Human Gait Modelling Using Hidden MarkovModel For Abnormality Detection

Sourav ChattopadhyayMachine Intelligence and Bio-Motion Research LabDepartment of Computer Science and Engineering

National Institute of Technology RourkelaRourkela, India

schat.rkl17@gmail.com

Anup NandyMachine Intelligence and Bio-Motion Research LabDepartment of Computer Science and Engineering

National Institute of Technology RourkelaRourkela, India

nandy.anup@gmail.com

Abstract—This paper presents a novel approach to humangait analysis using wearable Inertial Measurement Unit(IMU)sensor-based technique.The proposed system emphasizeson detection of certain abnormal gait patterns. It includeshemiplegic and equinus gait which are synthetically generatedin our lab.The designed prototype contains an IMU sensorwith 3 axial accelerometer and gyroscope. It provides linearacceleration and angular velocity of human foot.A probabilisticframework,Hidden Markov Model(HMM) is applied to modelbipedal human gait.This model uses Symbolic AggregateApproximation(SAX) method for generating observationsequences obtained from sample gait cycles.The detection ofabnormal gait pattern is based on maximum log-likelihoodof an unknown observerd sequence,generated from a gaitcycle.The experimental results demonstarte that the proposedHMM-based technique is able to detect gait abnormality ingait data.The proposed personalized gait modelling approachis cost effective and reliable to implement in gait rehabilatationprocess.

Index Terms—IMU sensor,Human gait, Accelerometer, Gy-roscope, HMM,Wearable sensor,Abnormal gait

I. IntroductionHuman gait is a spatio-temporal signal and it has its

own independent nature that differs individually. It maybe assumed that different gait features,extracted fromraw gait data can be analyzed using different machinelearning technique for several real world applications.Analysis of gait data can be employed for designing anintelligent system for biometric recognition. Gait datacan also be featured for modelling a system to detectdifferent gait modes. Similarly human gait analysis canalso be used in the clinical domain. There are severaltypes of gait abnormality that can be avoided by earlydetection of unnatural gait pattern. A proper human gaitmodelling for abnormality detection can also help in gaitrehabilation proess. An intelligent system can be designedin such an way to find abnormality in gait pattern.This kind of system may provide a better assessmenton an individual’s gait pattern than human supervisedmethod of gait assessment. The reason includes thathuman supervised approach for gait assessment depends

much on the observation of an observer which may vary.Human gait is a quasi-periodic signal that gets repeatedwithin a time interval. A single gait cycle is comprisedof eight phases. An individual with normal gait patternshould have a smooth and consecutive transition betweeenall this phases. On the other hand a person with abnormalgait pattern may not have smooth transition between twoconsecutive gait phases as it may have missed some ofthe gait phases due to abnormality in its gait pattern.It is extremely important to understand the normal andabnormal gait pattern.Therefore sensor-based gait analysismethod is adopted to detect gait abnormality.

A. Related workWang et.al [1] representd similarity comparisons be-

tween single–task walking and dual–task walking forAlzheimer’s disease patients.In that approach data acqui-sion was done using IMU sensor.Three axis Accelorometerand gyroscopic data were selected as features to be fed intothe proposed model.A cyclic left right discrete HMM wasproposed to model abnormal human gait. Chen et.al [2]proposed an HMM-based gait abnormality detection mod-elling using force plate and IMU sensor-based data.Thisapproach employed an intelligent shoe(sensors were placedinside the shoe sole) system for data acquisition.A six statediscrete left right HMM was used for modelling normaland two simulated abnormal type of human gait(toe inand toe out). Bae Joonbum et.al [5] illustrated an HMM-based gait modelling on the basis of analyzing the gaitphases.In that approach, continuous HMM was appliedto analyze the gait phases in gait motion.That approachemployed smart shoe sensor-based technique for dataacquisition.The Ground Reaction Force(GRF) was consid-ered as gait as input observation sequence to the HMM.Khorasani Abed et.al [6]demonstrated an HMM-basedmodel for classification of Parkinson’s disease(PD), basedon raw gait data.It incorporated Gaussian mixture modelwith HMM to separate healthy subjects and subjects withParkinson disease. Mannini Andrea et.al [7]recommendeda machine learning framework for gait classification.Itemployed inertial sensors for application of classification

to different pathological gait such as elderly, post-strokeand Huntington’s disease patients.That method used anSupport Vector Machine(SVM) classifier to the HMMderived information. Yang Yiding et.al [3] proposed anHMM based gait mode discrimination model.That methodused human lower limb gait accelation signal as featurefor the proposed model.Wavelet transformation approachwas employed for gait feature extraction.

