CN104757976A - Human gait analyzing method and system based on multi-sensor fusion - Google Patents

Human gait analyzing method and system based on multi-sensor fusion Download PDF

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CN104757976A
CN104757976A CN201510178450.4A CN201510178450A CN104757976A CN 104757976 A CN104757976 A CN 104757976A CN 201510178450 A CN201510178450 A CN 201510178450A CN 104757976 A CN104757976 A CN 104757976A
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gait
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CN104757976B (en
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王哲龙
仇森
赵红宇
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Dalian University of Technology
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    • A61B5/103Detecting, measuring or recording devices for testing the shape, pattern, colour, size or movement of the body or parts thereof, for diagnostic purposes
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Abstract

The invention relates to the technical field of gait analysis in biomedical engineering and provides a human gait analyzing method and system based on multi-sensor fusion. The method comprises the steps of filtering sensor signals to eliminate the signal noise error according to human motion features, and eliminating the integral error by means of the improved zero velocity updating algorithm, so that the method and system can be adapted to different walking scenes; fusing multiple sensor data with the Denavit-Hartenberg method, and reducing the leg position calculation error; calculating the step speed, step length, step frequency, walking period and walking track of a tested person accurately during walking after error correction is conducted; establishing a gait database, and conducting statistic analysis on gait data of different tested persons with the quantile regression analysis method. By the adoption of the method and system, gait parameter measurement precision can be improved, and gait parameters of different tested persons are comparable through standardization.

Description

A kind of Human Body Gait Analysis method and system based on Multi-sensor Fusion
Technical field
The present invention relates to gait analysis technical field, particularly relate to a kind of Human Body Gait Analysis method and system based on Multi-sensor Fusion.
Background technology
Body gait is the behavior characteristics of lower limb rapport in human locomotion process, relates to the factors such as individual sports custom, health status, sex, age, occupation, and body gait detects has significant meaning.Such as, in athletic rehabilitation, gait analysis can assess measured's the exercise ability of lower limbs recovery situation.In tele-medicine, it is on duty for a long time that portable gait analysis equipment can reduce nursing staff.In personal navigation, by can be implemented in without the location positioning under the environment of gps signal the calculating of pedestrian's lower extremity movement trace information.
Existing gait analysis method comprises traditional based on methods such as ocular estimate, footprinting method, optical signalling, ultrasonic signal, pressure signals.The patent No. be 7457439 United States Patent (USP) System and method formotion capture use multiple video camera to recover the three-dimensional motion information of health.But based on the movement measurement system ubiquity signal occlusion issue of optics, use restricted; Publication number be CN 102670207 patent describes a kind of gait analysis method based on plantar pressure, body gait phase place and lower extremity movement information pattern is identified over time by analyzing plantar nervous arch, but pressure when the method can only obtain foot and earth surface changes, and then cannot obtain the gait information of a complete gait cycle; Publication number is the system that the patent of CN101694499 describes a kind of pedestrian's walking speed measurement, obtains the motor message of measured in motor process by the double-axel acceleration sensor being fixed on abdominal part dead ahead.This method is easy to the impact being subject to soft tissues of abdomen's deformation, and system leg speed accuracy of detection is lower.
Along with the high speed development of Micro Electro Mechanical System (MEMS) technology, wearable sensor obtains extensive use at human motion rehabilitation field.The existing gait analysis method based on Wearable inertial sensor all employ zero velocity update algorithm and eliminates error accumulation, but the effect that zero velocity upgrades depends critically upon the selection of algorithm threshold value, the rate of change (first derivative) that the method for existing definite threshold often adopts the modulus value of 3-axis acceleration signal to change in conjunction with angular velocity determines to use the time period of zero velocity update algorithm.Due to non-vanishing at stance phase acceleration and accekeration, but fluctuate near zero, and from accekeration and magnitude of angular velocity curve, there is not an obvious crest or trough.Therefore be difficult to find a blanket threshold detection method.Existing gait analysis method is all calculate absolute leg speed, Stride length and frequency, and do not consider that height is on the impact of testing result, the measurement result obtained like this does not possess comparability for different measurands.In addition, because leg muscle exists deformation in motor process, sensor coordinate system and ground reference coordinate system relativeness can be caused to change.And each position of human body lower limbs only has foot to be suitable for zero velocity update algorithm elimination error, the position at all the other positions and azimuth information estimate inevitably there is comparatively big error.
Summary of the invention
The present invention mainly solves the technical problem being difficult to effectively eliminate use motor message integral error of prior art, propose a kind of Human Body Gait Analysis method and system based on Multi-sensor Fusion, improve the accuracy of lower extremity movement information calculating and the object of reliability in human locomotion process to reach.
The invention provides a kind of Human Body Gait Analysis method based on Multi-sensor Fusion, the described Human Body Gait Analysis method based on Multi-sensor Fusion comprises:
Step 100, utilize motor message and the dimensionally magnetic-field component signal of lower limb in sensor acquisition human locomotion process, described motor message comprises three-dimensional acceleration signal and three-dimensional angular velocity signal;
Step 200, according to the motor message gathered and dimensionally magnetic-field component signal, obtain the initial attitude of human body, described initial attitude comprises the angle of pitch of human body rest standing state, roll angle and yaw angle, the departure of sensor coordinate system and earth axes is obtained according to the initial attitude of human body, described departure correction is utilized to be transformed to the spin matrix of earth axes by sensor coordinate system, to compensate the angle of pitch, roll angle and yaw angle, and obtain the human body initial orientation information after compensating;
Step 300, according to the spin matrix of the motor message collected and correction, obtain human body is switched to walking states start time from the state of standing still, and bring into use extended BHF approach device to carry out Data Fusion of Sensor from described start time, upgrade person body orientation information, and according to the gait phase in the motor message human body gait processes gathered, and then obtain body gait parameter, wherein, described gait phase comprises support phase and swings phase, supporting phase is divided into heel to hit the ground phase, phase of standing mid-term, complete stance phase and heeloff phase, swing phase and be divided into accelerated period, shaking peroid and deceleration phase, described body gait parameter comprises leg speed, step-length, cadence, walking period and foot path in human walking procedure,
Step 400, eliminate sensor error accumulation, upgrade body gait parameter, comprising:
When phase shank in mid-term of standing moment perpendicular to the ground being detected, move forward using the lower limb landed as swinging axle measured centre of body weight, one-stage inverted pendulum model is set up to whole human body, performs zero velocity update algorithm and eliminate error, and upgrade the body gait parameter obtained;
When complete stance phase being detected, foot is fitted ground completely, foot shank forms with thigh the rigid body be connected by Hinge joint, Di Naweite-Ha Tan Burg's method is used to set up lower extremity movement model, and merge the motor message of leg and the motor message of foot, to eliminate error, and upgrade the body gait parameter obtained.
