case[214]. Here, the function f(x) = x sin x where

x1 = 0, ..., x100 = 10π and xn+1 − xn = xn − xn−1 is drawn. As figure shows,

the new trajectory formed by elbow points is almost identical to the original


0 5 10 15 20 25 30 35−40

−30

−20

−10

0

10

20

30

Full point trajectoryElbow point trajectory

Figure 5.10: An illustration of the elbow point concept. Red points are elbowpoints when κ > 0.05. Blue points with curvature less than 0.05 is removed fromthe trajectory.

trajectory with all the points. In this example, the value of 0.05 is used for the

threshold ε, hence half of the points from the trajectory have been removed.

Depending on the application, this threshold value can be chosen accordingly.

• Shape model

To tackle some situations where the bandwidth is insufficient to transfer el-

bow points, shape models can be further derived to encode motion trajecto-

ries. Apart from the curvature in (5.4.1), torsion is needed since the motion

trajectories are in three dimensions. It is derived as,

τn(t) =(vn(t)× an(t)) · jn(t)‖vn(t)× an(t)‖2

, (5.4.3)

where

jn(t) =

√(∂3xn(t)

∂t3

)2

+

(∂3yn(t)

∂t3

)2

+

(∂3zn(t)

∂t3

)2

(5.4.4)

is the jerk of the motion trajectory.

From the derivation, it is observed that the motion trajectory is encoded from

three dimensions (X, Y and Z) to two dimensions (κ and τ).


• Performance measurement

Two methods can be utilised to encode and measure the performance of

the tele-rehabilitation exercises, including smoothness based and elbow point

based measurements. As for the former [215], it is specially designed for

tele-rehabilitation service users with neurological movement disorders, such

as dyskinesia, that involve large amplitude involuntary movements, which

leads to less smooth motion trajectories than healthy people. Due to the fact

that the shape model [141] is very sensitive to noise in motion trajectories,

the sub-movements and jerky movements are also shown in the shape model.

As a result, the entropy of the shape models of these trajectories are com-

puted to represent the severity of involuntary movements, thereby indicating

the ability of patients to perform tele-rehabilitation exercises given by their

therapists. Another method that can be used for this encoding scheme is

the algorithm in [214]. In this approach, the authors used longest common

sub-sequence (LCSS) to match the trajectory from the patient and the corre-

sponding one from the therapist (model motion trajectory) and gave a score

for performance measurement.

5.4.2 Determine encoding level

The introduction of various encoding approaches naturally raises the question of

determining the encoding level that should be used depending on the computational

power and the speed used to upload data to the cloud from the mobile device.

The study in [216] introduces an approach for offloading decision by estimating

how much power is used for computations and transfer of data. this method is

adopted to determine which encoding level should be utilised with respect to the

bandwidth. Notations utilised in the estimation process are shown in table 1.

Unlike the approach introduced in [216], the computation time in the server is not

considered in this case. The reason is that the data communication between the


Table 5.1: Notations used in the process of estimating power consumption for dataencoding and transfer. Here i = 1, 2, 3, 4 for motion tele-rehabilitation and i =1, 2, 3 for respiratory tele-rehabilitation.

Notation Unit Description

d byte the size of memory occupied by a double value

Di -dimension of encoded data of each frame with ith encodingscheme

Li frame the length of exercise data encoded by the ith encoding scheme

N -the number of monitored points in the motion. N =1 forrespiratory monitoring

Si byte size of encoded data at the scheme ith

ui Joulethe energy consumed by the mobile device to encode 1 frameat the scheme ith

v Joulethe energy consumed by the mobile device to transfer encodedexercise data to the cloud

PLi Joule

the energy consumed by the mobile device to encode entiretrajectory at the scheme ith

P Ti Joule

the energy consumed by the mobile device to transfer entireencoded data to the cloud at the scheme ith

B kbps the speed of uploading data to the server

server and the mobile device uses asynchronous channels which means the channels

are not blocked when the server is engaged in the computation. Therefore, there is

no idle time in the mobile device. Further in this case, it is hard to estimate the

number of instructions required by the computation for data encoding. As a result,

the numbers of unit energy consumption (ui) utilized to perform encoding for each

frame of data was directly recorded, which can be retrieved automatically by the

system.

The formula to calculate data size is :

Si = d×Di × Li ×N (5.4.5)

The formula used to calculate local computational power with scheme i is

PLi = PL

i−1 + ui × Li−1 ×N, (5.4.6)

where u1 = 0; u2 is the average power consumption to determine whether a point

is an elbow point and it includes the calculation of curvature; u3 is the average


power consumption to calculate torsion value of 1 point; u4 is the average power

consumption to calculate the performance.

The formula used to calculate data transfer power is

P Ti =

Si

B× v, (5.4.7)

where v is the energy consumption for uploading data in 1 second and B is the

network speed. Table 5.2 summarises the power consumption of various encoding

scheme and encoded data transfer for motion tele-rehabilitation.

Table 5.2: Power consumption of various encoding scheme and encoded data trans-fer for motion tele-rehabilitation.

i D L Data size

Energyconsumption

of localcomputation

Energyconsumption

of datatransfer

Original trajectory 1 3 L1 24× L1 ×N 0 24× L1 ×N × v/BElbow points 2 3 ≈ 0.5× L1 12× L1 ×N u2 × L1 ×N 12× L1 ×N × v/BShape model 3 2 ≈ 0.5× L1 8× L1 ×N P2 + u3 × 0.5× L1 ×N 8× L1 ×N × v/BOverall performance 4 1 1 8 P3 + u4 × 1×N 8× v/B

The following cost function is used to determine which encoding scheme is to

be used

E(i) = argmini

(PLi + P T

i

)(5.4.8)

In some cases, if |E(i1 − E(i2)| < ε, and i1 < i2, the author select i = i1 so that

more data can be transferred to the cloud by consuming similar power. Here ε is a

small constant value.

5.4.3 Optimised bio-feedback

Traditionally, the feedback with regards to the rehabilitation exercises is given di-

rectly from therapists, which is the most effective approach. Therefore, this method

is implemented in the system as a bio-feedback option. However, it is only available

when the therapist reviews the exercises of the patient online so that the auditory

message is routed by the server side from the therapist to the selected patient and

vice versa for communication. It means that this method relies heavily on the high


bandwidth, which is not always available for MCC. Therefore, in the system, three

other types of bio-feedback are implemented, which can be selected according to

the availability and the bandwidth of the allocated network connection.

First of all, since the model motions recorded by therapists were utilised to

guide patients to perform tele-rehabilitation exercises, patients are able to receive

the visual bio-feedback directly by looking at the differences between their motion

trajectories and those from the model motions. However, due to the fact that the

motion trajectories on the screen are always in 2 dimensions and the third one is

unable to be observed by the patient, the top down view of both the model and

patient’s motion are presented in the another window to illustrate the differences

in the third dimension. By looking at the screen, the patient is able to see the

gap between his/her motion with the model, thereby correcting their motion in

time. Since the model motion is always available, either from the cloud (when the

speed of the Internet is fast enough) or from the local temporary database (when

the bandwidth is low or the Internet is disconnected), this type of bio-feedback is

always available.

Secondly, auditory bio-feedback is also an option in the introduced platform to

correct patient’s tele-rehabilitation exercises. For instance, fast rhythm indicates

that the patient should move the limbs or other body parts involved in the tele-

rehabilitation session faster and the slow rhythm tends to slow down the patient’s

movement. To modify the rhythm of the music, the speed of the patient’s movement

is derived from their motion trajectories in the server side and is compared with

that of the model motion. Eventually, a ratio is generated and sent to the patient

side to change the rhythm.

Although the performance measurement is utilised as an encoding scheme (refer

to 5.4), this value can also be utilised as a feedback indicating the performance of

doing specific rehabilitation exercises. As is mentioned in the previous subsection,

two approaches (including elbow-point based and entropy based) could be utilised


to represent the performance of a rehabilitation exercise session. This feedback not

only gives both the patient and the therapist an overview about the ability of the

patient to perform certain tasks, but also is able to stimulate the patient to perform

exercises more frequently, thereby achieving higher performance measurement.

5.4.4 Results and platform demonstration

Implementation of BioKin Cloud web system

The BioKin web system is developed under the AWS toolkit for Eclipse which

provides AWS Explorer. The AWS Explorer offers access to each service which is

made available by the AWS including the EC2 console and the RDS console. The

instances which are enabled for the account, are viewed under AWS Explorer and

the instances can be connected and disconnected directly through it. The BioKin

cloud web system is deployed under the hardware environment in table 5.3. It is

deployed in an EC2.t1.micro server and Amazon Elastic Beanstalk service [217].

Table 5.3: Hardware environment of the system

Server type Ec2.t1.micro

Server Software Windows 2003Memory capacity 5 GB

Load Balancer 1Deploying Environment AWS Elastic Beanstalk

Database MySQL

The system is evaluated under three categories such as total execution time,

CPU utilization and monetary costs. The application is developed and deployed

under the Amazon Business Plan and the charge for the computing in the cloud

service was less than fifty USD per month. The system is allowed to run contin-

uously on the server over a couple of days and the server was manually stopped.

The Amazon Elastic Beanstalk service was able to auto-start on the new server in

spite of the terminating pervious server and the web system was alive throughout

the testing period. The CPU utilization of the server was an average of 5% at the


non-data processing stage. The BioKin Cloud system is able to access unlimited

processing power and storage according to the capabilities of cloud technology.

With the BioKin Mobi and BioKin Cloud applications, it is expected that it

will enable true ambulatory operation of the BioKin remote physiotherapy system,

where patients and medical professionals can interact with each other while the

patients are in their home environment. Since the cloud resources can be scaled to

the demand, it is easy to expand the project to cover a larger capacity of data.

Computer simulation for multi-level encoding scheme

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.5

1

1.5

Connection Speed (kbps)

Ene

rgy

(J)

level1level2level3level4

Figure 5.11: Numerical experimental result

In this subsection, a numerical example is presented to demonstrate the effective-

ness of the multi-level encoding scheme for motion exercise monitoring in saving

energy in mobile devices. First of all, 18 motion trajectories are generated with

L1 = 1000 for each exercise. The author further assumed u1 = 0 μJ , u2 = 8.8 μJ ,


u3 = 21 μJ and u4 = 0.6 mJ . These assumptions were based on execution time

for each specific task which directly related to the complexity of the computations

and transmission. The author also assumed that the connection setting which cost

v = 50 mJ for transferring data in a second. The total energy consumption was ex-

amined for both local computations and data transfer for different uploading speeds

from 0 kbps to 2000 kbps. The numerical experimental result is shown in figure

5.11. In figure, the minimum energy for the uploading speed from 0 kbps to 50 kbps

can be achieved if level 4 of encoding scheme is used. Similarly, level 3 for uploading

speed from 50 kbps to 200 kbps, level 2 for uploading speed from 200 kbps to 1200

kbps and level 1 for above 1400 kbps. At the uploading speed of 50 kbps, the total

of energy spending for levels are 21.6 J , 10.9 J , 7.5 J and 1.3 J . The difference

of energy between levels can be up to 20.3 J and this means the use of encoding

schemes can save up to 20 times of energy for low connection speeds. Indeed, for

better connections, for example, uploading speed above 1400 kbps, sending all data

to the cloud for processing is the best in terms of saving energy and preserving

information.

