Cải tiến hệ thống định vị quán tính nhằm nâng cao độ chính xác ước lượng thông số bước đi trong chăm sóc sức khỏe TT TIENG ANH

THE UNIVERSITY OF DANANG UNIVERSITY OF SCIENCE AND TECHNOLOGY PHAM DUY DUONG IMPROVE THE INERTIAL NAVIGATION SYSTEM TO ENHANCE THE ACCURACY OF WALKING PARAMETERS ESTIMATION USING IN HEALTH CARE Major: Control and Automation Engineering Code: 52 02 16 SUMMARY OF DOCTORAL THESIS Da Nang, 2021 The work was completed at UNIVERSITY OF SCIENCE AND TECHNOLOGY - THE UNIVERSITY OF DA NANG Supervisors 1: PhD Doan Quang Vinh Supervisors 2: PhD Nguyen Anh Duy Reviewer 1: Reviewer 2: The thesis is defensed at the Distinguished Scholar-Doctorate thesis at University of Science and Technology on the day 17th month 7, 2021 The dissertation can be found at: - Learning Resources and Communication Center, University of Science and Technology - National Library of Vietnam PROEM Rationale of thesis Human walking parameters depend on the complex interplay of major parts of the nervous system, skeletal muscle, and cardiovascular system The walking parameters will be changed due to the damage in these systems Therefore, measuring the walking parameters is very important to support doctors in diagnosing diseases, evaluate health status, and the rehabilitation process Important walking parameters in health care are walking speed, step length, stride length, foot angle, step time, step width… The commercial walking parameter measurement systems are very expensive and limited in working range Therefore, they are difficult to widely apply in domestic medical facilities In this thesis, we propose low-cost, flexible, and unrestricted systems in walking parameters measurement using IMUs An IMU includes a 3D accelerometer and a 3D gyroscope The IMU is attached to body parts to estimate attitude, velocity and position of body movement using the Inertial Navigation Algorithm (INA) In which, the attitude in external reference coordinate system WCS is determined by integrating the angular velocity signal; the moving acceleration is determined by removing the gravitational acceleration using the moving attitude; the velocity in WCS is determined by integrating the moving acceleration; the moving position is determined by integrating the moving velocity Thurs, the walking parameters can be extracted from the attitude, velocity and position of IMU during moving A positioning system using IMUs is known as an Inertial Navigation System (INS) Page The drawback of INA is the estimation error will be increasing due to integrating the noise of IMUs Therefore, this thesis improves the accuracy of moving estimation using IMUs Objectives Research to build systems of walking parameters estimation, which can be used for walking parameters tests Object and scope of the thesis The Object of the thesis: The object of the thesis is systems for walking parameters estimation using IMUs Scope of the thesis: the scope of the thesis are building hardware and algorithms of the walking parameters estimation systems The walking parameters are walking speed, step/stride length, step time, step frequency Research Methods Research methodology is a combination of theoretical and experimental research, research from overview to details, inheriting research results that have been published in the world, especially the publication of the thesis author, and partner Scientific and practical significance In science: The thesis is a scientific-technological work in walking parameters estimation using Kalman Filter (KF) basing on INS Contribute to improving the accuracy of motion estimation in specific cases, creating an accurate and objective information channel to assist doctors in assessing health status as well as the rehabilitation process In practice: From research and experimental results in building INA and KF based on INS helps to master the technology of inertial positioning and then widely deploy INS into practice From the Page research results of the thesis, it is possible to manufacture equipment to estimate walking parameters, which can be used in health care and rehabilitation centers The new contributions of the thesis Propose and implement a new system to estimate the walking parameters using IMU on a foot and on a walker, improving the system’s accuracy to meet the requirements of medical facilities in health care The