Further, in described collection human locomotion process lower limb motor message and dimensionally magnetic-field component signal comprise:
By three-dimensional turntable and three-dimensional guide rail, sensor is demarcated;
Gather motor message and the dimensionally magnetic-field component signal of lower limb in human locomotion process;
To the motor message collected and dimensionally magnetic-field component signal carry out Denoising disposal;
By the motor message collected and dimensionally magnetic-field component signal be saved in memory device.
Further, after step 400, also comprise:
Step 500, standardization is carried out to the body gait parameter obtained, and then sets up human body gait database, comprising:
Pass through formula standardization is carried out to leg speed, passes through formula standardization is carried out to step-length, passes through formula standardization is carried out to cadence, obtains the body gait parameter after standardization, wherein, l 1for measured's height, l mthe average height of age bracket crowd belonging to measured; V is the measured's leg speed obtained sensor signal integral operation, V relfor standard leg speed, unit is meter per second, and L is the step-length obtained leg speed integral operation, L relfor standard step-length, unit is rice/step, and C is the cadence of walking in measured's unit interval of being calculated by walking period, C relfor standard cadence, unit is step/second.
Further, described utilize lower limb in sensor acquisition human locomotion process motor message and dimensionally magnetic-field component signal, comprising:
The motor message of lower limb in human locomotion process is gathered by three axis accelerometer and three-axis gyroscope;
The dimensionally magnetic-field component signal in human locomotion process is gathered by three axle electronic compass;
Three axis accelerometer, three-axis gyroscope and three axle electronic compass are arranged on the mid-thigh of measured, shank stage casing and position, instep.
Further, two constraintss set up by described lower extremity movement model are:
∫ ∫ 0 t a k G dt = [ x k G , y k G , z k G ] T + [ x h G , y h G , z h G ] T ;
∫ ∫ 0 t a a G dt = ∫ ∫ 0 t a k G dt + [ x a G , y a G , z a G ] T ;
Wherein, for the knee joint motion vector moved based on shank, for the ankle position vector calculated based on the sensor of foot, for the hip joint motion vector that the sensor by being placed in thigh position calculates.
Accordingly, present invention also offers a kind of human gait analysis system based on Multi-sensor Fusion, the described human gait analysis system based on Multi-sensor Fusion comprises: data acquisition unit and Data Analysis Services device, data acquisition unit is for utilizing motor message and the dimensionally magnetic-field component signal of lower limb in sensor acquisition human locomotion process, and described motor message comprises three-dimensional acceleration and three-dimensional angular velocity; Described Data Analysis Services device comprises initial attitude analytic unit, gait parameter computing unit and error correction unit;
Initial attitude analytic unit, for according to the motor message gathered and dimensionally magnetic-field component signal, obtain the initial attitude of human body, described motor message comprises three-dimensional acceleration signal and three-dimensional angular velocity signal, the departure of sensor coordinate system and earth axes is obtained according to the initial attitude of human body, described departure correction is utilized to be transformed to the spin matrix of earth axes by sensor coordinate system, to compensate the angle of pitch, roll angle and yaw angle, and obtain the human body initial orientation information after compensating;
Gait parameter computing unit, for the spin matrix according to the motor message collected and correction, obtain human body is switched to walking states start time from the state of standing still, and bring into use extended BHF approach device to carry out Data Fusion of Sensor from described start time, upgrade person body orientation information, and according to the gait phase in the motor message human body gait processes gathered, and then obtain body gait parameter, wherein, described gait phase comprises support phase and swings phase, supporting phase is divided into heel to hit the ground phase, phase of standing mid-term, complete stance phase and heeloff phase, swing phase and be divided into accelerated period, shaking peroid and deceleration phase, described body gait parameter comprises leg speed, step-length, cadence, walking period and foot path in human walking procedure,
Error correction unit, for eliminating sensor error accumulation, upgrade body gait parameter, comprise: when phase shank in mid-term of standing moment perpendicular to the ground being detected, move forward using the lower limb landed as swinging axle measured centre of body weight, one-stage inverted pendulum model is set up to whole human body, performs zero velocity update algorithm and eliminate error, and upgrade the body gait parameter obtained; When complete stance phase being detected, foot is fitted ground completely, foot shank forms with thigh the rigid body be connected by Hinge joint, Di Naweite-Ha Tan Burg's method is used to set up lower extremity movement model, and merge the motor message of leg and the motor message of foot, to eliminate error, and upgrade the body gait parameter obtained.
Further, described data acquisition unit comprises inertial sensor demarcation unit, collecting sensor signal unit, data filtering unit and self-tolerant data storage cell;
Unit demarcated by inertial sensor, for being demarcated sensor by three-dimensional turntable and three-dimensional guide rail;
Collecting sensor signal unit, for gathering motor message and the dimensionally magnetic-field component signal of lower limb in human locomotion process;
Data filtering unit, for the motor message collected and dimensionally magnetic-field component signal carry out Denoising disposal;
Self-tolerant data storage cell, for by the motor message collected and dimensionally magnetic-field component signal be saved in memory device.
Further, the described human gait analysis system based on Multi-sensor Fusion, also comprises:
Gait data library unit, for carrying out standardization to the body gait parameter obtained, and then sets up body gait parameter database, specifically for; Pass through formula standardization is carried out to leg speed, passes through formula standardization is carried out to step-length, passes through formula standardization is carried out to cadence, wherein, l 1for measured's height, l mthe average height of age bracket crowd belonging to measured; V is the measured's leg speed obtained sensor signal integral operation, V relfor standard leg speed, unit is meter per second; For the step-length obtained leg speed integral operation, L relfor standard step-length, unit is rice/step; C is the cadence of walking in measured's unit interval of being calculated by walking period, C relfor standard cadence, unit is step/second.
Further, described data acquisition unit comprises three axis accelerometer, three-axis gyroscope and three axle electronic compass;
Three axis accelerometer and three-axis gyroscope gather the motor message of lower limb in human locomotion process;
Three axle electronic compass gather the dimensionally magnetic-field component signal in human locomotion process;
Three axis accelerometer, three-axis gyroscope and three axle electronic compass are arranged on mid-thigh, shank stage casing and the position, instep of measured.