B. OverviewThis paper proposes a cost effective IMU sensor based

technique for human gait analysis. Accelerometer andgyroscopic data, captured using IMU sensor, are used inthis proposed approach as gait freatures to be fed as inputto the model. A left-to-right HMM for gait modellingis used instead of a cyclic left-to-right HMM.Proposedmethod employes SAX for generating discrete observationsequence.The proposed model is able to discriminatebetween normal and abnormal gait cycle pattern.A detaildescription about data acquisition and preprocessing ispresented in section II.Section III gives an overviewof HMM and illustrates proposed gait modelling viaHMM.Section IV depicts experiemental details and re-sult analysis.Finally this paper is ended with explainingconclusion and illustrates scope for future work.

II. DATA COLLECTIONThis research approach uses a single custom made pro-

totype that contains an IMU sensor(capable of measuring3 axial accelarometer and gyroscopic data). This IMUsensor captures accelerometer data, gyroscopic data andmagnetometer data in X, Y and Z direction from humangait. Only accelerometer and gyroscopic data is used forfeature extraction. Unlike IOT (Internet of Thing) basedIMU sensor this sensor has inbuilt slot for holding amemory card that stores the gait signal data.

A. Sensor specificationThe SparkFun 9DoF Razor IMU M0 has a SAMD21

microprocessor with an MPU-9250 9DoF.Fig 2(a) and2(b) below shows the front and back view of the senosorrespectively

(a) (b)

Fig. 1: IMU sensor

The 9DoF Razor’s MPU-9250 features three 3-axissensors—an accelerometer, gyroscope and magnetometer

that measures linear acceleration, angular rotation veloc-ity and magnetic field vectors.Data capturing is done atsampling frequency of 100 Hz using this sensor.

B. Positioning the sensorIn this research work sensor is placed at right shank

position for capturing the gait data.

(a) (b)

Fig. 2: Positioning the IMU sensor

Fig. 2(a) and 2(b) shows normal and simulated equinusgait data capture and position of the sensor. In all thecases, sensor is placed on right leg shank only consideringthe fact, gait follows symmetry for left and right leg in caseof normal gait.In case of simulated gait abnormality,sensoris placed on effected right leg shank.

C. Data captureTreadmill data is captured for 4 healthy subjects.They

were asked to walk for 6 minutes on the treadmill atnormal walking speed(2.5km per hour)to collect normaland simulated abnormal gait data.Each signal produceson an average 270 gait cycles.In this research we haveexplored large sample of gait cycles to train the modelfor detection of gait abnormaility instead of consideringentire gait signal (comprised of smaller number of gaitcycles) to train the model.Since the captured gait signalis noisy,the preprocessing technique is applied to removeunwanted information from the signal.

Fig. 3: Raw gyroscopic signal

The captured noisy gyroscopic signal in X,Y,Z axis isillustrated in Fig. 3.

D. Preprocessing of raw dataPre-processing mainly constitutes of three main phases.

First phase is clipping the gait signal part only and secondphase is to filter out the noise from the gait signal. Thirdphase identifies a single gait cycle from all the gait signals.

Fig. 4: Filtered gyroscopic signal

Fig. 4 shows filtered gyroscopic signal(at right).Firstphase of preprocessing is completed using framingconcept and for second phase low pass IIR (InfiniteImpulse Response) filtering is used with a cut offfrequency of 5 Hz.

Fig. 5: Extracted single gait cycle

Fig. 5 shows extracetd single gait cycle from Y axisgyroscopic signal which is obtained from third phase ofpre-processing.In this phase a single gait cycle is extractedfrom filtered signal using signal auto-correlation.

III. Proposed WorkSince gait signal is nondeterministic in nature it requires

a probabilistic technique for modelling human gait.TheGait phases are hidden from outside observation and theycan only be observed using some of the gait features.TheHMM is known as double stochastic process which issuitable for modelling gait signal to understand the uncer-tainty present in the signal.Accelarometer and gyroscopicdata provides three axial linear accelaration and angularvelocity of foot respectively.In the proposed method,gaitcycles are extracted from each of the gait signals.Each ofthe discretized cycles are used as observation sequence for

training and testing purpose of the model.Since cyclic na-ture of gait signal is not used for training or test purpose,a left right, first order Hidden Markov model(HMM) isused for modelling the gait instead of cyclic HMM.Fig. 6depicts the block diagram for the proposed system.