general layout of the thesis This thesis includes the introduction, contents, conclusions, references and appendices The content includes chapters The main contributions of the thesis are in Chapter and Chapter Chapter 1: Review of walking parameters estimation in health care Chapter 2: Research to implement the algorithm of the inertial navigation system Chapter 3: Research to build an inertial navigation system on a foot Chapter 4: Research to build an inertial navigation system on a walker Page CHAPTER REVIEW OF WALKING PARAMETERS ESTIMATION IN HEALTH CARE 1.1 Concepts about walking paramters The medically necessary walking parameters are arranged in order of importance to less important as follows: walking speed, step/stride length, step frequency, step time, step width, foot angle, swing time, stance time, distance traveled, 1.2 The importance of walking parameter The walking parameters estimation systems contribute to: - Early diagnosis and monitoring of the progression of diseases related to walking parameters in order to provide the best treatment plan - Evaluate health status and give advise on assistance, hospitalization, rehabilitation needs, discharge location, and the rehabilitation process - Monitoring rehabilitation progress, give good exercise plans to reduce rehabilitation time 1.3 The potential of IMU in medical applications Nowadays, IMU has an increasingly compact size, cheap price, high accuracy and stability, especially its ability to operate independently, so it has the most potential in medical applications Including artificial respiration support; monitoring activities; biological response monitoring; detecting patient falls; monitoring the posture of the patient's bed or patient; monitor the inclination of the patient's head and neck with the breathing tube and feeding tube to avoid clogging blood pressure monitoring; used in imaging equipment, scanners, surgical instruments, prosthetic devices; vibration detection for Parkinson patients; equipment wear monitoring; remote diagnosis, rehabilitation, Page 1.4 Overview of research on the application of IMU in walking parameters estimation The algorithm using IMUs to estimate walking parameters can be divided into models: abstraction model, human gait model, the ơpdirect integration model In which, direct integration model uses the integration of acceleration to obtain walking speed This model gives high accuracy, is easy to use and does not require training In particular, pedestrian navigation using INA is a new direction in this model The advantages of this direction are higher accuracy and 3D parameters to extract more information, which will extend the application of walking parameters in health care Therefore, this thesis uses the INA algorithm in pedestrian navigation and improves the accuracy of motion estimation 1.4.1 Abstraction Model 1.4.2 Human Gait Model Some 1.4.3 Direct Integration 1.4.4 Overview of research on walking parameters estimation using IMUs on a foot The foot is a great place to attach the IMU due to footsteps repetition There are zero velocity intervals (ZVIs) when the foot is on the floor Currently, there are many studies published on this issue However, each study has its advantages and disadvantages In which, the system simplicity in terms of hardware and algorithm, large error while the high accuracy systems are complex hardware and algorithms, even limited by the working range and need to pre-install the environment Therefore, the proposed system in Chapter is both simple, accurate and flexible in use 1.4.5 Overview of research on walking parameters estimation using IMUs on a walker The inertial navigation system, placed on the walker, for users in need of mobility assistance Currently, there are studies published Page on this issue However, most of them apply for a four-wheel walker (less common type) and estimate basic walking parameters only Therefore, the walking parameters estimation system in Chapter is proposed for the most common types of walkers (two front–wheel walkers and standard walkers), estimates a lot of walking parameters, and is flexible in use 1.4.6 Overview of research in Vietnam In general, there are not many published studies on INS and IMU in Vietnam, especially in applications in walking parameters estimation The studies on INS and IMU mainly focus on combining