Further, in error correction unit, two constraintss set up by lower extremity movement model are:
∫ ∫ 0 t a k G dt = [ x k G , y k G , z k G ] T + [ x h G , y h G , z h G ] T ;
∫ ∫ 0 t a a G dt = ∫ ∫ 0 t a k G dt + [ x a G , y a G , z a G ] T ;
Wherein, for the knee joint motion vector moved based on shank, for the ankle position vector calculated based on the sensor of foot, for the hip joint motion vector that the sensor by being placed in thigh position calculates.
A kind of Human Body Gait Analysis method and system based on Multi-sensor Fusion provided by the invention, compared with prior art has the following advantages:
1, the aiding sensors being placed on shank is used to significantly improve the effectiveness of foot zero velocity update algorithm.
2, robot field Di Naweite-Ha Tan Burger coordinate transformation method is applied in lower extremity movement model, reduces position calculation error, improve the computational accuracy of leg position information.
3, the leg speed in the body gait parameter calculated, step-length, cadence are carried out standardization, realize different measured's gait data and there is horizontal comparability.To different sexes, the gait data of all ages and classes measured carries out quantile estimate analysis, can obtain the variation tendency of gait parameter.
4, data acquisition does not rely on external equipment, and complete self-tolerant stores, and eliminates the drawback of wireless communication mode data packetloss.
5, certainty of measurement is high, highly sensitive, and cost is lower, and handled easily person uses, and the movable information of the accurate measurement and other positions of human body that can be used for gait information detects.
Accompanying drawing explanation
The realization flow figure of the Human Body Gait Analysis method based on Multi-sensor Fusion that Fig. 1 provides for the embodiment of the present invention;
Fig. 2 is sensor scheme of installation in the embodiment of the present invention;
Fig. 3 is the schematic diagram data that 3-axis acceleration in the embodiment of the present invention, three-axis gyroscope and three axle electronic compass gather;
Fig. 4 is the coordinate system transformation schematic diagram of human body lower limbs sensor in the embodiment of the present invention;
Fig. 5 is measured that in the embodiment of the present invention, example 1 the calculates three-dimensional angle information schematic diagrams along rectangle route walking two circle;
Fig. 6 is that measured that in the embodiment of the present invention, example 1 calculates linearly walks the foot three-dimensional perspective information schematic diagram of ten steps;
Fig. 7 is the relation schematic diagram of lower limb pain and the joint of the lower extremity anglec of rotation;
Fig. 8 is measured that in the embodiment of the present invention, example 2 calculates foot path schematic diagram when climbing two-layer stair under three-dimensional system of coordinate;
The structure chart of the human gait analysis system based on Multi-sensor Fusion that Fig. 9 provides for the embodiment of the present invention.
Detailed description of the invention
Clearly, below in conjunction with drawings and Examples, the present invention is described in further detail for the technical problem solved for making the present invention, the technical scheme of employing and the technique effect that reaches.Be understandable that, specific embodiment described herein is only for explaining the present invention, but not limitation of the invention.It also should be noted that, for convenience of description, illustrate only part related to the present invention in accompanying drawing but not full content.
Embodiment one
The realization flow figure of the Human Body Gait Analysis method based on Multi-sensor Fusion that Fig. 1 provides for the embodiment of the present invention.The human gait analysis system based on Multi-sensor Fusion that the Human Body Gait Analysis method based on Multi-sensor Fusion that the embodiment of the present invention provides can be provided by the embodiment of the present invention performs, and this system can be realized by software and/or hardware.As shown in Figure 1, the Human Body Gait Analysis method based on Multi-sensor Fusion that the embodiment of the present invention provides comprises:
Step 100, utilizes motor message and the dimensionally magnetic-field component signal of lower limb in sensor acquisition human locomotion process.
Wherein, described motor message comprises three-dimensional acceleration signal and three-dimensional angular velocity signal.Concrete, by three-dimensional turntable and three-dimensional guide rail, sensor is demarcated; Gather motor message and the dimensionally magnetic-field component signal of lower limb in human locomotion process; To the motor message collected and dimensionally magnetic-field component signal carry out Denoising disposal; By the motor message collected and dimensionally magnetic-field component signal be saved in memory device.Wherein, Denoising disposal can comprise to the three-dimensional acceleration signal detected, three-dimensional angular velocity signal and dimensionally magnetic-field component signal carry out high pass (0.001 hertz) filtering, low pass (5 hertz) filtering and trap (50 hertz) process.Fig. 2 is sensor scheme of installation in the embodiment of the present invention.With reference to Fig. 2, the motor message of lower limb in human locomotion process can be gathered by three axis accelerometer and three-axis gyroscope, gather the dimensionally magnetic-field component signal in human locomotion process by three axle electronic compass; Three axis accelerometer, three-axis gyroscope and three axle electronic compass are arranged on human thigh stage casing, shank stage casing and position, instep.Fig. 3 is the schematic diagram data that 3-axis acceleration in the embodiment of the present invention, three-axis gyroscope and three axle electronic compass gather.The data computer of 3-axis acceleration, three-axis gyroscope and three axle electronic compass collections is carried out process and can obtain Fig. 3.Three of X, Y and Z respectively representative sensor mutually orthogonal coordinate axess in Fig. 3, VPT represents motor message energy, and for detecting walking start time, ZUPT represents zero velocity update algorithm switching signal.
In order to the accuracy of image data, can be demarcated before image data by three-dimensional turntable and three-dimensional guide rail to sensor, object avoids drifting about the error brought because of sensor base line.The detailed process of demarcating is: accelerometer static parameter is demarcated, and utilizes gravity g, each axle of sensor is overlapped with gravity direction respectively, and detecting sensor exports the departure with g; Accelerometer dynamic parameter is demarcated, utilize three-dimensional guide rail, apply the acceleration in specified direction, sensor is individually fixed in guide rail three axis, the fixing acceleration that induction guide rail produces due to motor traction belts, compares with sensor output and calculates departure; Gyroscope static parameter is demarcated, and sensor leaves standstill, and it be zero that three axles export, if not zero, records each axial departure respectively; Gyroscope dynamic parameter is demarcated, sensor is fixed on turntable, make sensor center of gravity and turntable center heavy and, make gyrostatic three axles overlap with turntable rotating shaft respectively, open motor and apply fixed rotating speed to turntable, record gyroscope output valve and turntable rotating speed contrast and obtain side-play amount.Described side-play amount is eliminated in subsequent calculations formula, thus eliminates sensor constant error.