Real-data experiment for multi-level encoding scheme

To further illustrate the performance of the proposed multi-level encoding scheme,

a preliminary real-data experiment was performed with simulated motion trajec-

tory data and four various encoding methods. In this experiment, software named

BatteryMon (V2.1 build 1008) and NetBalancer were utilised to monitor the energy

consumption and to control the speed of the Internet connection. Furthermore, the

encoding algorithms and data transferring program was implemented in C#. The

experiment was done on a laptop with CPU of Inter R©CoreTM i7-3740QM and Wifi

card of Intel R©Centrino R©Ultimate-N 6300AGN. To eliminate the influences of other

software, first of all, BatteryMon was initialised for half an hour without running

any unnecessary program to estimate the energy consumption of the laptop in idle

state. All the following measurements were subtracted by this energy to compute


the power utilised in order to compute the proposed encoding methods or to transfer

the data to the cloud.

After that, a 3D trajectory with length of 1000000 frames was collected and

further encoded with the other three encoders. Each of the encoding was repeated

for 10 times (reliability test) where the average energy consumption of computing

for each encoder was recorded in terms of per frame.

Data Receiver

Wireless Router

Test Laptop (Data Transmitter)

WNetBalancer

Figure 5.12: Setup of the real-data experiment

Furthermore, the setup of the real-data experiment is shown in figure 5.12. The

data receiver component of the data transferring program was deployed in a desktop

connected to a wireless router with a network cable to secure the speed of the data

transfer. Additionally, the laptop is connected to the router with the Wifi card like

a normal mobile device. Moreover, NetBalancer was used to control the Internet

upload speed of the laptop to simulate the environment with different conditions

of the Internet. The author limited the upload speed from 80 to 800 Kbps with a

step of 80 Kbps for testing because the upload speed on 3G/4G is about 0.45Mbps

to 1.93Mbps [218]. Eventually, the average energy utilized to transfer one frame of

the encoded data was recorded with each respective speed.

Finally, the total power consumption was calculated for each encoding approach

and various uploading speed for a trajectory with 10000 frames. The result is shown

in figure 5.13.

From the result, a similar trend as the simulation was observed. When the

upload speed was smaller than about 160Kbps, level 4 encoder was the best option


80 160 240 320 400 480 560 640 720 8000

20

40

60

80

100

120

140

Upload Speed (Kbps)

Ener

gy C

onsu

mpt

ion

(Jou

le)

Level 1Level 2Level 3Level 4

Figure 5.13: Result of real-data experiment for the multi-level encoding scheme.

since it consumed the lowest energy to encode the motion data and transfer the

result to the cloud, while the level 3 encoding approach should be selected when the

upload speed of the Internet was ranging from 160 to 480 Kbps and subsequently,

level 2 encoder should be utilised. Using real experiment’s data, it shows that the

level 1 encoding method always consumes more energy than level 2 and level 3

encoder in this scenario.

5.5 Summary

This chapter basically attempts to solve two major challenges in computer-aided

tele-rehabilitation systems. One of the challenges is extending application as a

framework to add various wearable and non-wearable sensors for better analysis.

The cloud based web system will be the hub for processing such heterogeneous

data. Since most diseases are not single symptom, but rather a grouping of signs,

these are reflected with highly inter-correlated physiological measures [219] and


the development of the system combining other measurements will be a valuable

endeavour.

The other challenge is building a tele-rehabilitation system based on mobile

cloud computing (MCC) while minimising the energy expenditure of mobile de-

vices to extend the duration of accessing tele-rehabilitation services. In this study,

the characteristics of bio-kinematic signals were considered for achieving this goal.

More specifically, a multi-level encoding scheme is introduced to encode human

motion trajectories into various levels according to the computational power and

the Internet speed of the mobile device. The simulation and real-data experiment

have confirmed the effectiveness of the proposed scheme in saving power of mobile

devices.

Apart from that, an architecture of MCC-based tele-rehabilitation system was

introduced with analysis-oriented decision support system and security service layer

to provide advanced and secured data communication and analysis. As future work,

focus should be put on the development of suitable algorithms for AODSS under

various conditions.

.

Chapter 6

Conclusion

Rehabilitation is becoming one of essential part in medical treatments due to rapid

increase in aged population and people with disabilities. Capturing human posture

in real-time using wearable sensors is destined to have far reaching consequences in

many practical medical applications involving rehabilitation and long term monitor-

ing in health care sector. Further, wearable sensors are used for activity monitoring

in sports and motion capture in movie and gaming industries. Readily available

and low cost IMU sensors in an integrated and miniaturised form are considered

in wearable sensors for capturing human movement in medical, sport and virtual

reality.

However, there remain several challenges in implementing effective rehabilita-

tion services using IMUs. One of the challenges is accurately capturing human

movements while having affordable and robust system. These systems should be

able to access and archive information remotely for both patients and therapists for

further analyses. Additionally, the limb length is required to evaluate the severity

of limb length discrepancy which is a very common anatomical condition. Hence,

the second challenge is a machine driven process to estimate limb lengths using

IMUs. The third challenge is the improvement of sensor measurement accuracy

using appropriate misalignment calibration in order to obtain accurate orientation

estimation of the human body segments, because the orientation are used to cap-

ture human movements to distinguish and evaluate patients neurological conditions

153

Chapter 6. Conclusion 154

such as stroke and Parkinson’s disease affecting the movements. The effective sta-

tistical features to distinguish patients from healthy subjects and evaluate their

level of severity based on captured characteristics of kinematics are also an open

question in rehabilitation process. Finally, all these systems and automated eval-

uations should produce useful feedback to patients and supportive information to

therapists for their further analyses. Hence, the development of effective computer

solution which can be accessed fast and remotely by both patients and therapists

to perform data-extensive and complicated analyses is also challenging.

In this dissertation, one of the most important contribution is the representation

of limb orientations as a linear characterisation of an inherently nonlinear estimation

problem with improved overall estimation accuracy. This representation named as

robust extended Kalman filter with Linear Measurements (REKFLM), has shown

outperforming accuracy than non-linear characterisations such as extended Kalman

filter (EKF) and robust extended Kalman filter (REKF) comparable to when data

captured from optical systems: VICON and Kinect. Furthermore, an optimisation

based mathematical justification was introduced providing a systematic basis for

Quaternion normalisation typically performed in the pre-filtering stage. The intro-

duced optimisation was very effective on improving accuracy of estimations using

EKF, REKF and REKFLM approaches.

In this dissertation, the investigation on human movements are conducted as

both deterministic and qualitative analyses. The determination of angle of move-

ment and limb length are some of deterministic analyses and the distinguishing

the Parkinsons patients from healthy subjects based on their kinematic features

is performed as qualitative analysis. Here, three important physical features of

Parkinson’s patient such as rigidness, less flexibility and slower movement are con-

sidered to statistically distinguish patients from normal subjects. These analyses

were conducted based on gyroscope readings captured while trunk movements such

as thoracic rotation and turning body. The author could categorise patients and


healthy subjects based on these analyses. However, the large standard deviations of

both patients’ and controls’ analyses were observed, making it difficult to separate

the two groups as patients and normal subjects. Further, the gait activities such

as walking and running were considered to identify metabolic equation for energy

consumptions. The author could formulate a linear relationship between energy

expenditure and the level of exercise (walking to running) using gyroscope and ac-

celerometer readings. The major limitation of each of these qualitative analyses is

the larger number of influencing factors which are difficult to test in one experi-

ment and large variance in the distributions. In the future, the machine learning

techniques can be applied to obtain more accurate classifications.

Using the curvature of circular movements, two algorithms were introduced for

correcting the misalignment error and estimating the limb length. The misalign-

ment of sensor frame and earth frame is unavoidable in wearable systems due to

uneven nature of human limbs and the movements of users’ clothes, muscle or skin,

which is highly likely to vary with time and adversely affects the deviation of limb

orientations from sensor measurements. The curvature based calibration method

has used to overcome this problem and obtain more accurate measurements from

the sensors for patient’s assessment. Curvature and sample entropy based optimiza-

tion techniques were used to estimate limb lengths for determining and evaluating

the limb length discrepancy condition. The validity of limb length estimator is

verified with computer simulation and controlled experiments. The experimental

results indicated greater accuracy compared to manual measurements having low

root mean squared error (RMSE) percentages for arm length and lower limb lengths

with values ranging from - 8.6% to 14.4%. However, these methods are formulated

only for one degree-of-freedom movements formulated and verified for planar move-

ments to reduce the complexity in kinematics in the first stage. These methods

should be formulated to two-plane movements in future.

Last but not least, a mobile cloud computing (MCC) based architecture was


proposed to combine the techniques introduced in this dissertation to build a pro-

totype of a tele-rehabilitation system so that patients are able to access the tele-

rehabilitation service with their mobile devices regardless of their location and the

time. In this investigation, a multi-level encoding scheme was utilised to minimise

the energy expenditure of mobile devices by encoding the motion trajectories into

various levels. As a result, by selecting a suitable encoding method, both patients

and therapists could manage to archive and access the data and information even in

limited resources such as battery power and internet bandwidth with their mobile

devices.

All these contributions in this dissertation are to ensure accurate, convenient,

fast, affordable and automated service to patients in their day-to-day rehabilitation

activities. The author could achieve accuracy improvements of kinematic parame-

ter estimations due to novel state-based dynamic estimator (REKFLM) and proper

calibration for correcting misalignment error of inertial sensors. The novel algo-

rithms for deterministic analyses such as orientation estimation to capture human

movements and limb length estimation to evaluate limb length discrepancy were

introduced and evaluated real-time using inertial sensors. Furthermore, two quali-

tative analyses: investigation of Parkinson’s patients’ kinematics based on physical

features and energy expenditure for gait exercises were conducted. Eventually, all

these analyses were automated as a computer application with aid of mobile phone

and web clouds that could successfully achieve the objective to facilitate a better

rehabilitation experience to patients.

Appendix I 157

Consider the following optimization problems :

OP1 : minF (x) subjected to x ∈ Ω

OP2 : minG(x) subjected to x ∈ Ω

OP3 : minG(x) subjected to x ∈ Λ

Lemma 2. Consider the problem OP3. Assuming that x∗ is an optimal point ofthe problem and two points z1 ∈ Ω2, z

2 ∈ Λ. If there exists a real number λ ∈ (0; 1)such that x∗ = λz1 + (1− λ)z2 then z1 and z2 are also optimal points.

Proof. Since x∗ is an optimal point of problem and z1 ∈ Λ, z2 ∈ Λ, there areG(x∗) ≤ G(z1) and G(x∗) ≤ G(z2). If z1 is not an optimal point of problem (OP )3then G(x∗) < G(z1). By linearity of functional G(x), there is,

G(x∗) = G(λz1 + (1− λ)z2)

= λG(z1) + (1− λ)G(z2)

< λG(x∗) + (1− λ)G(x∗)

= G(x∗). (.0.1)

This is a contradiction. Thus, z1 is an optimal point. Similarly, z2 can be proovedas an optimal point.