with GPS in positioning problems 1.5 Conclusion of chapter In this chapter, the thesis shows the importance of the walking parameters and the potential of IMU in medical applications Then, the overview of research on the application of IMU in the walking parameters estimation is presented From the overview of research, the thesis chooses a research direction suitable to the trend of the world that is pedestrian navigation using INA The error of the INA algorithm is increasing over time, so the thesis proposes methods to improve the accuracy in two specific cases, namely, the INS placed on the foot and placed on the walker This is the main contribution of the thesis shown in Chapters and With the INS placed on the foot, the proposed system is both simple and accurate and flexible in use With the INS placed on the walker, the INS placed on the most common types of front-wheels or standard walkers, estimates a lot of walking parameters, and is flexible in use Page CHAPTER RESEARCH TO IMPLEMENT THE ALGORITHM OF AN INS 2.1 Inertial Measurement Unit 2.1.1 Sensor introduction 2.1.2 Inertial sensor IMU IMU consist of a 3D accelerometer and a 3D IMU (Strapdown) types MTi-100 (Chapter 3) and MTi-1 (Chapter 4) of Xsens are used in this thesis In this case, the INS is known as Strapdown-INS (SINS) 2.2 Implement inertial navigation system 2.2.1 Navigation systems 2.2.2 Implement the algorithm of SINS 1.1.1.1 Coordinate systems In this thesis, we apply INS in a very narrow environment, so we only use two coordinate systems, namely the body coordinate system (BCS) and the world coordinate system (WCS) The WCS is the external reference to determine the motion trajectory of the object Since an IMU is fixed to the moving object, the origin of BCS coincides with the physical coordinate system of an IMU WCS is used as a local coordinate system Origin of WCS coincides with the origin of BCS at the beginning, the 𝑧𝑤 -axis is pointing upward, the 𝑥𝑤 -axis is in the vertical plane of the 𝑥𝑏 -axis Symbols [𝑎]𝑏 or [𝑎]𝑤 present a vector 𝑎 in respect to BCS or WCS 1.1.1.2 Operation principle of SINS The measured angular velocity and acceleration signals are in the BCS coordinate The attitude of the moving object in the WCS coordinate is determined by integrating the measured angular velocity and the initial attitude of the moving object The attitude is used to transfer the measured acceleration from the BCS to the WCS and remove the gravity acceleration Then, the velocity of moving object is obtained by integrating the acceleration and initial velocity Similary, the position of the moving object is obtained by integrating Page the velocity and initial position Coordinate transferation and integrating implementation are presented in the following subsections 1.1.1.3 Transfer coordinate systems using quaternion A vector 𝑎 is transferred from the BCS to the WCS is [𝑎]𝑤 = 𝑤 [𝑎] 𝑤 𝑏 𝑏 𝐶𝑏 𝑏 and vice versa [𝑎]𝑏 = 𝐶𝑤 [𝑎]𝑤 In which, 𝐶𝑏 and 𝐶𝑤 are 𝑏 rotation matrices and 𝐶𝑏𝑤 = 𝐶 𝑇 𝑤 ∈ 𝑅 3×3 A rotation matrix can be obtained by DCM, Euler, and quaternion methods In which, the quaternion method is more advantage is low storage information and low computation load A quaternion 𝑞 = 𝑞𝑤 + 𝑞𝑥 𝒊 + 𝑞𝑦 𝒋 + 𝑞𝑧 𝒌 is defined as a threecomponent imaginary complex number used to represent the rotation from WCS to BCS When WCS is rotated around a unit vector 𝑢 = [𝑢𝑥 𝑢𝑦 𝑢𝑧 ] a suitable angle 𝜃 to coincide with BCS, a quaternion 𝑞 presents the rotation in matrix form is 𝑞 = [𝑞𝑤 𝑞𝑥 𝑞𝑦 𝑞𝑧 ] = [cos 𝜃 𝜃 sin 𝑢𝑥 𝜃 sin 𝑢𝑦 𝑇 𝜃 sin 𝑢𝑧 ] (2-6) A rotation matrix 𝐶𝑤𝑏 can be computed from quaternion 𝑞 as follows + 𝑞2 ) − 2(𝑞𝑤 𝑥 𝐶𝑤𝑏 = 𝐶(𝑞) = [2(𝑞𝑥 𝑞𝑦 − 𝑞𝑤 𝑞𝑧 ) 2(𝑞𝑥 𝑞𝑧 + 𝑞𝑤 𝑞𝑦 ) 2(𝑞𝑥 𝑞𝑦 + 𝑞𝑤 𝑞𝑧 ) 2(𝑞𝑥 𝑞𝑧 − 𝑞𝑤 𝑞𝑦 ) 2(𝑞𝑤 2(𝑞𝑦 𝑞𝑧 + 𝑞𝑤 𝑞𝑥 )] + 𝑞2 ) − 2(𝑞𝑤 𝑧 + 𝑞𝑦2 ) −1 2(𝑞𝑦 𝑞𝑧 − 𝑞𝑤 𝑞𝑥 ) (2-11) 1.1.1.4 Implement integral to determine the attitude, velocity and position Integrating to determine attitude 𝑞 ∈ 𝑅 , velocity 𝑣 ∈ 𝑅 and position 𝑟 ∈ 𝑅 of moving object in WCS can be implemented by Taylor expansion in third-order for the attitude, first-order for the velocity and position 2.3 Implement Kalman Filter MEKF for the INS The error of integrating will accumulate due to the noise in the sensor and the approximation Thus, the values of attitude, velocity, and position from this integral expansion are called the preliminary Page Besides, from the condition of the