Concrete, in the human locomotion process collected, the motor message (three-dimensional acceleration signal and three-dimensional angular velocity signal) of lower limb and the data of dimensionally magnetic-field component signal are kept at mobile memory card (SD card), be sent to afterwards carry out in the equipment of analyzing and processing data by card reader.
Step 200, according to the motor message gathered and dimensionally magnetic-field component signal, obtain the initial attitude of human body, the departure of sensor coordinate system and earth axes is obtained according to the initial attitude of human body, described departure correction is utilized to be transformed to the spin matrix of earth axes by sensor coordinate system, to compensate the angle of pitch, roll angle and yaw angle, and obtain the human body initial orientation information after compensating.
Wherein, described initial attitude comprises the angle of pitch of human body rest standing state, roll angle and yaw angle.Measure measured when starting and be in the state of standing still, obtain the angle of pitch and roll angle by measuring gravity at the component of sagittal plane and horizontal plane, electronic compass is measured magnetic field of the earth and is calculated initial yaw angle at the component of sensor three planes.Concrete process is: using gravity acceleration g as with reference to vector, obtain acceleration of gravity at the component of sagittal plane and horizontal plane and then to the angle of pitch and roll angle; Vectorial as reference at the component H of local level using geomagnetic fieldvector, by the horizontal direction X-axis of three axle electronic compass and the measured value H of Y-axis xand H ycalculate the angle of initial orientation and direct north with the ratio of H, and then obtain yaw angle.
Fig. 4 is the coordinate system transformation schematic diagram of human body lower limbs sensor in the embodiment of the present invention.With reference to Fig. 4, time human body is in and stands still state, in ground reference coordinate system, gravitational acceleration vector is [0,0, g] t, be [x, y, z] through spin matrix to the value of calculation of sensor coordinate system t, in sensor coordinate system, the measured value of acceleration is [a, b, c] t, [x, y, z] t[a, b, c] tall represent gravitational acceleration vector in sensor coordinate system, vector product is done to these two vectors and can obtain error [e x, e y, e z] t, utilize this error vector to revise spin matrix.Revised sensor coordinate system is as Fig. 4.Above-mentioned correction is just got up the X-O-Y planes overlapping of ground reference coordinate system and sensor coordinate system, and for the rotation around Z axis, be also yaw angle, accelerometer is at one's wit's end, and its measured value is always [0,0, g] t, magnetometer can only be relied on to compensate further.Three axle electronic compass measuring objects are magnetic vector, and under purer electromagnetic environment, electronic compass measuring object is earth's magnetic field, and the direction in earth's magnetic field is horizontal by an angle, and earth's magnetic field is designated as [u, v, w] at the component of three planes tif the X-axis of sensor aims at direct north, then v=0, and ground magnetic component is [u, 0, w] t, electronic compass is [i, j, k] in the output of sensor coordinate system t, obtain after accelerometer compensates (coordinate system rotation) [i ', j ', k '] t, in the X-O-Y plane of ground reference coordinate system, [u, 0, w] tbe projected as u, [i ', j ', k '] tbe projected as earth magnetism is necessarily identical in the projection vector size of X-O-Y plane, so have w=k ' simultaneously, like this after process [i ', j ', k '] ttransposition through spin matrix is turned back to sensor coordinate system, the vector obtained and [i, j, k] tdo vector product and ask error, again revise spin matrix, complete and yaw angle is compensated, accurate initial hypercomplex number after using described departure correction, can be obtained.Initial hypercomplex number is used for describing the initial azimuth information of measurand, and the Orientation differences of measurand can be calculated by hypercomplex number multiplication on the basis of initial hypercomplex number.The theoretical value of initial hypercomplex number is [1,0,0,0] t.
Step 300, according to the spin matrix of the motor message collected and correction, obtain human body is switched to walking states start time from the state of standing still, and bring into use extended BHF approach device to carry out Data Fusion of Sensor from described start time, upgrade person body orientation information, and according to the gait phase in the motor message human body gait processes gathered, and then obtain body gait parameter.
Wherein, human body is switched to the start time of walking states from the state of standing still, and namely steps the moment of the first step, and acquisition human body is switched to the mode of the start time of walking states and is from the state of standing still: detected by acceleration energy signal threshold value and realize.When measured is switched to ambulatory status from resting state, by calculating acceleration signal energy VPT = ( a x / | | g | | ) 2 + ( a y / | | g | | ) 2 + ( a z / | | g | | ) 2 Compare with the threshold value λ preset, being greater than the moment of threshold value λ when acceleration signal energy first time, is exactly the start time of human body walking, in formula, and a xrepresent the component of accelerometer output signal in earth axes X-axis, a yrepresent the component of accelerometer output signal in earth axes Y-axis, a zrepresent the component of accelerometer output signal at earth axes Z axis.
From described start time, bring into use extended BHF approach device to carry out Data Fusion of Sensor, upgrade person body orientation information, and according to the gait phase in the motor message human body gait processes gathered, and then obtain body gait parameter.Extended BHF approach device is a kind of optimized autoregression data processing algorithm.Utilize extended BHF approach device in the present invention near filter value, nonlinear system is launched by application Taylor expansion algorithm, higher order term more than second order is all cast out, thus original system just becomes a linear system, the thought of recycling standard Kalman filtering algorithm carries out filtering fusion to system linearization model, thus realizes Data Fusion of Sensor.Use extended BHF approach device upgrades person body orientation information, namely upgrades hypercomplex number after carrying out Data Fusion of Sensor, and according to the gait phase in the motor message human body gait processes gathered, and then obtain body gait parameter.Wherein, gait phase comprises and supports phase and swing phase, supports phase and is divided into heel to hit ground phase, phase of standing mid-term, completely stance phase and phase heeloff, swing phase and be divided into accelerated period, shaking peroid and deceleration phase.Such as, the gait phase of human body can be analyzed by Fig. 3.Body gait parameter comprises leg speed, step-length, cadence, walking period and foot path in human walking procedure.The process obtaining body gait parameter is: carry out integral operation to three-dimensional acceleration vector and obtain three-dimensional velocity vector, carry out integration afterwards obtain three-D displacement vector to three-dimensional velocity vector; In conjunction with the walking period information calculated, leg speed, Stride length and frequency parameter can be calculated; By the relation of hypercomplex number and Eulerian angles, three-dimensional position angle can be calculated; Comprehensive described three-D displacement vector sum azimuth, uses 3-D walls and floor to be described can to obtain foot path to whole gait processes.Initial foot three-dimensional position is set as [X 0, Y 0, Z 0] t, by being [X to three-dimensional velocity vector integration by the foot position information updating of each data sampling instants t, Y t, Z t] t, described azimuth comprises foot movement roll angle, the angle of pitch and yaw angle in gait processes.The initial orientation specified by initial hypercomplex number by the angular velocity information that gyroscope detects, hypercomplex number multiplying is used to be updated in orientation comprehensive described three-dimensional position and azimuth can obtain foot path.