Lemma 3. Problem OP3 has at least an optimal point which belong to Ω.

Proof. From lemma 2, it implies that problem OP3 has a optimal point x∗ whichbelongs to boundary of Λ. It means that x∗ ∈ ∂Λ. Note that Λi∩Λj = ∅, λi∩Ω = ∅,i = j, i, j = 4 · · · 8 and

∂Λ = Ω ∪( 8⋃

i=4

Λi

).

Therefore, if x∗ ∈ Ω then there is an index i ∈ {4, 5, · · · , 8} such that x∗ ∈ Λi.Without loss of generality, the author assume that x∗ ∈ Λ4. By using lemma 2, itimplies that one of three points A2, A3 and A4 must be an optimal point. It meansthat problem OP3 has at least an optimal point which belong to Ω. �

Now. let’s recall the definition of equivalence of optimisation problems as given

in [223] as follows:

Definition Two optimisation problems are equivalent if from a solution of one, a

solution of the other is readily found and vice versa.

Lemma 4. The problems are equivalent

Appendix I 158

Proof. By expanding functional F (x) and using the constraint x24+x25+x

26+x

27 = 1,

that OP1 = 1+P 2+Q2+R2+S2+OP2 can be found. This implies that if x∗ is anoptimal point of problem OP1 then it is also an optimal point of problem OP2 andvice versa. Therefore, problem OP1 is equivalent to problem OP2. On the otherhand, it is easy to see that if x∗ ∈ Ω is an optimal point of problem OP3 then italso is an an optimal point of problem OP2. Note that in case x∗ ∈ Ω then usinglemma 3, it can find another optimal point x∗∗ ∈ Ω. Certainly, this point x∗∗ is anoptimal point of problem OP2. The rest of the proof is to prove converse. It meansthat if x∗ ∈ Ω is an optimal point of problem OP2 then the author must prove thatit also is an optimal point of problem OP3. If the author assume that x∗ is not anoptimal point of problem OP3 then there is another point z1 ∈ (Λ\Ω) such thatG(z1) < G(x∗). By lemma 3, there exist z2 ∈ Ω such that G(z2) = G(z1). Thisimplies that G(z2) < G(x∗). This contradicts with that x∗ is an optimal point ofproblem OP2. Therefore,x∗ must be an optimal point of problem OP3. The proofof lemma 4 is completed. �

Appendix I 159

Table 1: Notations used in dynamic model.

Notation Description

N The weight on the initial solutionQ Weighting on the uncertainty of human arm movementsR Weighting on the measurment noiset Time durationA Weighting on u(t)u(t) The uncertanity ouputsz(t) The uncertanity ouputsw(t) The uncertanity inputsx1 Angular rates (ω1) in x axisx2 Angular rates (ω2) in x axisx3 Angular rates (ω3) in x axisx4 The first component of the quaternion (q1)x5 The second component of the quaternion (q2)x6 The third component of the quaternion (q3)x7 The fourth component of the quaternion (q4)x8 The gyro drift (δ) of x axisx9 The gyro drift (δ) of y axisx10 The gyro drift (δ) of z axisy Measurment vector : [y1 · · · y13]yc Measurment vector : [y1, y2, y3, y10, y11, y12, y13]y1 Pre-filtered angular rates (ω1) in x axisy2 Pre-filtered angular rates (ω2) in y axisy3 Pre-filtered angular rates (ω3) in z axisy4 Pre-filtered accelerometer readings (a1) in x axisy5 Pre-filtered accelerometer readings (a2) in y axisy6 Pre-filtered accelerometer readings (a3) in z axis

y7 Calibrated magnetometer readings (h1) in x axis

y8 Calibrated magnetometer readings (h2) in y axis

y9 Calibrated magnetometer readings (h3) in z axisy10 First component of estimated quaternion in previous state (q1)y11 Second component of estimated quaternion in previous state (q2)y12 Third component of estimated quaternion in previous state (q3)y13 Fourth component of estimated quaternion in previous state (q4)

List of Figures

1.1 Plane of motion [10] . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 Osteokinematic motions [10] . . . . . . . . . . . . . . . . . . . . . . 6

1.3 An illustration of available human movement tracking system [34, 35] 10

1.4 Classification of human motion tracking using sensor technologies . 11

1.5 Various goniometers [10] . . . . . . . . . . . . . . . . . . . . . . . . 12

1.6 Demonstration of position tracking using marker based visual track-

ing system: (a) markers attached to the joints; (b - d) marker posi-

tions captured by three cameras [40] . . . . . . . . . . . . . . . . . 13

1.7 Marker based visual systems . . . . . . . . . . . . . . . . . . . . . . 13

1.8 Appearance and components of Kinect c© version 1[46] . . . . . . . 14

1.9 The pinhole camera model of Kinect c© version 1[47]. . . . . . . . . 15

1.10 Earth and sensor co-ordinate systems . . . . . . . . . . . . . . . . . 17

1.11 Rotational angles of inertial sensors . . . . . . . . . . . . . . . . . . 18

1.12 BioKin sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.1 Block diagram of MARG algorithm implementation [88] . . . . . . . 38

2.2 Traditional complementary filter [60] . . . . . . . . . . . . . . . . . 39

2.3 Adaptive complementary filter . . . . . . . . . . . . . . . . . . . . 41

2.4 Orientation estimation using solutions of Wahba’s problem and IMUs 42

160

List of Figures 161

2.5 Simulation Result: (a), (b) and (c) - RMSE of movement angle in

X, Y and Z axis for shoulder exercise, (d),(e) and (f) - RMSE of

movement angle in respectively X, Y and Z axis for lifting a bottle

exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.6 Experiment result: (a) - movement angle for abduction exercise, (b)

- root mean square error in movement angle for abduction exercise,

(c) - movement angle for lifting water bottle exercise and (d) - root

mean square error in movement angle for lifting a bottle exercise . . 45

2.7 Experiment result: (a), (b) and (c) - root mean squared error of

movement angle for extension/flexion exercise, abduction/adduction

exercise and lifting a bottle exercise respectively . . . . . . . . . . . 46

2.8 The Kalman filter [119] . . . . . . . . . . . . . . . . . . . . . . . . 48

2.9 Extended Kalman filter [113] . . . . . . . . . . . . . . . . . . . . . . 50

2.10 Block diagram for first approach of implementing Kalman filter [113] 51

2.11 Block diagram for second approach of implementing QUEST algo-

rithm and Kalman filter [113] . . . . . . . . . . . . . . . . . . . . . 51

2.12 Lifting a bottle: VICON markers and BioKin sensors were attached

to the arm (Left arm). . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.13 Elbow angles were calculated with different filtering and sensor fusion

techniques compared to VICON optical motion capture system for

subject 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

2.14 Block diagram of the algorithm . . . . . . . . . . . . . . . . . . . . 65

2.15 RMSE of the estimated angle . . . . . . . . . . . . . . . . . . . . . 66

2.16 The error in estimated angle with against the uncertainty bias . . . 67

2.17 RMSE subjected to introduced noise . . . . . . . . . . . . . . . . . 69

2.18 Percentage improvement due to quaternion optimisation . . . . . . 69

2.19 Experiment Setup and Procedure: S1, S2 and S3 are sensor and worn

marker positions: distal end of elbow, wrist and palm respectively . 71

List of Figures 162

2.20 RMSE in angle estimation for Forward Extension Exercise in com-

parison to VICON optical system . . . . . . . . . . . . . . . . . . . 72

2.21 RMSE in angle estimation for the upper arm exercises in comparison

to Kinect c© optical System . . . . . . . . . . . . . . . . . . . . . . 73

2.22 Percentage improvement due to optimisation of the experiment with

Kinect c© optical system . . . . . . . . . . . . . . . . . . . . . . . . 73

2.23 Root mean square error of upper arm exercises compared to VICON

optical system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

2.24 Percentage improvement due to optimisation of the experiment with

VICON optical system . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.1 The sensor misalignment error in a shoulder abduction exercise . . . 80

3.2 Proposed algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.3 The geometrical relationships between error-θ and arm movement-α 83

3.4 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

3.5 The error of estimated curvature with noisy data. The top figure

shows the errors when noise was introduced to acceleration while the

lower one illustrates the errors when noise was added to angular rates.

The colour bar is the amount of noise in the form of signal-to-noise

ratio with unit of dB. . . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.6 Visualization of impact of noise to estimation . . . . . . . . . . . . 87

3.7 Algorithm of limb length estimator . . . . . . . . . . . . . . . . . . 91

3.8 Experimentally Determined LNT . . . . . . . . . . . . . . . . . . . 95

3.9 Experimental setup. (a) and (b) - Lifting the arm: inertial sensors

were attached close to elbow and wrist on the left arm, (c) and (d) -

Lifting the leg: inertial sensors were attached close to knee and ankle

on the right leg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

List of Figures 163

3.10 Comparison between measured length and calculated length for the

targeted limbs (A) to (D): (A) - Shoulder joint to elbow , (B) -

Shoulder joint to wrist, (C) - Hip joint to knee, (D) - Hip joint to

ankle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

3.11 The mean value between measured length and calculated length: x

axis indicates the target limbs such as 1 - Shoulder to wrist, 2 -

Shoulder to elbow, 3 - Hip to ankle and 4 - Hip to knee . . . . . . . 99

4.1 Sensor suite having 13 sensor positions . . . . . . . . . . . . . . . . 106

4.2 Exercise 1: (a) and (b) are the initial posture and end posture of

thoracic rotation, (a) and (c) are the initial posture and end posture

of body rotation with leg displacements . . . . . . . . . . . . . . . 106

4.3 Pointing exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4.4 Angular rates for thoracic rotation . . . . . . . . . . . . . . . . . . 107

4.5 Angular rates for rotation with steps . . . . . . . . . . . . . . . . . 108

4.6 Frequency spectrum after applying FFT technique . . . . . . . . . 108

4.7 Gradient analyses of angular rates . . . . . . . . . . . . . . . . . . 109

4.8 Comparison of healthy subjects and Parkinson’s patients . . . . . . 110

4.9 Magnitude in relative movement based on angular rates of a cycle . 111

4.10 Cycle time of a pointing cycle . . . . . . . . . . . . . . . . . . . . . 112

4.11 Comparison of relative orientation between upper trunk and lower

trunk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

4.12 Scatter diagrams: (A)- Cycle time and relative averaged maximum

span of a cycle, (B) - Cycle time and relative average maximum

magnitude in angular rates of a cycle, (C) - Cycle time and averaged

movement angle of hip in a cycle and (D) - Cycle time and average

maximum magnitude in angular rates of a cycle . . . . . . . . . . . 114

List of Figures 164

4.13 Classification between healthy subjects and patients: (A)- Cycle time

and relative averaged maximum span of a cycle, (B) - Cycle time and

relative average maximum magnitude in angular rates of a cycle, (C)

- Cycle time and averaged movement angle of hip in a cycle and (D)