unit vector, we have ‖𝑛𝐷 ‖ = Another measurement equation for the MEKF filter can be derived from the condition 3.5 Implement MEKF filter for this system MEKF filter implementation procedures for the system are described in detail in Figure 3.2 Begin T: True F: False 𝐼𝑛𝑖𝑡 𝑥0− = 015×1 𝑃0− = 015×15 F ZVI=1 T 𝐶𝑜𝑚𝑝𝑢𝑡𝑒 𝐻𝑘 , 𝑅𝑘 (3-11) Compute 𝐾𝑘 (2-33) Update 𝑥𝑘 (2-34) Update 𝑃𝑘 (2-35) F 𝑑𝐷 > T 𝐶𝑜𝑚𝑝𝑢𝑡𝑒 𝐻𝑘 (3-25) 𝑅𝑘 (3-26) Compute 𝐴𝑘 (3-7) Compute 𝑄𝑘 (2 − 29) − Update 𝑥𝑘+1 (2-30) − Update 𝑃𝑘+1 (2-31) End Hình 3.2 MEKF filter implementation procedures 3.6 Extract walking parameters from the position of the foot The algorithm of INS using the MEKF filter estimates attitude, velocity and position of the foot during walking The walking parameters (such as walking speed, step length, step time, ) can be easily computed basing on ZVIs Since the IMU is fixed to a foot only, the stride cycle is the interval between the middle of 𝑖-th ZVI and the middle of 𝑖 + 1-th ZVI Page 11 3.7 Experiments for system validation and results analysis An experimental system to verify the accuracy of the proposed system is implemented as in Figure 3.3 In which, an IMU (Mti-100, Xsens, Netherlands) and two distance sensors (VL6180) are attached to a shoe In the experimental system, we set up two distance sensors instead of one distance sensor to evaluate the effect of the position and number of the distance sensor There are markers fixed in the experimental system to track the motion of the foot using a reference camera system (OptiTrack Six Flex 13) Hạt phản quang Cảm biến khoảng cách Cảm biến khoảng cách Cảm biến quán tính Figure 3.3 Experimental system on a foot 3.7.1 Experiment with the OptiTrack system An experiment is implemented times with a three-stride walking under the tracking of the OptiTrack system The purpose of this experiment is to analyze the 3D position of the foot in each step and evaluate the role of KF and measurement updating Figure 3.10 shows the 3D estimated position and the error of the 3D estimated position In which, the left figure shows the estimated position in the blue line and the reference position in the red-dash line tracked by the OptiTrack system The right figure shows the error of the estimated position As can be seen, the estimated position is close to the reference position with respect to all axes Page 12 Hình 3.10 Estimated position of the foot using the proposed system In quantity, the error evaluation criteria including the maximum axial error, the average error on the axes, position error, relative distance error are extracted in the following cases: using INA only, using KF uses ZUPT update, uses ZUPT update to incorporate the height at ZVI intervals and the proposed system uses distance sensor After only strides, the error in the estimated distance was 1216% when using INS without the MEKF filter When using ZUPT velocity update at ZVI intervals, the error of the distance decreased from 1216% to 0.51% compared with the preliminary estimate without using KF When using the height update at the ZVI intervals, the maximum vertical error decreased from about cm to about cm and the average vertical error decreased from 1.48 cm to 1.01 cm compared to the case only use the ZUPT velocity update Although the error of estimating the vertical foot position is eliminated after each step, the height error during moving is not updated The distance sensor is now used to update foot height When using information from the distance sensor, Page 13 the maximum of estimated vertical error significantly reduces from 3.96 cm to 2.15 cm and the mean of error reduces from 1.01 cm to 0.56 cm The estimated position error of 2.2 cm in strides corresponds to an error of about 3.5 mm per step This is a very small error in the step length estimation application Walking parameters of the 4-times experiment with 3-strides of users are shown in Table 3.3 Besides, the parameters of a step can be computed from the parameters of a stride Basing on the experimental results, the position of the distance sensor does not affect to estimated parameters Using more distance sensors gives slightly better results than the case of using one distance sensor but the number of state variables to be estimated must be increased, so it was not suitable for real-time processing Bảng 3.3 Estimated walking parameters of 3-strides