Step 400, eliminates sensor error accumulation, upgrades body gait parameter.
Because twice integral operation in step 300 can produce and amplify integral error, the phase mid-term of standing of each step in gait processes, if meet zero velocity update algorithm condition, just eliminate sensor error accumulation according to the foot special domain hypothesis that the speed in ground moment and acceleration be zero of fitting completely, make body gait parameter more accurate, the limits of error, within the every little step of walking movement, reduces error to greatest extent.
When phase shank in mid-term of standing moment perpendicular to the ground being detected, move forward using the lower limb landed as swinging axle measured centre of body weight, one-stage inverted pendulum model is set up to whole human body, performs zero velocity update algorithm and eliminate error, and upgrade the body gait parameter obtained.Detailed process is: in gait processes, human body supports ground with single foot, move forward using that lower limb landed as swinging axle measured centre of body weight, one-stage inverted pendulum model can be set up to whole human body, gravitional force according to inverted pendulum model reaches maximum at peak, speed reaches the principle of minima, and find in conjunction with the sensor acceleration signal being placed in shank position phase leg speed minimal instant of standing, this moment is the initial time being suitable for zero velocity update algorithm.Utilize the sensor detection speed minimal instant that shank place is fixing, determine to be the shank moment perpendicular to the ground herein, also namely zero velocity update algorithm starts the moment of execution.Perform zero velocity update algorithm and eliminate error, avoid integral error to be incorporated into next gait cycle, the effectiveness of zero velocity update algorithm can be improved.
When complete stance phase being detected, foot is fitted ground completely, foot, shank and thigh can be considered the rigid body be connected by Hinge joint, Di Naweite-Ha Tan Burg's method (Denavit-Hartenberg) is used to set up lower extremity movement model, and merge the motor message of leg and the motor message of foot, to eliminate error, and upgrade the body gait parameter obtained.Detailed process is: with reference to Fig. 2, in conjunction with thigh, physiology's restriction of shank and foot and interaction relation, such as knee joint only has a freedom of movement, ankle joint has three freedom of movement, for the leg sensor localization that directly cannot use zero velocity update algorithm, uses Di Naweite-Ha Tan Burg's method to set up lower extremity movement model, by two constraintss that lower extremity movement model is set up, reduce leg sensing station and azimuth estimation error.Two constraintss of lower extremity movement model are:
∫ ∫ 0 t a k G dt = [ x k G , y k G , z k G ] T + [ x h G , y h G , z h G ] T ;
∫ ∫ 0 t a a G dt = ∫ ∫ 0 t a k G dt + [ x a G , y a G , z a G ] T ;
Wherein, represent the knee joint motion vector based on shank motion, represent the ankle position vector calculated based on the sensor of foot, represent the hip joint motion vector calculated by the sensor being placed in thigh position,
x k G = L 1 ± L 1 1 - [ 1 + ( cos α cos β cos γ ) 2 [ 1 - cos 2 γ + cos 2 β cos 2 γ - ( cos α cos β cos γ ) 2 ] 1 + ( cos α cos β cos γ ) 2 ;
y k G = L 1 2 - z k G sin γ ;
z k G = L 1 2 - x k G sin α ;
Wherein, α, β, γ are respectively the Eulerian angles rotated around X, Y, Z axis, L 1for the lower-leg length measured by anthropometer.
Step 500, carries out standardization to the body gait parameter obtained, and then sets up human body gait database.
Because everyone can select the leg speed of its motor capacity the most applicable by the light of nature, Stride length and frequency, the remarkable decline of leg speed is an obvious pathological index.So a large amount of leg speeds obtained experiment, step-length, cadence carry out standardization, need to consider that height is on the impact of testing result.Clearly leg speed and Leg length l 0close positive correlation, l 0be difficult to Measurement accuracy, so use height l 1replace, measured's average height is designated as L m.The process of the body gait parameter obtained being carried out to standardization is: pass through formula standardization is carried out to leg speed, passes through formula standardization is carried out to step-length, passes through formula standardization is carried out to cadence, wherein, l 1for measured's height, l mthe average height of age bracket crowd belonging to measured; V is the measured's leg speed obtained sensor signal integral operation, V relfor standard leg speed, unit is meter per second, and L is the step-length obtained leg speed integral operation, L relfor standard step-length, unit is rice/step, and C is the cadence of walking in measured's unit interval of being calculated by walking period, C relfor standard cadence, unit is step/second, and the gait index obviously departing from critical field means unstable gait.Standardization is carried out to the leg speed calculated, Stride length and frequency parameter, the gait parameter calculated can be made to have horizontal comparability.
By setting up the data base of the body gait parameters such as leg speed, step-length, cadence, walking period and foot path, to different sexes, all ages and classes measured, can realize carrying out quantile estimate analysis to magnanimity gait data, draw the variation tendency of body gait parameter.And the gait parameters such as the leg speed calculated, step-length, cadence, foot path can be presented at database interface with formal intuitions such as pie chart, block diagram and radar maps.