- Cycle time and average maximum magnitude in angular rates of a

cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

4.14 (a)- Experimental Setup: Metamax metabolic measurement system

was attached to the subject while performing the treadmill based

exercises. (b) - Capturing inertial data: BioKin-WMS inertial mea-

surement sensor was attached to the subject’s ankle while performing

the treadmill based exercises. . . . . . . . . . . . . . . . . . . . . . 121

4.15 Variation of treadmill speed derived, normalized energy expenditure

(ψr) with activity levels for all test subjects . . . . . . . . . . . . . 122

4.16 (a)- Variation of rate gyro derived, normalized energy expenditure

(ψr) with activity levels for all test subjects, (b)- Variation of metabolic

measurement based, normalized energy expenditure (ψm) with ac-

tivity levels for all test subjects, (c)- Variation of treadmill speed

derived, normalized energy expenditure (ψs) with activity levels for

all test subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

5.1 Proposed architecture bridging BioKin, BioKin Mobi and BioKin

Cloud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

5.2 3D skeletal visualization of human posture . . . . . . . . . . . . . . 131

5.3 The patients and therapists interaction scenario . . . . . . . . . . . 132

5.4 Home page of the web system . . . . . . . . . . . . . . . . . . . . . 133

5.5 The overview of the tele-rehabilitation system . . . . . . . . . . . . 133

5.6 Data flow model in therapist side (except for online review) . . . . . 134

5.7 Data flow model in patient side (with online review for therapists) . 135

List of Figures 165

5.8 The conceptual architecture for analysis oriented decision support

system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

5.9 Multi-level exercise data encoding scheme . . . . . . . . . . . . . . 140

5.10 An illustration of the elbow point concept. Red points are elbow

points when κ > 0.05. Blue points with curvature less than 0.05 is

removed from the trajectory. . . . . . . . . . . . . . . . . . . . . . . 142

5.11 Numerical experimental result . . . . . . . . . . . . . . . . . . . . . 148

5.12 Setup of the real-data experiment . . . . . . . . . . . . . . . . . . . 150

5.13 Result of real-data experiment for the multi-level encoding scheme. 151

List of Tables

1.1 Length of upper limb segments . . . . . . . . . . . . . . . . . . . . 7

1.2 Angle limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 Comparison of sensor technologies use in rehabilitation . . . . . . . 18

1.4 Magnetic fields in Geelong . . . . . . . . . . . . . . . . . . . . . . . 25

1.5 Advantages and disadvantages of solutions to the Wahba’s problem 32

2.1 Root mean square error for flexion-extension exercise . . . . . . . . 45

2.2 Root mean square error for abduction-adduction exercise . . . . . . 46

2.3 Root mean square error for lifting a bottle exercise . . . . . . . . . 47

2.4 The root mean square error comparison of each methods . . . . . . 55

2.5 Advantages and disadvantages of data fusion algorithms . . . . . . 55

2.6 Averaged RMSE Error in angle estimation for arm exercises in com-

parison to Kinect c© and VICON systems based measurements . . . 73

3.1 The results of curvature after introducing noise to accelerometer

readings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.2 The results of curvature after introducing noise to gyroscope readings 86

3.3 RMSEs, error percentages with respect to the actual lengths and

mean length of measure and estimated target limb elements . . . . 98

4.1 The result of averaged relative magnitude in angular rates . . . . . 111

4.2 The result of averaged cycle time of pointing cycle . . . . . . . . . 112

4.3 The result of averaged relative maximum span . . . . . . . . . . . 112

166

167

5.1 Notations used in the process of estimating power consumption for

data encoding and transfer. Here i = 1, 2, 3, 4 for motion tele-

rehabilitation and i = 1, 2, 3 for respiratory tele-rehabilitation. . . . 144

5.2 Power consumption of various encoding scheme and encoded data

transfer for motion tele-rehabilitation. . . . . . . . . . . . . . . . . . 145

5.3 Hardware environment of the system . . . . . . . . . . . . . . . . . 147

1 Notations used in dynamic model. . . . . . . . . . . . . . . . . . . 159

Bibliography

[1] A. Bakhai, “The burden of coronary, cerebrovascular and peripheral arterial disease,” Phar-macoeconomics, vol. 22, no. 4, pp. 11–18, 2004.

[2] P. Deb, S. Sharma, and K. Hassan, “Pathophysiologic mechanisms of acute ischemic stroke:An overview with emphasis on therapeutic significance beyond thrombolysis,” Pathophysi-ology, vol. 17, no. 3, pp. 197 – 218, 2010.

[3] Stroke Association, “Stroke statistics,” http://www.stroke.org.uk, accessed: 2013-01-01.

[4] “Australia’s demographic challenges,” http://demographics.treasury.gov.au/content/download/austral04.asp, accessed: 2015-11-20.

[5] Australian Institute of Health and Welfare, National Heart Foundation ofAustralia, “Heart, stroke and vascular diseases: Australian facts 2004,”http://www.aihw.gov.au/WorkArea/DownloadAsset.aspx?id=6442454948, accessed:2016-01-27.

[6] d. J. B. Wade D, “Recent advances in rehabilitation,” Journal of British Medical, p. 320,2000.

[7] S. o. R. W. N. L. H. R. van Exel N, Koopmanschap M, “Cost-effectiveness of integratedstroke services,” Journal of Medicine, vol. 98, no. 6, pp. 415–425, 2005.

[8] P. J. Mansfield and D. A. Neumann, Essentials of Kinesiology for the Physical TherapistAssistant. Elsevier Health Sciences, 2014.

[9] N. Reese and W. Bandy, Joint Range of Motion and Muscle Length Testing, 2nd ed. USA:Saunders, 2009.

[10] N. B. Reese and W. D. Bandy, Joint range of motion and muscle length testing. ElsevierHealth Sciences, 2013.

[11] P. L. Williams et al., “Gray’s anatomy,” 1980.

[12] J. Jankovic and A. E. Lang, “Classification of movement disorders,” Neurosurgical Treatmentof Movement Disorders. Park Ridge, IL: AANS, pp. 3–18, 1998.

[13] A. P. Moore, “Classification of movement disorders,” Neuroimaging Clinics of North Amer-ica, vol. 20, no. 1, pp. 1–6, 2010.

[14] E. D. Louis, “Essential tremor,” The Lancet Neurology, vol. 4, no. 2, pp. 100–110, 2005.

[15] E. D. Louis, R. Ottman, and W. Allen Hauser, “How common is the most common adultmovement disorder? estimates of the prevalence of essential tremor throughout the world,”Movement Disorders, vol. 13, no. 1, pp. 5–10, 1998.

[16] R. Helmich, I. Toni, G. Deuschl, and B. Bloem, “The pathophysiology of essential tremorand parkinsons tremor,” Current Neurology and Neuroscience Reports, vol. 13, no. 9, pp.1–10, 2013.

168

Bibliography 169

[17] A. H. Rajput and A. Rajput, “Medical treatment of essential tremor,” Journal of Cen-tral Nervous System Disease, vol. 6, no. 4165-JCNSD-Medical-Treatment-of-Essential-Tremor.pdf, pp. 29–39, 2014.

[18] M. Bilodeau, D. A. Keen, P. J. Sweeney, R. W. Shields, and R. M. Enoka, “Strength trainingcan improve steadiness in persons with essential tremor,” Muscle & Nerve, vol. 23, no. 5,pp. 771–778, 2000.

[19] L. M. de Lau and M. M. Breteler, “Epidemiology of parkinson’s disease,” The Lancet Neu-rology, vol. 5, no. 6, pp. 525–535, 2006.

[20] C. A. Davie, “A review of parkinson’s disease,” British medical bulletin, vol. 86, no. 1, pp.109–127, 2008.

[21] Z.-X. Zhang, G. C. Roman, Z. Hong, C.-B. Wu, Q.-M. Qu, J.-B. Huang, B. Zhou, Z.-P.Geng, J.-X. Wu, H.-B. Wen, H. Zhao, and G. E. P. Zahner, “Parkinson’s disease in china:prevalence in beijing, xian, and shanghai,” The Lancet, vol. 365, no. 9459, pp. 595–597,2005.

[22] I. Niehaus and J. Lange, “Endotoxin: is it an environmental factor in the cause of parkinson’sdisease?” Occupational and environmental medicine, vol. 60, no. 5, p. 378, 2003.

[23] M. Paolini, A. Sapone, and F. J. Gonzalez, “Parkinson’s disease, pesticides and individualvulnerability,” Trends in Pharmacological Sciences, vol. 25, no. 3, pp. 124–129, 2004.

[24] M. E. Morris, “Movement disorders in people with parkinson disease: A model for physicaltherapy,” Physical Therapy, vol. 80, no. 6, pp. 578–597, 2000.

[25] Y. Sharabi, S.-T. Li, R. Dendi, C. Holmes, and D. Goldstein, “Neurotransmitter specificityof sympathetic denervation in parkinsons disease,” Neurology, vol. 60, no. 6, pp. 1036–1039,2003.

[26] S. H. Keus, B. R. Bloem, E. J. Hendriks, A. B. BrederoCohen, and M. Munneke, “Evidence-based analysis of physical therapy in parkinson’s disease with recommendations for practiceand research,” Movement Disorders, vol. 22, no. 4, pp. 451–460, 2007.

[27] C. Warlow, J. van Gijn, M. Dennis, J. Wardlaw, J. Bamford, G. Hankey, P. Sandercock,G. Rinkel, P. Langhorne, C. Sudlow, and P. Rothwell, Introduction. Blackwell PublishingLtd, 2008, pp. 1–5.

[28] P. Langhorne, F. Coupar, and A. Pollock, “Motor recovery after stroke: a systematic re-view,” The Lancet Neurology, vol. 8, no. 8, pp. 741–754, 2009.

[29] K. Strong, C. Mathers, and R. Bonita, “Preventing stroke: saving lives around the world,”The Lancet Neurology, vol. 6, no. 2, pp. 182–187, 2007.

[30] Panel, R. L. Sacco, E. J. Benjamin, J. P. Broderick, M. Dyken, J. D. Easton, W. M. Feinberg,L. B. Goldstein, P. B. Gorelick, G. Howard, S. J. Kittner, T. A. Manolio, J. P. Whisnant,and P. A. Wolf, “Risk factors,” Stroke, vol. 28, no. 7, pp. 1507–1517, 1997.

[31] J. Jordn, I. Ikuta, J. Garca-Garca, S. Calleja, and T. Segura, “Stroke pathophysiology: man-agement challenges and new treatment advances,” Journal of Physiology and Biochemistry,vol. 63, no. 3, pp. 261–277, 2007.

[32] A. Pollock, G. Baer, P. Langhorne, and V. Pomeroy, “Physiotherapy treatment approachesfor the recovery of postural control and lower limb function following stroke: a systematicreview,” Clinical Rehabilitation, vol. 21, no. 5, pp. 395–410, 2007.

[33] J. Newman, H. Zhou, and H. Hu, “Inertial sensors for motion detection of human upperlimbs,” Sensor Review, vol. 27, no. 2, pp. 151–158, 2007.

[34] H. Zhou and H. Hu, “Human motion tracking for rehabilitationa survey,” Biomedical SignalProcessing and Control, vol. 3, no. 1, pp. 1–18, 2008.