A. HMM overviewAn HMM is collection of finite set of states S =

s1, s2...sn interconnected by transitions. Each state hasnumber of distinct observation symbols V= v1, v2...vn [8][4].An HMM model can be represented as follows:

λ = (A,B, π) (1)

A: State transition probability distribution =aij .aij = State transition from si to sjB: Observation symbol=bj(Ot).bj(Ot)=Emission at state j at time t.π =initial state probability distribution vector.Transition matrix for a four state first order left-to-right

HMM can be defined as:

a11 a12 0 00 a22 a23 00 0 a33 a340 0 0 a44

According to this above state transition matrix a state canhave a self loop or it can go to the immediate next stateonly but it can’t go back to any of it’s previous state.

B. Proposed ModelIn proposed HMM model all the eight gait phases have

been divided into four states.Hence there is four hiddenstates in this model.State 1 includes initial contact andloading response phase.State 2 is comprised of mid-stanceand terminal stance phase.State 3 consists of preswing andinitial swing phase.Mid swing and terminal swing phasesare merged into state 4.Hidden states in fig. 7 can beconsidered as discussed above.

Fig. 6: Block diagram of proposed system

The proposed model λ = (A;B;π) uses Forwardalgorithm for forward recursion.Backward algorithm forbackward recursion which is time reversed version offorward algorithm.Baum-Welch algorithm is used for

learning or re-estimation of the parameters for the pro-posed model.Learning of HMM parameters(the transitionprobabilities aij and emission probabilities bjk) is the mostimportant part in a HMM model. There is no knownmethod for obtaining the optimal or most likely set ofparameters from the data. But this can be always nearly

Fig. 7: Proposed model

determined by this Baum-Welch algorithm. It is an in-stance of generalized expectation maximization algorithm.The general approach is to iteratively update the weightsof the model parameters in order to better explain theobserved training sequences [8].

C. Observation sequence generation using SAX algorithmEach of the gait cycle extracted from gait signal is

discretized in order to be fed as input to the HMM.Fordiscretization of gait cycle SAX [11] technique isemployed [1]. SAX is a simple but efficient techniquefor representing a time series data into a series ofsymbols.Thus implementing SAX a signal can beconverted into a string of symbols.Generated SAXsymbols are multiplied by a factor in order to generatea discrete observation sequence.SAX algorithm isimplemented using two steps.In first step, it transformsthe time series data into a representaion,known asPiecewise Aggregate Approximation(PAA).Second stepconverts the PAA data into a series of symbols.

1) PAA : PAA divides a signal into N windows andthen calculates a representing value for that window.

V̄n =

l∑m=1

vmn/l (2)

V̄n is the representing value at nth window where l is thelength of the window.vmn means mth value in nth window.

Fig. 8: Piecewise approximation aggregation

Fig. 8 shows PAA representation of a signal.2) Conversion of PAA values into symbols: Represent-

ing value of each window is converted into a symbolicvalue using following equations:

V̂n = 1, if V̄n > µV̂n = 0, if V̄n < µ

(3)

µ is the mean value of the representing window values,obtained from PAA process of SAX technique.

Fig. 9: Encoding of symbol

Fig. 9 illustrates encoding of symbols from PAA rep-resented vallues.Once symbolic values are generated ,ob-servation sequence is generated using following equation:

obsn = V̂gn,x ∗ 25 + V̂ gn,y ∗ 24 + V̂ gn,z ∗ 23+V̂ an,x ∗ 22 + V̂ an,x ∗ 21 + V̂ an,x ∗ 20

(4)

obsn is observation symbol at nth window. V̂ gn,x,V̂ gn,y,V̂ gn,zare symbolic values in x,y,z axis respectively afterapplying SAX algorithm for nth window for gyroscopicsignal.Similarly V̂ an,x,V̂ bn,y,V̂ cn,z are symbolic values in x,y,zaxis respectively after applying SAX algorithm for nthwindow for accelarometer signal.

D. HMM AlgorithmsForward algorithm [8] in HMM is used to find log-

likelihood of a given sequence.Output of forward algorithmis probabillity of generating a given sequence.Input to theforward algorithm is the observation sequence generatedby SAX algorithm when applied to gait signal.