Human Body Gait Analysis method based on Multi-sensor Fusion provided by the invention, is not only applicable to level walking, is suitable for for stair activity motion is same.By way of example the scheme that the present embodiment provides is described below:
Example 1, in the embodiment of indoor level walking, measured performs once " stamping one's foot " action after binding gait analysis system, and the sensor sensing that measured is worn is to an obvious initial signal, and this signal has been used for the data syn-chronization of video frequency following system VICON and sensor.Test respectively for subsequently two groups: measured is along rectangle route walking two circle in optical tracking system VICON measured zone; Measured linearly to walk ten steps with oneself comfortable paces.Host computer is that data calculate and outlet terminal, and the data collected by slave computer by mobile memory medium import gait analysis upper computer software into, calculate every gait parameter.Data analysis and handling process are as shown in Figure 1.The gait data of slave computer collection uploads to host computer gait analysis software, and first through high pass and low-pass digital filter process, elimination and gait analysis apply irrelevant high and low frequency signal.Because measured starts there is the stage stood still in measurement, meet system initialization condition, now accelerometer only experiences acceleration of gravity, utilizes accelerometer readings to calculate initial pitch angle and roll angle.Utilize electronic compass to detect ground magnetic component, calculate initial yaw angle.Phase of standing after walking starts uses zero velocity update algorithm to eliminate error mid-term.Fig. 5 is the three-dimensional angle information that measured that in the embodiment of the present invention, example 1 calculates encloses along the walking two of rectangle route, the numerical value that the result of calculation of Fig. 5 and video frequency following system calculate is contrasted, angular error is less than 2 °, illustrates that this method can accurate Calculation gait information for a long time.In order to obtain foot angle details, get rid of the impact that walking direction changes, measured linearly to walk ten steps according to oneself comfortable paces, the change at its gait processes mesopodium angle is calculated by the sensor being placed in foot, the degree of sufficient inward turning or strephexopodia can be assessed, help measured to select suitable shoes.Foot three-dimensional perspective information schematic diagram when Fig. 6 is example 1 measured's straight line moving in the embodiment of the present invention.Fig. 7 is the relation schematic diagram of lower limb pain and the joint of the lower extremity anglec of rotation.
Example 2, in the present embodiment, measured completes the motion of climbing two-layer stair, and first the data collected are stored in SD card, imports gait analysis upper computer software into after experiment terminates by card reader, calculates parameters.Within the unit interval, repeatedly stair movement experiment is carried out to same measured, its endurance can be assessed.Stair movement can improve cardiovascular function, strong myocardial contraction, improves pulmonary function, increases vital capacity, and development muscular strength of lower limb, improves knee joint toughness.Stair movement ability reflects cardiovascular and the lung function index of measured indirectly, and the intensity of joint of the lower extremity and toughness.Fig. 8 is measured that in the embodiment of the present invention, example 2 calculates foot path schematic diagram when climbing two-layer stair under three-dimensional system of coordinate.
The Human Body Gait Analysis method based on Multi-sensor Fusion that the present embodiment provides, the validity problem that prior art uses zero velocity update algorithm can be solved, by merging the sensing data of foot and leg, can accurately find the initial time being suitable for zero velocity update algorithm, error or the accumulation of error is reduced based on the foot special domain hypothesis that the moment speed on ground and acceleration be zero of fitting completely, by the limits of error in the every little step of gait processes, avoid the accumulation of error; Calculate the situation of inapplicable zero velocity update algorithm for leg position, the constraints can set up by the topology controlment of lower limb, reach the effect reducing position calculation error.For the impact of height factor for gait parameter, the present invention carries out standardization to leg speed, Stride length and frequency parameter, can eliminate the impact of height factor on gait parameter, and the gait parameter reaching different people has the effect of comparability.Standardized gait parameter is gathered and sets up gait data storehouse, body gait parameter can be obtained with sex by quantile estimate analysis, the variation tendency at age.The method that the present embodiment provides can accurately find the initial time being suitable for zero velocity update algorithm, ensures the effectiveness of zero velocity update algorithm, thus reduces integral error, improves the reliability that gait parameter calculates.The movable information that method provided by the invention also may be used for other body part of human body is measured.
Embodiment two
The structural representation of the human gait analysis system based on Multi-sensor Fusion that Fig. 9 provides for the embodiment of the present invention.As shown in Figure 9, the human gait analysis system based on Multi-sensor Fusion that the embodiment of the present invention provides comprises: data acquisition unit and Data Analysis Services device, data acquisition unit is for utilizing motor message and the dimensionally magnetic-field component signal of lower limb in sensor acquisition human locomotion process, and described motor message comprises three-dimensional acceleration and three-dimensional angular velocity; Described Data Analysis Services device comprises initial attitude analytic unit, gait parameter computing unit and error correction unit;
Initial attitude analytic unit, for according to the motor message gathered and dimensionally magnetic-field component signal, obtain the initial attitude of human body, described motor message comprises three-dimensional acceleration signal and three-dimensional angular velocity signal, the departure of sensor coordinate system and earth axes is obtained according to the initial attitude of human body, described departure correction is utilized to be transformed to the spin matrix of earth axes by sensor coordinate system, to compensate the angle of pitch, roll angle and yaw angle, and obtain the human body initial orientation information after compensating;
Gait parameter computing unit, for the spin matrix according to the motor message collected and correction, obtain human body is switched to walking states start time from the state of standing still, and bring into use extended BHF approach device to carry out Data Fusion of Sensor from described start time, upgrade person body orientation information, and according to the gait phase in the motor message human body gait processes gathered, and then obtain body gait parameter, wherein, described gait phase comprises support phase and swings phase, supporting phase is divided into heel to hit the ground phase, phase of standing mid-term, complete stance phase and heeloff phase, swing phase and be divided into accelerated period, shaking peroid and deceleration phase, described body gait parameter comprises leg speed, step-length, cadence, walking period and foot path in human walking procedure,
Error correction unit, for eliminating sensor error accumulation, upgrade body gait parameter, comprise: when phase shank in mid-term of standing moment perpendicular to the ground being detected, move forward using the lower limb landed as swinging axle measured centre of body weight, one-stage inverted pendulum model is set up to whole human body, performs zero velocity update algorithm and eliminate error, and upgrade the body gait parameter obtained; When complete stance phase being detected, foot is fitted ground completely, foot shank forms with thigh the rigid body be connected by Hinge joint, Di Naweite-Ha Tan Burg's method is used to set up lower extremity movement model, and merge the motor message of leg and the motor message of foot, to eliminate error, and upgrade the body gait parameter obtained.