Bibliography 170

[35] Y. Zhang, H. Hu, and H. Zhou, “Study on adaptive kalman filtering algorithms in humanmovement tracking,” in Information Acquisition, 2005 IEEE International Conference on,June 2005, pp. 11 – 15.

[36] J. Isacson, L. Gransberg, and E. Knutsson, “Three-dimensional electrogoniometric gaitrecording,” Journal of Biomechanics, vol. 19, no. 8, pp. 627 – 635, 1986. [Online]. Available:http://www.sciencedirect.com/science/article/pii/0021929086901685

[37] C. G. A. H. R. Y. L. Kambiz Saber-Sheikh, Elizabeth C. Bryant, “Feasibility of using inertialsensors to assess human movement,” Journal of Manual Therapy, vol. 15, no. 1, pp. 122 –125, February 2010.

[38] http://www.vicon.com/, accessed: 2016-03-06.

[39] M. S. Karunarathne, S. W. Ekanayake, and P. N. Pathirana, “An adaptive complementaryfilter for inertial sensor based data fusion to track upper body motion,” in 7th InternationalConference on Information and Automation for Sustainability, Dec 2014, pp. 1–5.

[40] Y. Tao and H. Hu, “Building a visual tracking system for home-based rehabilitation,” inProc. of the 9th Chinese Automation and Computing Society Conf. In the UK, 2003, pp.343 – 448.

[41] J. P. Joanne k. Gronley, “Gait analysis techniques: Rancho los amigos hospital gait labo-ratory,” Journal of the Amarican Physical Therapy Asscoiciation and Physical Theraphy,vol. 64, pp. 1831–1838, 1984.

[42] M. Windolf, N. Gotzen, and M. Morlock, “Systematic accuracy and precision analysis ofvideo motion capturing systemsexemplified on the vicon-460 system,” Journal of biome-chanics, vol. 41, no. 12, pp. 2776–2780, 2008.

[43] M. S. Karunarathne, S. Li, S. W. Ekanayake, and P. N. Pathirana, “A machine-drivenprocess for human limb length estimation using inertial sensors,” in 2015 IEEE 10th In-ternational Conference on Industrial and Information Systems (ICIIS). IEEE, 2015, pp.429–433.

[44] http://www.qualisys.se/, accessed: 2016-03-06.

[45] Z. Zhengyou, “Microsoft kinect sensor and its effect,” MultiMedia, IEEE, vol. 19, no. 2, pp.4–10, 2012.

[46] https://www.ifixit.com/Teardown/Xbox+360+Kinect+Teardown/4066, accessed: 2015-05-22.

[47] L. Wang, R. Vanderhout, and T. Shi, “Computer vision detection of negative obstacles withthe microsoft kinect,” 2012.

[48] A. Shpunt and Z. Zalevsky, “Depth-varying light fields for three dimensional sensing,”2008. [Online]. Available: http://www.google.com/patents/US20080106746

[49] H. Gonzalez-Jorge, B. Riveiro, E. Vazquez-Fernandez, J. Martnez-Snchez, and P. Arias,“Metrological evaluation of microsoft kinect and asus xtion sensors,” Measurement, vol. 46,no. 6, pp. 1800–1806, 2013.

[50] P. Grossmann, “Depth from focus,” Pattern Recognition Letters, vol. 5, no. 1, pp. 63–69,1987.

[51] E. Lachat, H. Macher, M. Mittet, T. Landes, and P. Grussenmeyer, “First experiences withkinect v2 sensor for close range 3d modelling,” The International Archives of Photogram-metry, Remote Sensing and Spatial Information Sciences, vol. 40, no. 5, p. 93, 2015.

[52] http://blog.zopper.com/microsoft-announces-kinect-windows-v2-available-pre-order/,accessed: 2015-05-22.

Bibliography 171

[53] D. Webster and O. Celik, “Experimental evaluation of microsoft kinect’s accuracy and cap-ture rate for stroke rehabilitation applications,” in 2014 IEEE Haptics Symposium (HAP-TICS), Feb 2014, pp. 455–460.

[54] S. Obdrzalek, G. Kurillo, F. Ofli, R. Bajcsy, E. Seto, H. Jimison, and M. Pavel, “Accuracyand robustness of kinect pose estimation in the context of coaching of elderly population,” inEngineering in medicine and biology society (EMBC), 2012 annual international conferenceof the IEEE. IEEE, 2012, pp. 1188–1193.

[55] X. Xu and R. W. McGorry, “The validity of the first and second generation microsoft kinectfor identifying joint center locations during static postures,” Applied Ergonomics, vol. 49,no. 0, pp. 47–54, 2015.

[56] D. Antn, A. Goni, A. Illarramendi, J. J. Torres-Unda, and J. Seco, “Kires: A kinect-basedtelerehabilitation system,” in e-Health Networking, Applications & Services (Healthcom),2013 IEEE 15th International Conference on, pp. 444–448.

[57] L. Luna-Oliva, R. M. Ortiz-Gutirrez, R. Cano-de la Cuerda, R. M. Pidrola, I. M. Alguacil-Diego, C. Snchez-Camarero, and M. d. C. Martnez Culebras, “Kinect xbox 360 as a ther-apeutic modality for children with cerebral palsy in a school environment: A preliminarystudy,” NeuroRehabilitation, vol. 33, no. 4, pp. 513–521, 2013.

[58] R. Ortiz-Gutirrez, R. Cano-de-la Cuerda, F. Galn-del Ro, I. M. Alguacil-Diego, D. Palacios-Cea, and J. C. Miangolarra-Page, “A telerehabilitation program improves postural controlin multiple sclerosis patients: a spanish preliminary study,” International journal of envi-ronmental research and public health, vol. 10, no. 11, pp. 5697–5710, 2013.

[59] Y. Zhang, Y. Fei, L. Xu, and G. Sun, “Micro-imu-based motion tracking system for virtualtraining,” in Control Conference (CCC), 2015 34th Chinese, July 2015, pp. 7753–7758.

[60] S. Tseng, W.-L. Li, C.-Y. Sheng, J.-W. Hsu, and C.-S. Chen, “Motion and attitude es-timation using inertial measurements with complementary filter,” in Control Conference(ASCC), 2011 8th Asian, May 2011, pp. 863–868.

[61] Y. Uno, M. Kawato, and R. Suzuki, “Formation and control of optimal trajectory in humanmultijoint arm movement,” Biological cybernetics, vol. 61, no. 2, pp. 89–101, 1989.

[62] E. Nebot and H. Durrant-Whyte, “Initial calibration and alignment of low-cost inertialnavigation units for land vehicle applications,” Journal of Robotic Systems, vol. 16, no. 2,pp. 81–92, 1999.

[63] J. Zhao and N. I. Badler, “Inverse kinematics positioning using nonlinear programmingfor highly articulated figures,” ACM Transactions on Graphics (TOG), vol. 13, no. 4, pp.313–336, 1994.

[64] S. You, U. Neumann, and R. Azuma, “Hybrid inertial and vision tracking for augmentedreality registration,” in Virtual Reality, 1999. Proceedings., IEEE. IEEE, 1999, pp. 260–267.

[65] M. C. Boonstra, R. M. van der Slikke, N. L. Keijsers, R. C. van Lummel, M. C. de Waal Male-fijt, and N. Verdonschot, “The accuracy of measuring the kinematics of rising from a chairwith accelerometers and gyroscopes,” Journal of biomechanics, vol. 39, no. 2, pp. 354–358,2006.

[66] S. O. Madgwick, “An efficient orientation filter for inertial and inertial/magnetic sensorarrays,” Report x-io and University of Bristol (UK), 2010.

[67] D. Simsık, J. Karchnak, B. Jobbagy, and A. Galajdova, “Design of inertial module forrehabilitation device,” in 11th International Symposium on Applied Machine Intelligenceand Informatics, 2013, pp. 33–36.

[68] O. J. Woodman, “An introduction to inertial navigation,” University of Cambridge, Com-puter Laboratory, Tech. Rep. UCAMCL-TR-696, vol. 14, p. 15, 2007.

Bibliography 172

[69] W. Flenniken, J. Wall, and D. Bevly, “Characterization of various imu error sources andthe effect on navigation performance,” in ION GNSS, 2005, pp. 967–978.

[70] https://www.xsens.com/products/mti/, accessed: 2016-03-07.

[71] K. Zhang, P. Werner, M. Sun, F. X. Pi-Sunyer, and C. N. Boozer, “Measurement of humandaily physical activity,” Obesity research, vol. 11, no. 1, pp. 33–40, 2003.

[72] S. L. Kozey, K. Lyden, C. A. Howe, J. W. Staudenmayer, and P. S. Freedson, “Accelerometeroutput and met values of common physical activities,” Medicine and science in sports andexercise, vol. 42, no. 9, p. 1776, 2010.

[73] D. Rowlands, T. McNab, L. Laakso, and D. James, “Cloud based activity monitoring sys-tem for health and sport,” in Neural Networks (IJCNN), The 2012 International JointConference on, June 2012, pp. 1–5.

[74] H. B. Menz, S. R. Lord, and R. C. Fitzpatrick, “Acceleration patterns of the head andpelvis when walking on level and irregular surfaces,” Gait & posture, vol. 18, no. 1, pp.35–46, 2003.

[75] M. Henriksen, H. Lund, R. Moe-Nilssen, H. Bliddal, and B. Danneskiod-Samsøe, “Test–retest reliability of trunk accelerometric gait analysis,” Gait & posture, vol. 19, no. 3, pp.288–297, 2004.

[76] R. Moe-Nilssen and J. L. Helbostad, “Interstride trunk acceleration variability but not stepwidth variability can differentiate between fit and frail older adults,” Gait & posture, vol. 21,no. 2, pp. 164–170, 2005.

[77] T. Jamsa, A. Vainionpaa, R. Korpelainen, E. Vihriala, and J. Leppaluoto, “Effect of dailyphysical activity on proximal femur,” Clinical Biomechanics, vol. 21, no. 1, pp. 1–7, 2006.

[78] J. J. Kavanagh, S. Morrison, D. A. James, and R. Barrett, “Reliability of segmental ac-celerations measured using a new wireless gait analysis system,” Journal of biomechanics,vol. 39, no. 15, pp. 2863–2872, 2006.

[79] J. K. Sinha, “On standardisation of calibration procedure for accelerometer,” Journal ofSound and Vibration, vol. 286, no. 1, pp. 417–427, 2005.

[80] C. V. Bouten, K. Koekkoek, M. Verduin, R. Kodde, and J. D. Janssen, “A triaxial ac-celerometer and portable data processing unit for the assessment of daily physical activity,”Biomedical Engineering, IEEE Transactions on, vol. 44, no. 3, pp. 136–147, 1997.

[81] S. Microelectronics, “Using lsm303dlh for a tilt compensated electronic compass,”http://www. st. com/stonline/products/literature/an/17, vol. 3, no. 5, p. 3, 2010.

[82] S. Bonnet and R. Heliot, “A magnetometer-based approach for studying human move-ments,” Biomedical Engineering, IEEE Transactions on, vol. 54, no. 7, pp. 1353–1355,2007.