walking Stride parameters Moving time (s) Time 0.8833 Time 0.87 Time 0.8667 Time 0.9033 Average 0.8808 Stance time (s) 0.37 0.28 0.4 0.34 0.3475 Cycle (s) 12,533 1.15 12,667 12,433 12,283 Length (m) 0.929 0.9942 0.8659 0.9424 0.9329 Height (m) 0.0453 0.0759 0.0481 0.0743 0.0609 Speed (m/s) 0.7412 0.8645 0.6836 0.7579 0.7618 Frequency (stride/s) 0.6834 0.7194 0.6818 0.6834 0.692 3.7.2 An experiment of walking along a corridor 30 m The experiment was implemented with users walking 30 m along the corridor, times for each user The average error of the estimated distance is 0.43 m over a total of 30 m travel The error is very small (1.4%) in the application of walking parameters estimation The average error is less than cm in each step This is a very small error on foot length of 71 cm in this experiment Page 14 3.8 Evaluate the performance of the proposed system The proposed system has simple hardware and algorithms, small errors and flexible use The system has overcome the limitations of related studies 3.9 Conclusion of chapter In this chapter, an INS on a foot is proposed to estimate walking parameters using a distance sensor The distance sensor is pointing to the floor during walking to update the height of the foot in order to improve the accuracy of walking parameters estimation The new contribution of the thesis in this chapter is to propose and implement a new system to estimate the walking parameters using the IMU sensor placed on the foot to achieve advantages such as small error, simple hardware, simple algorithm and flexibility in use In particular, the specific new contributions are as follows: - Propose hardware of the INS system consisting of an IMU and a distance sensor The distance sensor is pointing to the floor to correct the foot’s trajectory, especially the height of the foot during walking - Propose a model of the Kalman filter for the INS system In which, two state variables (𝑟̅𝐷 𝑛̅𝐷 ) of the distance sensor are added to accurately estimate the position 𝑟𝐷 and direction 𝑛𝐷 of the distance sensor The measured distance is used to build updating equations for the INS system - Propose the updating equations of the Kalman filter for the INS system using the measured distance to improve the accuracy of the height of the foot during moving Page 15 CHAPTER RESEARCH TO BUILD AN INS ON A WALK 4.1 Introduction of chapter In this chapter, an INS on a walker (2 front-wheel and standard type) is proposed to estimate the walking parameters for users in need of mobility assistance In which, an IMU is fixed to the frame of a walker and two encoders are used to monitor the rotation of the walker’s wheels 4.2 Propose an INS on a walker 4.2.1 System overview The proposed system, consists of an IMU fixed to the frame of a walker and two encoders to monitor the rotation of wheels WCS, BCS and ICS are used for this system as in Figure 4.2 In which, ICS takes the role of BCS shown in Chapters and BCS is set on the walker’s frame Figure 4.2 Coordinate systems 4.2.2 Hardware connection and data synchronization 4.2.3 Estimate the relationship between ICS and BCS Let 𝑇𝑏𝐼 ∈ 𝑅 and 𝐶𝑏𝐼 ∈ 𝑅 3×3 are translation vector and rotation matrix to convert a vector in BCS to ICS In this case, 𝑇𝑏𝐼 is the position of an IMU in BCS and can be measured by rulers The 𝑧𝑏 axis at the beginning time coincide with the direction of gravity acceleration measured by IMU The 𝑥𝑏 -axis coincides with the Page 16 moving direction of the walker in an experiment with continuous rolling meter forward We have 𝐶𝑏𝐼 = [[𝑥𝑏 ]𝐼 [𝑧𝑏 ]𝐼 × [𝑥𝑏 ]𝐼 [𝑧𝑏 ]𝐼 ] 4.3 Algorithm for movement detection and classification 4.3.1 Movement definition of a walker The movement of a two front-wheel walker can be classified by: continuous rolling, step-by-step rolling, two back-tip lifting, complete lifting and rotating 4.3.2 Algorithm for movement detection An interval is considered a moving interval if the number of encoder pulses obtained during the sampling time is greater than a threshold for a sufficiently large time (about 0.3 s) When the angle of rotation in the 𝑦𝑏 direction is sufficiently larger than a threshold in a sufficiently large period (about 0.3 s), that interval is also considered a moving interval 4.3.3 Algorithm for movement classification Begin Movement detection: - Using encoders - Around y-axis using IMU - Around z-axis using IMU