Algorithm 1 Forward algorithmInput: observation sequence obsT generated from single

gait cycleOutput: log-likelihood of given obsT

Initialisation t = 0 ,T ,aij ,bjk,αj(0)LOOP Process

1: for t = t+ 1 to T do2: αj(t) = bjkobsT (t)

∑Ni=1 αi(t− 1)aij

3: end for4: return log

∑Ni=1 α(T )

Backward algorithm [8] is used here to find the theprobability of generating rest of the symbols of a givenobservation sequence generated from a single gait cycle.

Algorithm 2 Backward algorithmInput: observation sequence obsT generated from single

gait cycleOutput: Backward probability of given obsT

Initialisation t = T ,aij ,bjk,βj(T )LOOP Process

1: for t = t− 1 to 0 do2: βi(t) =

∑Nj=1 βj(t+ 1)aijbjkobs

T (t)3: end for4: return βi(0)

From calculated α and β matrix a new variable γ iscalculated.

γij = αi(t− 1)aijbjkβj(t)/prob(obsT |λ) (5)

aij =

T∑t=1

γij(t)/

T∑t=1

∑k

γik(t) (6)

bjk =

T∑t=1obs(t)=k

γjl(t)/

T∑t=1

∑l

γil(t) (7)

Learning is the most important part of HMMtechnique.Baum-Welch algorithm [4] [8] which is basicallyan expectation-maximization algorithm is implemented forHMM parameter learning.It does not ensure a globallyoptimized values.

Algorithm 3 HMM learning algorithmInput: aij , bjk,training sequence obsTOutput: refined aij , bjk

Initialisation diff_likelihood, new_likelihood,old_likelihood, convergence_threshold:θ,iteration =0,max_iteration,aij ,bjkLOOP Process

1: while (iteration < max_iteration)or(diff_likelihood >θ) do

2: compute new_likelihood of obsT3: compute aij(iteration) from aij(iteration− 1) and

bjk(iteration− 1) ...by equation (6)4: compute bjk(iteration) from aij(iteration− 1) and

bjk(iteration− 1) ...by equation (7)5: diff_likelihood=new_likelihood−old_likelihood6: iteration=iteration+17: end while8: return refined aij and bjk

This HMM learning algorithm presented here is mod-ified Baum-Welch algorith for training of the multipleobservation sequence according to the classic paper ofRabinier [4] [8] [9] [10].

IV. Results and DiscussionExperiments are done using data captured from 4

healthy subjects.Table I and Table II show the experi-mental results for classification of normal and abnormalgait cycle detection for two kinds of abnormality detectionfor subject1.

TABLE I: Log-likelihood calculation for Equinus gaitLog-likelihood of normal and equinus gait

Log-likelihood M1(Normal gait ) M2(Abnormal gait)S1N-OS1 -14.34540342 -14.18745553S1N-OS2 -14.42071205 -14.67719142S1N-OS3 -14.48198901 -14.55779299S1N-OS4 -14.80423508 -15.03437918S1N-OS5 -14.25107514 -14.52106819S1N-OS6 -14.13267604 -14.70796865S1N-OS7 -14.15164197 -14.1785745S1N-OS8 -14.22850167 -14.47307013S1N-OS9 -14.26631103 -14.10508605S1N-OS10 -14.12640173 -14.63065957S1N-OS11 -14.22788245 -14.40307065S1ABN-OS1 -14.56738661 -14.91299052S1ABN-OS2 -14.75255629 -14.2137046S1ABN-OS3 -14.32937907 -14.37568544S1ABN-OS4 -14.1916366 -14.54954757S1ABN-OS5 -14.69153203 -14.56546745S1ABN-OS6 -14.43012332 -15.27524695S1ABN-OS7 -14.45491733 -14.21540613S1ABN-OS8 -14.66677913 -14.46674408S1ABN-OS9 -14.62681627 -14.28622814S1ABN-OS10 -14.58441958 -14.10381757S1ABN-OS11 -14.40854811 -14.088285