[83] E. R. Bachmann, X. Yun, and C. W. Peterson, “An investigation of the effects of magneticvariations on inertial/magnetic orientation sensors,” in Robotics and Automation, 2004.Proceedings. ICRA’04. 2004 IEEE International Conference on, vol. 2. IEEE, 2004, pp.1115–1122.

[84] K. Tong and M. H. Granat, “A practical gait analysis system using gyroscopes,” Medicalengineering & physics, vol. 21, no. 2, pp. 87–94, 1999.

[85] B. Coley, B. Najafi, A. Paraschiv-Ionescu, and K. Aminian, “Stair climbing detection duringdaily physical activity using a miniature gyroscope,” Gait & posture, vol. 22, no. 4, pp. 287–294, 2005.

[86] R. Y. Lee, J. Laprade, and E. H. Fung, “A real-time gyroscopic system for three-dimensionalmeasurement of lumbar spine motion,” Medical engineering & physics, vol. 25, no. 10, pp.817–824, 2003.

Bibliography 173

[87] S. Belongie, “Rodrigues rotation formula,” MathWorld–A Wolfram Web Resource, 1999.

[88] S. O. Madgwick, A. J. Harrison, and R. Vaidyanathan, “Estimation of imu and marg orien-tation using a gradient descent algorithm,” in Rehabilitation Robotics (ICORR), 2011 IEEEInternational Conference on. IEEE, 2011, pp. 1–7.

[89] G. Wahba, “A least squares estimate of satellite attitude,” SIAM review, vol. 7, no. 3, pp.409–409, 1965.

[90] F. L. Markley and D. Mortari, “Quaternion attitude estimation using vector observations.”Journal of the Astronautical Sciences, vol. 48, no. 2, pp. 359–380, 2000.

[91] F. L. Markley and D. Mortari, “How to estimate attitude from vector observations,” 1999.

[92] S. M. R. C. P. Lima, “Comparison of small satellite attitude determination methods,” p. 1,2000.

[93] F. L. Markley and J. L. Crassidis, Fundamentals of spacecraft attitude determination andcontrol. Springer, 2014, vol. 33.

[94] M. D. Shuster and W. F. Dellinger, “Spacecraft attitude determination and control,” Fun-damentals of Space Systems, pp. 236–325, 1994.

[95] J. R. Wertz, Spacecraft attitude determination and control. Springer Science & BusinessMedia, 2012, vol. 73.

[96] M. J. Sidi, Spacecraft dynamics and control: a practical engineering approach. Cambridgeuniversity press, 1997, vol. 7.

[97] X. Yun and E. Bachmann, “Design, implementation, and experimental results of aquaternion-based kalman filter for human body motion tracking,” Robotics, IEEE Transac-tions on, vol. 22, no. 6, pp. 1216–1227, Dec 2006.

[98] M. D. Shuster, “A survey of attitude representations,” Navigation, vol. 8, no. 9, pp. 439–517,1993.

[99] H. D. Black, “Early development of transit, the navy navigation satellite system,” Journalof Guidance, Control, and Dynamics, vol. 13, no. 4, pp. 577–585, 1990.

[100] C. Hajiyev, D. Cilden, and Y. Somov, “Gyroless attitude and rate estimation of smallsatellites using singular value decomposition and extended kalman filter,” in CarpathianControl Conference (ICCC), 2015 16th International, May 2015, pp. 159–164.

[101] F. L. Markley, “Attitude determination using vector observations and the singular valuedecomposition,” The Journal of the Astronautical Sciences, vol. 36, no. 3, pp. 245–258,1988.

[102] F. C. Moon, The Machines of Leonardo Da Vinci and Franz Reuleaux: kinematics of ma-chines from the Renaissance to the 20th Century. Springer, 2007, vol. 2.

[103] P. B. Davenport, A vector approach to the algebra of rotations with applications. NationalAeronautics and Space Administration, 1968, vol. 4696.

[104] M. D. Shuster, “Approximate algorithms for fast optimal attitude computation,” in Guid-ance and Control Conference, vol. 1, 1978, pp. 88–95.

[105] F. L. Markley, “Equivalence of two solutions of wahbas problem,” The Journal of the As-tronautical Sciences, vol. 60, no. 3-4, pp. 303–312, 2013.

[106] J. Music, R. Kamnik, and M. Munih, “Model based inertial sensing of human body motionkinematics in sit-to-stand movement,” Simulation Modelling Practice and Theory, vol. 16,no. 8, pp. 933–944, 2008.

Bibliography 174

[107] M. S. Karunarathne, N. D. Nguyen, M. P. Menikidiwela, and P. N. Pathirana, The Studyto Track Human Arm Kinematics Applying Solutions of Wahba’s Problem upon Iner-tial/Magnetic Sensors. Cham: Springer International Publishing, 2016, pp. 395–406.

[108] M. S. Karunarathne, S. Li, S. W. Ekanayake, and P. N. Pathirana, “An adaptive orientationmisalignment calibration method for shoulder movements using inertial sensors: A feasibilitystudy,” in Bioelectronics and Bioinformatics (ISBB), 2015 International Symposium on, Oct2015, pp. 99–102.

[109] G. L. Williams, M. S. Karunarathne, S. W. Ekanayake, and P. N. Pathirana, AmbulatoryEnergy Expenditure Evaluation for Treadmill Exercises. Cham: Springer InternationalPublishing, 2015, pp. 331–336.

[110] M. S. Karunarathne, S. A. Jones, S. W. Ekanayake, and P. N. Pathirana, “Remote moni-toring system enabling cloud technology upon smart phones and inertial sensors for humankinematics,” in Big Data and Cloud Computing (BdCloud), 2014 IEEE Fourth InternationalConference on, Dec 2014, pp. 137–142.

[111] S. Li, H. T. Pham, M. S. Karunarathne, Y. S. Lee, S. W. Ekanayake, and P. N. Pathirana,“A mobile cloud computing framework integrating multilevel encoding for performance mon-itoring in telerehabilitation,” Mathematical Problems in Engineering, vol. 2015, p. 14, 2015.

[112] P. Cerveri, A. Pedotti, and G. Ferrigno, “Robust recovery of human mo-tion from video using kalman filters and virtual humans,” Human Move-ment Science, vol. 22, no. 3, pp. 377 – 404, 2003. [Online]. Available:http://www.sciencedirect.com/science/article/pii/S0167945703000046

[113] X. Yun and E. R. Bachmann, “Design, implementation, and experimental results of aquaternion-based kalman filter for human body motion tracking,” Robotics, IEEE Transac-tions on, vol. 22, no. 6, pp. 1216–1227, 2006.

[114] M. Euston, P. Coote, R. Mahony, J. Kim, and T. Hamel, “A complementary filter forattitude estimation of a fixed-wing uav,” in Intelligent Robots and Systems, 2008. IROS2008. IEEE/RSJ International Conference on, Sept 2008, pp. 340–345.

[115] J. Vasconcelos, C. Silvestre, P. Oliveira, P. Batista, and B. Cardeira, “Discrete time-varyingattitude complementary filter,” in American Control Conference, 2009. ACC ’09., June2009, pp. 4056–4061.

[116] S. K. Hong, “Fuzzy logic based closed-loop strapdown attitude system for unmanned aerialvehicle (uav),” Journal of Sensors and Actuators A: Physical, vol. 107, no. 2, pp. 109 – 118,2003.

[117] R. E. Kalman, “A new approach to linear filtering and prediction problems,” Journal ofbasic Engineering, vol. 82, no. 1, pp. 35–45, 1960.

[118] “The president’s national medal of science: Recipient details,”http://www.nsf.gov/od/nms/recipdetails.jsp, accessed: 2016-03-29.

[119] M. I. Ribeiro, “Kalman and extended kalman filters: Concept, derivation and properties,”Institute for Systems and Robotics, p. 43, 2004.

[120] L. Kleeman, “Understanding and applying kalman filtering,” in Proceedings of the SecondWorkshop on Perceptive Systems, Curtin University of Technology, Perth Western Australia(25-26 January 1996), 1996.

[121] R. Azuma and G. Bishop, “Improving static and dynamic registration in an optical see-through hmd,” in Proceedings of the 21st Annual Conference on Computer Graphics andInteractive Techniques, ser. SIGGRAPH ’94. New York, NY, USA: ACM, 1994, pp. 197–204.

Bibliography 175

[122] R. Azuma and G. Bishop, “A frequency-domain analysis of head-motion prediction,” inProceedings of the 22nd annual conference on Computer graphics and interactive techniques.ACM, 1995, pp. 401–408.

[123] E. Foxlin, “Pedestrian tracking with shoe-mounted inertial sensors,” IEEE Computer Graph-ics and Applications, vol. 25, no. 6, pp. 38–46, Nov 2005.

[124] S. Wan and E. Foxlin, “Improved pedestrian navigation based on drift-reduced mems imuchip,” in Proceedings of the 2010 International Technical Meeting of the The Institute ofNavigation, San Diego, CA, USA, vol. 2527, 2010, pp. 220–229.

[125] J. L. Marins, X. Yun, E. R. Bachmann, R. B. McGhee, and M. J. Zyda, “An extendedkalman filter for quaternion-based orientation estimation using marg sensors,” in IntelligentRobots and Systems, 2001. Proceedings. 2001 IEEE/RSJ International Conference on, vol. 4.IEEE, 2001, pp. 2003–2011.

[126] E. R. Bachmann, “Inertial and magnetic tracking of limb segment orientation for insertinghumans into synthetic environments,” DTIC Document, Tech. Rep., 2000.

[127] A. M. Sabatini, “A digital signal-processing technique for compensating ultrasonic sensors,”Instrumentation and Measurement, IEEE Transactions on, vol. 44, no. 4, pp. 869–874, 1995.

[128] A. M. Sabatini, “Quaternion-based extended kalman filter for determining orientation byinertial and magnetic sensing,” Biomedical Engineering, IEEE Transactions on, vol. 53,no. 7, pp. 1346–1356, 2006.

[129] A. M. Sabatini, “Estimating three-dimensional orientation of human body parts by iner-tial/magnetic sensing,” Sensors, vol. 11, no. 2, pp. 1489–1525, 2011.

[130] G. Ligorio and A. M. Sabatini, “Extended kalman filter-based methods for pose estima-tion using visual, inertial and magnetic sensors: Comparative analysis and performanceevaluation,” Sensors, vol. 13, no. 2, pp. 1919–1941, 2013.

[131] I. R. Petersen and A. V. Savkin, Robust Kalman filtering for signals and systems with largeuncertainties. Springer Science & Business Media, 1999.

[132] A. V. Savkin and I. R. Petersen, “Robust state estimation and model validation for discrete-time uncertain systems with a deterministic description of noise and uncertainty,” Automat-ica, vol. 34, no. 2, pp. 271–274, 1998.

[133] P. N. Pathirana, N. Bulusu, A. V. Savkin, and S. Jha, “Node localization using mobile robotsin delay-tolerant sensor networks,” Mobile Computing, IEEE Transactions on, vol. 4, no. 3,pp. 285–296, 2005.