In such scheme, described data acquisition unit comprises inertial sensor and demarcates unit, collecting sensor signal unit, data filtering unit and self-tolerant data storage cell; Unit demarcated by inertial sensor, for being demarcated sensor by three-dimensional turntable and three-dimensional guide rail; Collecting sensor signal unit, for gathering motor message and the dimensionally magnetic-field component signal of lower limb in human locomotion process; Data filtering unit, for the motor message collected and dimensionally magnetic-field component signal carry out Denoising disposal; Self-tolerant data storage cell, for by the motor message collected and dimensionally magnetic-field component signal be saved in memory device.Concrete, the Denoising disposal of data pre-processing unit comprise to the three-dimensional acceleration signal detected, three-dimensional angular velocity signal and dimensionally magnetic-field component signal carry out high pass (0.001 hertz) filtering, low pass (5 hertz) filtering and trap (50 hertz) process.Wherein, self-tolerant data storage cell, be that the data of the motor message of lower limb in the human locomotion process collected and dimensionally magnetic-field component signal are kept at mobile memory card (SD card), be sent to Data Analysis Services device by card reader afterwards.
Wherein, described data acquisition unit comprises three axis accelerometer, three-axis gyroscope and three axle electronic compass; Three axis accelerometer and three-axis gyroscope gather the motor message of lower limb in human locomotion process; Three axle electronic compass gather the dimensionally magnetic-field component signal in human locomotion process; Three axis accelerometer, three-axis gyroscope and three axle electronic compass are arranged on mid-thigh, shank stage casing and the position, instep of measured.
Further, the described human gait analysis system based on Multi-sensor Fusion, also comprises:
Gait data library unit, for carrying out standardization to the body gait parameter obtained, and then sets up body gait parameter database, specifically for; Pass through formula standardization is carried out to leg speed, passes through formula standardization is carried out to step-length, passes through formula standardization is carried out to cadence, wherein, l 1for measured's height, l mthe average height of age bracket crowd belonging to measured; V is the measured's leg speed obtained sensor signal integral operation, V relfor standard leg speed, unit is meter per second; L is the step-length obtained leg speed integral operation, L relfor standard step-length, unit is rice/step; C is the cadence of walking in measured's unit interval of being calculated by walking period, C relfor standard cadence, unit is step/second.
In error correction unit, two constraintss set up by lower extremity movement model are:
∫ ∫ 0 t a k G dt = [ x k G , y k G , z k G ] T + [ x h G , y h G , z h G ] T ;
∫ ∫ 0 t a a G dt = ∫ ∫ 0 t a k G dt + [ x a G , y a G , z a G ] T ;
Wherein, for the knee joint motion vector moved based on shank, for the ankle position vector calculated based on the sensor of foot, for the hip joint motion vector that the sensor by being placed in thigh position calculates.
The human gait analysis system based on Multi-sensor Fusion that the present embodiment provides, motor message and the dimensionally magnetic-field component signal of lower limb in human locomotion process is gathered by data acquisition unit, human body initial orientation information is obtained by initial attitude analytic unit, body gait parameter is obtained by gait parameter computing unit, and eliminate sensor error accumulation by error correction unit, upgrade body gait parameter, the system that the present embodiment provides can accurately find the initial time being suitable for zero velocity update algorithm, ensure the effectiveness of zero velocity update algorithm, thus reduction integral error, improve the reliability that gait parameter calculates.
Last it is noted that above each embodiment is only in order to illustrate technical scheme of the present invention, be not intended to limit; Although with reference to foregoing embodiments to invention has been detailed description, those of ordinary skill in the art is to be understood that: it is modified to the technical scheme described in foregoing embodiments, or equivalent replacement is carried out to wherein some or all of technical characteristic, does not make the essence of appropriate technical solution depart from the scope of various embodiments of the present invention technical scheme.

Claims (10)

1. based on a Human Body Gait Analysis method for Multi-sensor Fusion, it is characterized in that, the described Human Body Gait Analysis method based on Multi-sensor Fusion comprises:
Step 100, utilize motor message and the dimensionally magnetic-field component signal of lower limb in sensor acquisition human locomotion process, described motor message comprises three-dimensional acceleration signal and three-dimensional angular velocity signal;
Step 200, according to the motor message gathered and dimensionally magnetic-field component signal, obtain the initial attitude of human body, described initial attitude comprises the angle of pitch of human body rest standing state, roll angle and yaw angle, the departure of sensor coordinate system and earth axes is obtained according to the initial attitude of human body, described departure correction is utilized to be transformed to the spin matrix of earth axes by sensor coordinate system, to compensate the angle of pitch, roll angle and yaw angle, and obtain the human body initial orientation information after compensating;
Step 300, according to the spin matrix of the motor message collected and correction, obtain human body is switched to walking states start time from the state of standing still, and bring into use extended BHF approach device to carry out Data Fusion of Sensor from described start time, upgrade person body orientation information, and according to the gait phase in the motor message human body gait processes gathered, and then obtain body gait parameter, wherein, described gait phase comprises support phase and swings phase, supporting phase is divided into heel to hit the ground phase, phase of standing mid-term, complete stance phase and heeloff phase, swing phase and be divided into accelerated period, shaking peroid and deceleration phase, described body gait parameter comprises leg speed, step-length, cadence, walking period and foot path in human walking procedure,
Step 400, eliminate sensor error accumulation, upgrade body gait parameter, comprising:
When phase shank in mid-term of standing moment perpendicular to the ground being detected, move forward using the lower limb landed as swinging axle measured centre of body weight, one-stage inverted pendulum model is set up to whole human body, performs zero velocity update algorithm and eliminate error, and upgrade the body gait parameter obtained;
When complete stance phase being detected, foot is fitted ground completely, foot shank forms with thigh the rigid body be connected by Hinge joint, Di Naweite-Ha Tan Burg's method is used to set up lower extremity movement model, and merge the motor message of leg and the motor message of foot, to eliminate error, and upgrade the body gait parameter obtained.
2. the Human Body Gait Analysis method based on Multi-sensor Fusion according to claim 1, is characterized in that, in described collection human locomotion process lower limb motor message and dimensionally magnetic-field component signal comprise:
By three-dimensional turntable and three-dimensional guide rail, sensor is demarcated;
Gather motor message and the dimensionally magnetic-field component signal of lower limb in human locomotion process;
To the motor message collected and dimensionally magnetic-field component signal carry out Denoising disposal;
By the motor message collected and dimensionally magnetic-field component signal be saved in memory device.
3. the Human Body Gait Analysis method based on Multi-sensor Fusion according to claim 1, is characterized in that, after step 400, also comprise:
Step 500, standardization is carried out to the body gait parameter obtained, and then sets up human body gait database, comprising:
Pass through formula standardization is carried out to leg speed, passes through formula standardization is carried out to step-length, passes through formula standardization is carried out to cadence, obtains the body gait parameter after standardization, wherein, l 1for measured's height, l mthe average height of age bracket crowd belonging to measured; V is the measured's leg speed obtained sensor signal integral operation, V relfor standard leg speed, unit is meter per second, and L is the step-length obtained leg speed integral operation, L relfor standard step-length, unit is rice/step, and C is the cadence of walking in measured's unit interval of being calculated by walking period, C relfor standard cadence, unit is step/second.