T: True Đ Movement using encoder Movement around y-axis Movement around y-axis S Đ Movement interval > T step (Tb) S Đ Continuous rolling Step-by-step rolling F: False S S Movement around y-axis Đ S Đ Two backtips lifting Movement around z-axis Complete lifting Đ Rotation S Not moving End Figure 4.4 Algorithm for movement classification Page 17 4.4 Estimate the trajectory of the walker Walker’s movement estimation using IMU is performed by the INS algorithm using KF (type MEKF) shown in Chapter with the input state variables 𝑥 = [𝑞̅ 𝑏𝑔 𝑟̅ 𝑣̅ 𝑏𝑎 ]𝑇 At ZVI intervals, the ZUPT update is used to update the velocity and the height of the walker 4.4.1 Measurement equation for quaternion using vertical direction In the rolling case, the 𝑧𝑏 -axis of the walker is pointing upward and coincides with the 𝑧𝑤 -axis, which can be determined by the acceleration 𝑦𝑎 measured by an IMU at the beginning time A measurement equation is derived using this information 4.4.2 Measurement equation for quaternion using yaw angle In the rolling case, the yaw angle can be computed by encoders and can be used to derive a measurement equation for KF 4.4.3 Measurement equation for position using encoders In the rolling case, the position of the walker can be computed using two encoders The computed position is used to update the position of KF 4.4.4 Combine the estimated trajectory using IMU and estimated trajectory using encoders The second method of estimating the movement of the walker is a combination of the estimated trajectory using IMU in lifting intervals and the estimated trajectory using encoders in rolling intervals 4.5 Walking parameters extraction A new BCS coordinate system (BCSN) is defined In which, the origin is in the middle of two back tips of the walker and axes of BCSN coincide with the axes of BCS During walking the origin of BCSN coincide with the heel of the user Thurs, the walking parameters can be extracted using the trajectory of BCSN The results Page 18 of walking parameters extraction during walking 20 times along a corridor 20 m long using four different walking styles are shown in Table 4.3 Furthermore, it is also possible to access the movement trajectory and posture of the walker during walking This is quite useful for physicians or experts in assessing the user's ability to walk and health conditions Bảng 4.3 Walking parameters of an user walk 20 m using walker Walking style Time Step-by3 step rolling Continuous rolling 2 back-tip lifting Complete lifting Average of error Distance (m) 19,95 19,94 19,89 19,9 19,99 19,78 19,85 19,81 19,63 19,85 20,42 19,84 20,03 20,26 19,66 20,32 20,26 20,04 20,23 20,62 1% Number of step (step) 42 41 46 48 48 32 35 34 33 33 38 38 39 39 39 35 35 34 33 34 Walking time (s) 146,54 148,9 146,84 152,76 168,38 22,76 27,17 26,06 26,54 25,19 136,12 130,6 138,94 138,57 132,1 136,78 135,58 138,31 135,1 140,76 Step length (mm) 476,71 489,08 435,41 417,77 418,16 620,72 575,15 589,86 587,94 614,45 539,05 523,94 514,93 521,12 506,13 582,06 581,12 591,25 615,19 608,57 Step cycle (s) 3,49 3,63 3,19 3,18 3,51 0,71 0,78 0,77 0,8 0,76 3,58 3,44 3,56 3,55 3,39 3,91 3,87 4,07 4,09 4,14 Walking speed (mm/s) 136,92 135,01 136,7 131,09 119,28 933,58 776,97 797,96 798,23 837,86 150,63 152,67 144,68 146,7 149,71 150,19 151,33 146,12 151,16 147,67 4.6 Experiments for algorithm analyzation 4.6.1 Experimental system 4.6.2 Experiment description 4.6.3 Analysis of the combination the estimated trajectory using IMU and estimated trajectory using encoders The first experiment is implemented by five users of the proposed walker system along a 20-m corridor In which, the Page 19 continuous rolling is used in the first m, the step-by-step rolling is used in the second m, the two back-tip lifting is used in the third m and the complete lifting is used in the last m The average error of the estimated distance is 0.8% of 20 m traveling distance So, the average error is about 0,42 cm in each step This is an acceptable error in the application of walking parameters measurement Figure 4.12 The results of movement detection and classification 4.6.4 Analysis of the measurement updating using encoder The second experiment is implemented with five users In which, each user walks along a 20 m corridor 20 times (five times for each walking style) using the walker The average error is 1.47% in the