Model1(M1) is trained with all healthy gait cycles ob-tained from subject1 and Model2(M2) is trained withabnormal gait cycles obtained from simulated abnor-mal(equinus) gait pattern of subject1.Now both themodel are tested with some unknown gait cycles foreach of the class: normal and abnormal one.Total 250cycles are used for training purpose.Table I and Ta-ble II shows log-likelihood values of the test obser-vation sequences.Terms used in I and Table II aredescribed here.S1N-OS’X’:Observation sequence(OS) ’X’generated from normal gait(N) of Subject1(S1).S1ABN-OS’X’:Observation sequence(OS) ’X’ generated from ab-normal gait(ABN) of Subject1(S1). In case of correctclassification test observation sequence shows higher valueof log-likelihood for the model M1 if it is obtained fromnormal gait pattern and for model M2 if it is obtainedfrom abnormal gait pattern. In case of hemiplegic gaitclassification ’z’ axis gyroscope data is not taken accountbecause experimental result has not shown much impactfor ’z’ axis gyroscope data in case of hemiplegic gaitpattern.Experimental results demonstrates classificationaccuracy of normal and abnormal gait cycles.A properthreshold value is chosen on classification accuracy forcorrect classification of abnormal gait.We have made ahypothesis that if 60% of gait cycles of a person’s gait

pattern is classified as normal then that person’s gaitpattern treated as normal where as if more than 60% gaitcycles of a person’s gait pattern is found to be abnormalthen her or his gait pattern is considered as abnormal.Inthis method, classification accuracy of gait cycles of agait pattern is incorporated with a suitable threshold. Theproposed approach is robust enough to detect abnormalityfor each of the subjects and produces a 100% accuracy forabnormal gait pattern classification.

TABLE II: Classification result for Equinus gaitclassification result of normal and abnormal gait(equinus)

Count M1 M2 AccuracyS1N-OS 9 2 81%S1ABN-OS 4 7 63%

TABLE III: Log-likelihood calculation for Hemiplegic gaitLog-likelihood of test observation sequence

Count M1(Normal gait ) M2(Abnormal gait)S1N-OS1 -12.03524019 -11.97098397S1N-OS2 -11.8092911 -12.31288088S1N-OS3 -12.13452507 -12.39798012S1N-OS4 -12.07099728 -11.77009159S1N-OS5 -11.98172752 -12.03702437S1N-OS6 -12.10371747 -12.18459808S1N-OS7 -11.82523449 -12.18726981S1N-OS8 -12.1972103 -12.12991209S1N-OS9 -11.96288124 -12.00354937S1N-OS10 -12.13532087 -12.13814056S1N-OS11 -12.05899107 -12.25221977S1ABN-OS1 -12.1196267 -12.05082355S1ABN-OS2 -12.05398188 -11.74591902S1ABN-OS3 -11.94491075 -12.05286717S1ABN-OS4 -11.91638192 -11.47622636S1ABN-OS5 -12.10518114 -11.6965143S1ABN-OS6 -11.97424737 -11.93497431S1ABN-OS7 -11.91819425 -12.23157458S1ABN-OS8 -11.95137167 -11.97121798S1ABN-OS9 -12.4274885 -12.02331618S1ABN-OS10 -11.9882695 -11.49315648S1ABN-OS11 -11.85335339 -12.04940352

TABLE IV: Classification result for Hemiplegic gaitNormal and abnormal gait(Hemiplegic) classification result

Count M1 M2 AccuracyS1N-OS 8 3 72%S1ABN-OS 4 7 63%

V. CONCLUSION AND FUTURE WORKThe proposed approach for abnormality detection is

based on classification accuracy of the gait cycles obtainedfrom a person’s gait pattern.The gait pattern is said to bea normal or abnormal person’s gait if detection accuracyof the gait cycles is more than a threshold value then itcan be said that person is having normal or abnormal

gait pattern. Apart from abnormality detection,thisapproach may be useful for rehabilitation process ofgait assessment.We can infer that patient is improvingfrom past condition if accuracy of normal gait cycledetection is increased.Similarly with increasing accuracyof abnormal gait cycle detection indicates the increasedvalue of patient’s gait abnormality.Hence increment inaccuracy of normal gait cycle detection or decrement inaccuracy of abnormal gait cycle detection of a personsignifies improvement of gait condition.On the other handincrement in accuracy of abnormal gait cycle detection ordecrement in accuracy of normal gait cycle detection ofa person indicates degradation of gait condition of thatperson.Our current research scope is restricted to workwith single IMU sensor placed at shank.Use of more thanone sensor may improve the result by placing them into different parts of the upper and lower limb.Finallyensembling of features collected from different sensorscould improve the detection rate of gait abnormality.

Acknowledgments : We would like to be extremelythankful to Science and Engineering Research Board(SERB), DST, Govt. of India to support this researchwork. The IMU sensors used in our research experimentare purchased from the project funded by SERB withFILE NO: ECR/2017/000408.

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