4. the Human Body Gait Analysis method based on Multi-sensor Fusion according to claim 1, is characterized in that, described utilize lower limb in sensor acquisition human locomotion process motor message and dimensionally magnetic-field component signal, comprising:
The motor message of lower limb in human locomotion process is gathered by three axis accelerometer and three-axis gyroscope;
The dimensionally magnetic-field component signal in human locomotion process is gathered by three axle electronic compass;
Three axis accelerometer, three-axis gyroscope and three axle electronic compass are arranged on the mid-thigh of measured, shank stage casing and position, instep.
5. the Human Body Gait Analysis method based on Multi-sensor Fusion according to claim 1, is characterized in that, two constraintss set up by described lower extremity movement model are:
∫ ∫ 0 t a k G dt = [ x k G , y k G , z k G ] T + [ x h G , y h G , z h G ] T ;
∫ ∫ 0 t a a G dt = ∫ ∫ 0 t a k G dt + [ x a G , y a G , z a G ] T ;
Wherein, for the knee joint motion vector moved based on shank, for the ankle position vector calculated based on the sensor of foot, for the hip joint motion vector that the sensor by being placed in thigh position calculates.
6. the human gait analysis system based on Multi-sensor Fusion, it is characterized in that, the described human gait analysis system based on Multi-sensor Fusion comprises: data acquisition unit and Data Analysis Services device, data acquisition unit is for utilizing motor message and the dimensionally magnetic-field component signal of lower limb in sensor acquisition human locomotion process, and described motor message comprises three-dimensional acceleration and three-dimensional angular velocity; Described Data Analysis Services device comprises initial attitude analytic unit, gait parameter computing unit and error correction unit;
Initial attitude analytic unit, for according to the motor message gathered and dimensionally magnetic-field component signal, obtain the initial attitude of human body, described motor message comprises three-dimensional acceleration signal and three-dimensional angular velocity signal, the departure of sensor coordinate system and earth axes is obtained according to the initial attitude of human body, described departure correction is utilized to be transformed to the spin matrix of earth axes by sensor coordinate system, to compensate the angle of pitch, roll angle and yaw angle, and obtain the human body initial orientation information after compensating;
Gait parameter computing unit, for the spin matrix according to the motor message collected and correction, obtain human body is switched to walking states start time from the state of standing still, and bring into use extended BHF approach device to carry out Data Fusion of Sensor from described start time, upgrade person body orientation information, and according to the gait phase in the motor message human body gait processes gathered, and then obtain body gait parameter, wherein, described gait phase comprises support phase and swings phase, supporting phase is divided into heel to hit the ground phase, phase of standing mid-term, complete stance phase and heeloff phase, swing phase and be divided into accelerated period, shaking peroid and deceleration phase, described body gait parameter comprises leg speed, step-length, cadence, walking period and foot path in human walking procedure,
Error correction unit, for eliminating sensor error accumulation, upgrade body gait parameter, comprise: when phase shank in mid-term of standing moment perpendicular to the ground being detected, move forward using the lower limb landed as swinging axle measured centre of body weight, one-stage inverted pendulum model is set up to whole human body, performs zero velocity update algorithm and eliminate error, and upgrade the body gait parameter obtained; When complete stance phase being detected, foot is fitted ground completely, foot shank forms with thigh the rigid body be connected by Hinge joint, Di Naweite-Ha Tan Burg's method is used to set up lower extremity movement model, and merge the motor message of leg and the motor message of foot, to eliminate error, and upgrade the body gait parameter obtained.
7. the human gait analysis system based on Multi-sensor Fusion according to claim 6, it is characterized in that, described data acquisition unit comprises inertial sensor and demarcates unit, collecting sensor signal unit, data filtering unit and self-tolerant data storage cell;
Unit demarcated by inertial sensor, for being demarcated sensor by three-dimensional turntable and three-dimensional guide rail;
Collecting sensor signal unit, for gathering motor message and the dimensionally magnetic-field component signal of lower limb in human locomotion process;
Data filtering unit, for the motor message collected and dimensionally magnetic-field component signal carry out Denoising disposal;
Self-tolerant data storage cell, for by the motor message collected and dimensionally magnetic-field component signal be saved in memory device.
8. the human gait analysis system based on Multi-sensor Fusion according to claim 6, is characterized in that, the described human gait analysis system based on Multi-sensor Fusion, also comprises:
Gait data library unit, for carrying out standardization to the body gait parameter obtained, and then sets up body gait parameter database, specifically for; Pass through formula standardization is carried out to leg speed, passes through formula standardization is carried out to step-length, passes through formula standardization is carried out to cadence, wherein, l 1for measured's height, l mthe average height of age bracket crowd belonging to measured; V is the measured's leg speed obtained sensor signal integral operation, V relfor standard leg speed, unit is meter per second; L is the step-length obtained leg speed integral operation, L relfor standard step-length, unit is rice/step; C is the cadence of walking in measured's unit interval of being calculated by walking period, C relfor standard cadence, unit is step/second.
9. the human gait analysis system based on Multi-sensor Fusion according to claim 6, is characterized in that, described data acquisition unit comprises three axis accelerometer, three-axis gyroscope and three axle electronic compass;
Three axis accelerometer and three-axis gyroscope gather the motor message of lower limb in human locomotion process;
Three axle electronic compass gather the dimensionally magnetic-field component signal in human locomotion process;
Three axis accelerometer, three-axis gyroscope and three axle electronic compass are arranged on mid-thigh, shank stage casing and the position, instep of measured.
10. the human gait analysis system based on Multi-sensor Fusion according to claim 6, is characterized in that, in error correction unit, two constraintss set up by lower extremity movement model are:
∫ ∫ 0 t a k G dt = [ x k G , y k G , z k G ] T + [ x h G , y h G , z h G ] T ;
∫ ∫ 0 t a a G dt = ∫ ∫ 0 t a k G dt + [ x a G , y a G , z a G ] T ;
Wherein, for the knee joint motion vector moved based on shank, for the ankle position vector calculated based on the sensor of foot, for the hip joint motion vector that the sensor by being placed in thigh position calculates.
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