[134] I. R. Manchester and A. V. Savkin, “Circular navigation missile guidance with incompleteinformation and uncertain autopilot model,” Journal of guidance, control, and dynamics,vol. 27, no. 6, pp. 1078–1083, 2004.

[135] V. Malyavej, I. R. Manchester, and A. V. Savkin, “Precision missile guidance usingradar/multiple-video sensor fusion via communication channels with bit-rate constraints,”Automatica, vol. 42, no. 5, pp. 763–769, 2006.

[136] I. R. Manchester, A. V. Savkin, and F. A. Faruqi, “Optical-flow based precision missileguidance inspired by honeybee navigation,” in 42nd IEEE Conference on Decision andControl, 2003, pp. 5444–5449.

[137] W. T. Higgins, “A comparison of complementary and kalman filtering,” IEEE Transactionson Aerospace and Electronic Systems, vol. 11, no. 3, pp. 321–325, 1975.

[138] X. Yun and E. R. Bachmann, “Design, implementation, and experimental results of aquaternion-based kalman filter for human body motion tracking,” IEEE Transactions onRobotics, vol. 22, no. 6, pp. 1216–1227, December 2006.

Bibliography 176

[139] A. Kim and M. F. Golnaraghi, “A quaternion-based orientation estimation algorithm us-ing an inertial measurement unit,” in Position Location and Navigation Symposium, 2004.PLANS 2004, April 2004, pp. 268–272.

[140] V. Rovenski, Curvature and Torsion of Curves. Boston, MA: Birkhauser Boston, 2000, pp.125–132.

[141] L. Saiyi, M. Ferraro, T. Caelli, and P. N. Pathirana, “A syntactic two-component encodingmodel for the trajectories of human actions,” Biomedical and Health Informatics, IEEEJournal of, vol. 18, no. 6, pp. 1903–1914, 2014.

[142] B. R. Mandelbaum, M. S. Myerson, and R. Forster, “Achilles tendon ruptures a new methodof repair, early range of motion, and functional rehabilitation,” The American Journal ofSports Medicine, vol. 23, no. 4, pp. 392–395, 1995.

[143] D. Jack, R. Boian, A. S. Merians, M. Tremaine, G. C. Burdea, S. V. Adamovich, M. Recce,and H. Poizner, “Virtual reality-enhanced stroke rehabilitation,” IEEE Transactions onNeural Systems and Rehabilitation Engineering, vol. 9, no. 3, pp. 308–318, Sept 2001.

[144] G. Fleisig, S. Barrentine, R. Escamilla, and J. Andrews, “Biomechanics of overhand throwingwith implications for injuries,” Sports Medicine, vol. 21, no. 6, pp. 421–437, 1996.

[145] Z. Luo, C. K. Lim, W. Yang, K. Y. Tee, K. Li, C. Gu, K. D. Nguen, I.-M. Chen, andS. H. Yeo, “An interactive therapy system for arm and hand rehabilitation,” in RoboticsAutomation and Mechatronics (RAM), 2010 IEEE Conference on, June 2010, pp. 9–14.

[146] D. Roetenberg, H. Luinge, and P. Slycke, “Xsens mvn: full 6dof human motion trackingusing miniature inertial sensors,” Xsens Motion Technologies BV, Tech. Rep, 2009.

[147] E. Nebot and H. Durrant-Whyte, “Initial calibration and alignment of low-cost inertialnavigation units for land vehicle applications,” Journal of Robotic Systems, vol. 16, no. 2,pp. 81–92, 1999.

[148] I. Prayudi and D. Kim, “Design and implementation of imu-based human arm motioncapture system,” in Mechatronics and Automation (ICMA), 2012 International Conferenceon. IEEE, 2012, pp. 670–675.

[149] J. Favre, R. Aissaoui, B. Jolles, J. de Guise, and K. Aminian, “Functional calibration pro-cedure for 3d knee joint angle description using inertial sensors,” Journal of Biomechanics,vol. 42, no. 14, pp. 2330 – 2335, 2009.

[150] N. Yazdi, F. Ayazi, and K. Najafi, “Micromachined inertial sensors,” Proceedings of theIEEE, vol. 86, no. 8, pp. 1640–1659, Aug 1998.

[151] V. Grecu, L. Grecu, M. Demian, and G. Demian, “A virtual system for simulation of humanupper limb,” in Proceedings of the World Congress on Engineerin g (WCE), London, UK.Citeseer, 2009.

[152] B. Gurney, “Leg length discrepancy,” Gait & posture, vol. 15, no. 2, pp. 195–206, 2002.

[153] H. T. Nguyen, D. N. Resnick, S. G. Caldwell, E. W. Elston, B. B. Bishop, J. B. Steinhouser,T. J. Gimmillaro, and J. C. Keating, “Interexaminer reliability of activator method’s rel-ative leg-length evaluation in the prone extended position,” Journal of manipulative andphysiological therapeutics, vol. 22, no. 9, pp. 565–569, 1999.

[154] P. Gibbons, C. Dumper, and C. Gosling, “Inter-examiner and intra-examiner agreement forassessing simulated leg length inequality using palpation and observation during a standingassessment,” Journal of Osteopathic Medicine, vol. 5, no. 2, pp. 53–58, 2002.

[155] S. I. Subotnick, “Limb length discrepancies of the lower extremity (the short leg syndrome),”Journal of Orthopaedic & Sports Physical Therapy, vol. 3, no. 1, pp. 11–16, 1981.

Bibliography 177

[156] A. L. Woerman and S. A. Binder-Macleod, “Leg length discrepancy assessment: accuracyand precision in five clinical methods of evaluation*,” Journal of Orthopaedic & SportsPhysical Therapy, vol. 5, no. 5, pp. 230–239, 1984.

[157] D. Reid and B. Smith, “Leg length inequality: a review of etiology and management,”Physiotherapy Canada, vol. 36, no. 4, pp. 177–182, 1984.

[158] H. Junker, O. Amft, P. Lukowicz, and G. Trster, “Gesture spotting with body-worn inertialsensors to detect user activities,” Pattern Recognition, vol. 41, no. 6, pp. 2010 – 2024, 2008.

[159] K. Altun, B. Barshan, and O. Tunel, “Comparative study on classifying human activitieswith miniature inertial and magnetic sensors,” Pattern Recognition, vol. 43, no. 10, pp. 3605– 3620, 2010.

[160] A. Avci, S. Bosch, M. Marin-Perianu, R. Marin-Perianu, and P. Havinga, “Activity recog-nition using inertial sensing for healthcare, wellbeing and sports applications: A survey,” inArchitecture of computing systems (ARCS), 2010 23rd international conference on. VDE,2010, pp. 1–10.

[161] O. Amft and G. Trster, “Recognition of dietary activity events using on-body sensors,”Artificial Intelligence in Medicine, vol. 42, no. 2, pp. 121 – 136, 2008, wearable Computingand Artificial Intelligence for Healthcare Applications.

[162] Y. Tao, H. Hu, and H. Zhou, “Integration of vision and inertial sensors for 3d arm motiontracking in home-based rehabilitation,” The International Journal of Robotics Research,vol. 26, no. 6, pp. 607–624, 2007.

[163] H. Zhou, H. Hu, N. D. Harris, and J. Hammerton, “Applications of wearable inertial sensorsin estimation of upper limb movements,” Biomedical Signal Processing and Control, vol. 1,no. 1, pp. 22–32, 2006.

[164] S. Madgwick, A. Harrison, and R. Vaidyanathan, “Estimation of imu and marg orienta-tion using a gradient descent algorithm,” in Rehabilitation Robotics (ICORR), 2011 IEEEInternational Conference on, June 2011, pp. 1–7.

[165] M. Marschollek, “A method to find generic thresholds for identifying relevant physical ac-tivity events in sensor data,” Journal of medical systems, vol. 40, no. 1, pp. 1–8, 2016.

[166] J. S. Richman, D. E. Lake, and J. Moorman, “Sample entropy,” in Numerical ComputerMethods, Part E, ser. Methods in Enzymology. Academic Press, 2004, vol. 384, pp. 172 –184.

[167] J. S. Richman and J. R. Moorman, “Physiological time-series analysis using approximateentropy and sample entropy,” American Journal of Physiology-Heart and Circulatory Phys-iology, vol. 278, no. 6, pp. H2039–H2049, 2000.

[168] X. Chen, I. Solomon, and K. Chon, “Comparison of the use of approximate entropy andsample entropy: applications to neural respiratory signal.” in Conference proceedings:...Annual International Conference of the IEEE Engineering in Medicine and Biology Society.IEEE Engineering in Medicine and Biology Society. Annual Conference, vol. 4, 2004, pp.4212–4215.

[169] C. E. Clauser, J. T. McConville, and J. W. Young, “Weight, volume, and center of mass ofsegments of the human body,” DTIC Document, Tech. Rep., 1969.

[170] S. W. Ekanayake, A. J. Morris, M. Forrester, and P. N. Pathirana, “Biokin: an ambulatoryplatform for gait kinematic and feature assessment,” Healthcare Technology Letters, vol. 2,no. 1, pp. 40–45, 2015.

[171] N. Abaid, P. Cappa, E. Palermo, M. Petrarca, and M. Porfiri, “Gait detection in childrenwith and without hemiplegia using single-axis wearable gyroscopes,” PloS one, vol. 8, no. 9,p. e73152, 2013.

Bibliography 178

[172] R. C. Gonzalez, A. M. Lopez, J. Rodriguez-Urıa, D. Alvarez, and J. C. Alvarez, “Real-timegait event detection for normal subjects from lower trunk accelerations,” Gait & posture,vol. 31, no. 3, pp. 322–325, 2010.

[173] S. J. M. Bamberg, A. Y. Benbasat, D. M. Scarborough, D. E. Krebs, and J. A. Paradiso,“Gait analysis using a shoe-integrated wireless sensor system,” Information Technology inBiomedicine, IEEE Transactions on, vol. 12, no. 4, pp. 413–423, 2008.

[174] K. Aminian, B. Najafi, C. Bula, P.-F. Leyvraz, and P. Robert, “Spatio-temporal param-eters of gait measured by an ambulatory system using miniature gyroscopes,” Journal ofbiomechanics, vol. 35, no. 5, pp. 689–699, 2002.

[175] J. Bae and M. Tomizuka, “Gait phase analysis based on a hidden markov model,” Mecha-tronics, vol. 21, no. 6, pp. 961–970, 2011.

[176] M. Hansen, M. K. Haugland, and T. Sinkjær, “Evaluating robustness of gait event detec-tion based on machine learning and natural sensors,” Neural Systems and RehabilitationEngineering, IEEE Transactions on, vol. 12, no. 1, pp. 81–88, 2004.

[177] C. B. Liden, M. Wolowicz, J. Stivoric, A. Teller, S. Vishnubhatla, R. Pelletier, J. Farring-don, and S. Boehmke, “Accuracy and reliability of the sensewear armband as an energyexpenditure assessment device,” BodyMedia White Papers, 2002.

[178] C. Olanow and W. Tatton, “Etiology and pathogenesis of parkinson’s disease,” Annualreview of neuroscience, vol. 22, no. 1, pp. 123–144, 1999.