estimated distance, respectively of 0.77 cm for each step with 0,53 m average step length This is an acceptable error in the application of walking parameters measurement 4.6.5 Analyze and evaluate the effect of measurement updatings using encoders The measurement updatings take an important role in continuous rolling cases (the average error reduces from 9.337 m to 0.327 m) However, the measurement updatings have little effect in Page 20 step-by-step rolling cases (the average error reduces from 445 m to 0.059 m) In which, the measurement equation for position using encoders gives the best result The measurement updating is ineffective in the lifting case In this case, the ZUPT for the velocity and the height of the walker has been updated to improve the accuracy of estimated walking parameters 4.6.6 Accuracy analysis using OptiTrack system Hình 4.13 Estimated a reference trajectory of the walker The accuracy of the proposed system is also verified by the OptiTrack system through the third experiment In which, two markers are fixed on feet and a marker is fixed to the origin of BCS to obtain the reference trajectory of the walker The estimated trajectory (the blue line in the left figure), reference trajectory (the dash-red line in the left figure) and the error of estimated trajectory (the blue line in the right figure) are shown in Figure 4.13 In which, the error of the final position is less than cm and the average error is 7.3 mm in each step This is an acceptable error in the application of walking parameters measurement Page 21 Figure 4.15 Step point detection using OptiTrack system 4.6.7 Evaluate the role of the KF in the INS system To evaluate the role of the KF in the INS system, the results of the experiment with the OptiTrack system are estimated without the KF The error of the estimated final position is over 60 m This error is too large compared to the travel distance of m Hence INS must be used with filters, in this case, the KF 4.6.8 Evaluate the accuracy in rotation movement Average results are 0.638 𝑚 in 40 𝑚 traveling (1,6%) with an 1800 rotation and 0.712 𝑚 in 48 𝑚 traveling with 7-time 900 rotation (1,4%) 4.6.9 Experiment with the patients An experiment is implemented at the department of physiotherapy and rehabilitation – C17 Military Hospital at Danang City from 25/12/2020 to 2/1/2021 The experiment was carried out with 10 patients who have difficulty walking, due to diseases such as ligament rupture, cerebral hemorrhage and left tibial plateau rupture, and are undergoing rehabilitation treatment Page 22 Extracted walking parameters are the number of steps, the length of step, the time of step, walking speed, frequency of step and walking style using a walker The distance error is 1,38% This is a small error in the application of walking parameters measurement Thus, the proposed system is used to collect data and extract walking parameters of patients who are recovering walking function at the hospital 4.7 Evaluate the performance of the proposed system The proposed system has small errors and used for standard walker and two front-while walker The system has overcome the limitations of related studies 4.8 Conclusion of chapter The new contribution of the thesis in this chapter is to propose and implement a new system to estimate the walking parameters using an IMU placed on the walker, to obtain the small error, flexible in use, using for 2-wheel or non-wheel walker In particular, the specific new contributions are as follows: - Proposed hardware system including an IMU placed on the walker combined with two encoders attached to two wheels - Propose a method to calibrate the relationship between the IMU and the walker - Propose an algorithm to detect and classify the walker's movement - Propose updating equations for the INS system using information from encoders to improve accuracy in the time intervals of walkers being pushed on the ground when the basic INS system cannot estimate exactly - Propose an algorithm to detect the event that the foot is on the ground in case the walker is pushed continuously on the ground Page 23 CONCLUSIONS AND SUGGESTIONS A Contributions of the thesis Propose and implement a new system to estimate the walking parameters using IMU on a foot and a walker, improving the system’s accuracy to meet the requirements of medical facilities in