[179] B. R. Bloem, Y. A. Grimbergen, M. Cramer, M. Willemsen, and A. H. Zwinderman,“Prospective assessment of falls in parkinson’s disease,” Journal of neurology, vol. 248,no. 11, pp. 950–958, 2001.

[180] P.-Y. Chou and S.-C. Lee, “Turning deficits in people with parkinson’s disease,” Tzu ChiMedical Journal, vol. 25, no. 4, pp. 200–202, 2013.

[181] S. Rahman, H. J. Griffin, N. P. Quinn, and M. Jahanshahi, “Quality of life in parkinson’sdisease: the relative importance of the symptoms,” Movement Disorders, vol. 23, no. 10,pp. 1428–1434, 2008.

[182] R. Van Emmerik and R. Wagenaar, “Dynamics of movement coordination and tremor duringgait in parkinson’s disease,” Human Movement Science, vol. 15, no. 2, pp. 203–235, 1996.

[183] R. E. Van Emmerik, R. C. Wagenaar, A. Winogrodzka, and E. C. Wolters, “Identificationof axial rigidity during locomotion in parkinson disease,” Archives of physical medicine andrehabilitation, vol. 80, no. 2, pp. 186–191, 1999.

[184] G. Buzsaki, A. Smith, S. Berger, L. Fisher, F. Gage, G. Aston-Jones, and F. Bloom, “Petitmal epilepsy and parkinsonian tremor: hypothesis of a common pacemaker,” Neuroscience,vol. 36, no. 1, pp. 1–14, 1990.

[185] B. Mariani, C. Hoskovec, S. Rochat, C. Bula, J. Penders, and K. Aminian, “3d gait assess-ment in young and elderly subjects using foot-worn inertial sensors,” Journal of biomechan-ics, vol. 43, no. 15, pp. 2999–3006, 2010.

[186] R. Margaria, P. Cerretelli, P. Aghemo, and G. Sassi, “Energy cost of running,” Journal ofApplied Physiology, vol. 18, pp. 367–370, 1962.

[187] A. Panagiota, S. Layal, and H. Stefan, “Assessment of human gait speed and energy ex-penditure using a single triaxial accelerometer,” in Wearable and Implantable Body SensorNetworks (BSN), 2012 Ninth International Conference on, pp. 184–188.

[188] G. Panahandeh, N. Mohammadiha, A. Leijon, and P. Handel, “Continuous hidden markovmodel for pedestrian activity classification and gait analysis,” Instrumentation and Mea-surement, IEEE Transactions on, vol. 62, no. 5, pp. 1073–1083, 2013.

Bibliography 179

[189] H. Vathsangam, A. Emken, E. T. Schroeder, D. Spruijt-Metz, and G. S. Sukhatme, “De-termining energy expenditure from treadmill walking using hip-worn inertial sensors: Anexperimental study,” Biomedical Engineering, IEEE Transactions on, vol. 58, no. 10, pp.2804–2815, 2011.

[190] H. Vathsangam, B. A. Emken, E. T. Schroeder, D. Spruijt-Metz, and G. Sukhatme, “Energyestimation of treadmill walking using on-body accelerometers and gyroscopes,” in Engineer-ing in Medicine and Biology Society (EMBC), 2010 Annual International Conference of theIEEE, pp. 6497–6501.

[191] H. Vathsangam, B. A. Emken, E. T. Schroeder, D. Spruijt-Metz, and G. Sukhatme, “To-wards a generalized regression model for on-body energy prediction from treadmill walking,”in Pervasive Computing Technologies for Healthcare (PervasiveHealth), 2011 5th Interna-tional Conference on, pp. 168–175.

[192] H. Vathsangam, B. A. Emken, D. Spruijt-Metz, and G. S. Sukhatme, “Toward free-livingwalking speed estimation using gaussian process-based regression with on-body accelerom-eters and gyroscopes,” in Pervasive Computing Technologies for Healthcare (Pervasive-Health), 2010 4th International Conference on-NO PERMISSIONS, pp. 1–8.

[193] H. Vathsangam, E. T. Schroeder, and G. S. Sukhatme, “On determining the best physiolog-ical predictors of activity intensity using phone-based sensors,” in Point-of-Care HealthcareTechnologies (PHT), 2013 IEEE, pp. 140–143.

[194] M. Schulze, T. Calliess, M. Gietzelt, K. H. Wolf, T. H. Liu, F. Seehaus, R. Bocklage,H. Windhagen, and M. Marschollek, “Development and clinical validation of an unobtrusiveambulatory knee function monitoring system with inertial 9dof sensors,” in Engineering inMedicine and Biology Society (EMBC), 2012 Annual International Conference of the IEEE,pp. 1968–1971.

[195] M. Schulze, L. Tsung-Han, X. Jiang, Z. Wu, K.-H. Wolf, T. Calliess, H. Windhagen, andM. Marschollek, “Unobtrusive ambulatory estimation of knee joint angles during walkingusing gyroscope and accelerometer data - a preliminary evaluation study,” in Biomedical andHealth Informatics (BHI), 2012 IEEE-EMBS International Conference on, pp. 559–562.

[196] H. J. Luinge and P. H. Veltink, “Measuring orientation of human body segments usingminiature gyroscopes and accelerometers,” Medical and Biological Engineering and comput-ing, vol. 43, no. 2, pp. 273–282, 2005.

[197] The American College of Sports Medicines, Guidelines for Exercise Testing and Prescription,7th ed. Philadelphia: Lippincott Willims & Wilkins, 2006.

[198] K. Pandey, V. Singh, A. K. Upadhyay, A. D. Shukla, A. B. Asthana, and D. Kumar, “Effectof bmi on maximum oxygen uptake of high risk individuals in a population of eastern uttarpradesh,” Indian Journal of Community Health, vol. 26, no. 1, pp. 20–24, 2014.

[199] X. Wang, Q. Gui, B. Liu, Z. Jin, and Y. Chen, “Enabling smart personalized healthcare: ahybrid mobile-cloud approach for ecg telemonitoring.”

[200] M. Karunarathne, L. Nanayakkara, and K. Ponnamperuma, “Sentence prediction on smsin sinhala language,” International Journal of Scientific and Research Publications, vol. 3,no. 12, p. 392.

[201] J. Oresko, Z. Jin, J. Cheng, S. Huang, Y. Sun, H. Duschl, and A. Cheng, “A wearablesmartphone-based platform for real-time cardiovascular disease detection via electrocardio-gram processing,” Information Technology in Biomedicine, IEEE Transactions on, vol. 14,no. 3, pp. 734–740, May 2010.

[202] A. Pantelopoulos and N. Bourbakis, “A survey on wearable sensor-based systems for healthmonitoring and prognosis,” Systems, Man, and Cybernetics, Part C: Applications and Re-views, IEEE Transactions on, vol. 40, no. 1, pp. 1–12, Jan 2010.

Bibliography 180

[203] M. Blondet, A. Badarinath, C. Khanna, and Z. Jin, “A wearable real-time bci systembased on mobile cloud computing,” in Neural Engineering (NER), 2013 6th InternationalIEEE/EMBS Conference on, Nov 2013, pp. 739–742.

[204] R. Panchumarthy, R. Subramanian, and S. Sarkar, “Biometric evaluation on the cloud:A case study with humanid gait challenge,” in Proceedings of the 2012 IEEE/ACM FifthInternational Conference on Utility and Cloud Computing. IEEE Computer Society, 2012,pp. 219–222.

[205] P. Mell and T. Grance, “The nist definition of cloud computing,” 2011.

[206] S. Ramgovind, M. Eloff, and E. Smith, “The management of security in cloud computing,”in Information Security for South Africa (ISSA), 2010, Aug 2010, pp. 1–7.

[207] Z. Jin, X. Wang, Q. Gui, B. Liu, and S. Song, “Impr’oving diagnostic accuracy usingmultiparameter patient monitoring based on data fusion in the cloud,” in Future InformationTechnology. Springer, 2014, pp. 473–476.

[208] User guide. [Online]. Available: http://docs.aws.amazon.com/AWSEC2/

[209] User guide. [Online]. Available: http://docs.aws.amazon.com/AmazonRDS/

[210] H. Demirkan and D. Delen, “Leveraging the capabilities of service-oriented decision supportsystems: Putting analytics and big data in cloud,” Decision Support Systems, vol. 55, no. 1,pp. 412–421, 2013.

[211] K. Sartipi, M. H. Yarmand, and N. P. Archer, Challenges in developing effective clinicaldecision support systems. INTECH Open Access Publisher, 2011.

[212] W. Liu and E. K. Park, “E-Healthcare cloud computing application solutions: Cloud-enabling characteristices, challenges and adaptations,” in 2013 International Conferenceon Computing, Networking and Communications, ICNC 2013, 2013, pp. 437–443.

[213] W. Liu and E. K. Park, “e-Healthcare security solution framework,” 2012 21st InternationalConference on Computer Communications and Networks, ICCCN 2012 - Proceedings, 2012.

[214] H.-T. Pham, J.-J. Kim, T. L. Nguyen, and Y. Won, “3d motion matching algorithm usingsignature feature descriptor,” Multimedia Tools and Applications, pp. 1–12, 2014.

[215] S. Li and P. Pathirana, A Kinematic Based Evaluation of Upper Extremity MovementSmoothness for Tele-Rehabilitation, ser. Lecture Notes in Computer Science. SpringerInternational Publishing, 2015, vol. 9102, book section 18, pp. 221–231.

[216] K. Karthik, “Cloud computing for mobile users: Can offloading computation save energy?”vol. 43, no. 4, pp. 51–56, 2010, computer.

[217] Aws elastic beanstalk. [Online]. Available: http://docs.aws.amazon.com/AmazonRDS/

[218] T. Jing, X. Cui, W. Cheng, S. Zhu, and Y. Huo, Enabling Smartphone Based HD VideoChats by Cooperative Transmissions in CRNs, ser. Lecture Notes in Computer Science.Springer International Publishing, 2014, vol. 8491, book section 57, pp. 636–647.

[219] G. Clifford, W. Long, G. Moody, and P. Szolovits, “Robust parameter extraction for decisionsupport using multimodal intensive care data,” Philosophical Transactions of the RoyalSociety A: Mathematical, Physical and Engineering Sciences, vol. 367, no. 1887, pp. 411–429, 2009.

[220] R. Palisano, P. Rosenbaum, S. Walter, D. Russell, E. Wood, and B. Galuppi, “Developmentand reliability of a system to classify gross motor function in children with cerebral palsy,”Developmental Medicine & Child Neurology, vol. 39, no. 4, pp. 214–223, 1997.

[221] J. A. DeLisa, Gait analysis in the science of rehabilitation. Diane Publishing, 1998, vol. 2.

Bibliography 181

[222] A. Ahmadi, D. D. Rowlands, and D. A. James, “Investigating the translational and rota-tional motion of the swing using accelerometers for athlete skill assessment,” in Sensors,2006. 5th IEEE Conference on. IEEE, 2006, pp. 980–983.

[223] S. Boyd and L. Vandenberghe, Convex Optimization. New York, NY, USA: CambridgeUniversity Press, 2004.

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