health care Contributions include: - Propose suitable hardware systems in case of the IMU placed on a foot and a walker - Propose a Kalman filter model in the case of the IMU placed on the foot, including the information of a distance sensor - Propose updating equations for Kalman filter using information from a distance sensor and encoders - Propose a method to estimate the relationship between an IMU and a walker - Propose an algorithm to detect and classify the walker's movements - Propose an algorithm to detect the event that the foot is on the ground in case the walker is pushed continuously on the ground B Further works of the thesis Study the effect of the Taylor expansion order on the accuracy as well as the computational volume of the system Using other filters for the INS system such as USQUE, MRPUKF and DoEuler-UKF or smoothers to improve accuracy Develop the system's functions to automatically evaluate some basic information about health status from walking parameters Page 24 THE PUBLICATION OF THE AUTHOR [1] Quang Vinh Doan and Duy Duong Pham, Fast calibration for parameters of an inertial measurement unit fixed to a standard walker Heliyon Journal No: 6(8) Pages: 1-9 Year 2020 (Scopus) [2] Quang Vinh Doan and Duy Duong Pham, Inertial navigation algorithm for trajectory of front-wheel walker estimation Heliyon Journal No: 5(6) Pages: 1-7 Year 2019 (Scopus) [3] Duy Duong Pham, Huu Toan Duong and Young Soo Suh, Walking Monitoring for Users of Standard and Front-Wheel Walkers IEEE Transactions on Instrumentation and Measurement No: vol PP, no 99 Pages: 1-10 Year 2017 (SCI) [4] Duy Duong Pham and Quang Vinh Doan, “Combination an inertial sensor and a distance sensor to estimate the foot pose” The 5th Vietnam international conference and exhibition on control and automation (VCCA 2019) Pages: 1824 Year 2019 [5] Duy Duong Pham and Quang Vinh Doan, “Implement an Extended-Kalman Filter for Inertial Navigation System” Journal of Science and Technology (JST-UD) No: 9(17) Pages: 45-50 Year 2019 [6] Duy Duong Pham, Quang Vinh Doan and Thi Hoai Phan, “Implement an Inertial Navigation Algorithm to estimate the movement of a two front-wheel walker”, Journal of Science and Technology - (JST-UD) No 17(10) Pages: 24-29 Year 2019 [7] Duy Duong Pham, Thanh Ha Tran and Anh Duy Nguyen, “Movement classification for user of two front-wheel walker” Journal of Science and Technology - (JST-UD) No 11(132).2018 Pages: 19-24 Year 2018 [8] Duy Duong Pham, Anh Duy Nguyen and Quang Vinh Doan, “Combination an inertial sensor and a distance sensor to update the position and heading for indoor pedestrian navigation” The 4th Vietnam international conference and exhibition on control and automation (VCCA 2017) Pages: 55 Year 2017 [9] University science and technology project: Design and implement an equipment for walking parameter tests for user of walker Coordinator: Thanh Ha Tran Member: Duy Duong Pham Code number: T2018-06-88 Year: 2019 [10] Ministry science and technology project: Appying the inertial navigation algorithm to estimate walking parameters for health care Coordinator: Quang Vinh Doan Members: Duy Duong Pham, Anh Duy Nguyen, Bich Thanh Truong Thi, Dinh Thanh Ngo Code number: B218-DNA-07 Year: 2019 [11] University of Danang science and technology project: Appying inertial sensor to estimate the walking parameters for user of walker Coordinator: Duy Duong Pham Members: Anh Duy Nguyen, Quang Thien Duong, Van Nam Nguyen Code number: B2018-ĐN06-l0 Year: 2020 [12] Consolation prize of Vietnam Fund for Sopporting Teachnological Creations Award (VIFOTEC) Year 2018 No 1411/QĐ-LHHVN for “Device for walking parameters estimation for healthcare using modified INA”, Authors: Duy Duong Pham, Quang Vinh Doan Page 25 ... 3D gyroscope The IMU is attached to body parts to estimate attitude, velocity and position of body movement using the Inertial Navigation Algorithm (INA) In which, the attitude in external reference... coordinate The attitude of the moving object in the WCS coordinate is determined by integrating the measured angular velocity and the initial attitude of the moving object The attitude is used... parameters for health care Coordinator: Quang Vinh Doan Members: Duy Duong Pham, Anh Duy Nguyen, Bich Thanh Truong Thi, Dinh Thanh Ngo Code number: B218-DNA-07 Year: 2019 [11] University of Danang science