Accelerometer Based Joint Step Detection and Adaptive Step Length Estimation Algorithm Using Handheld Devices

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1 Joural of Commuicatios Vol. 0, No. 7, July 205 Accelerometer Based Joit Step Detectio ad Adaptive Step Legth Estimatio Algorithm Usig Hadheld Devices Yu Liu, Yapig Che, Lili Shi2*, Zegsha Tia2, Mu Zhou2, ad Ligxia Li2 Istitute of Optical Commuicatio Techology, Chogqig Uiversity of Posts ad Telecommuicatios, Chogqig , Chia 2 Chogqig Key Lab of Mobile Commuicatios Techology, Chogqig Uiversity of Posts ad Telecommuicatios, Chogqig , Chia {liuyu, tiazs, zhoumu, {chogyoucheyp, slili202}@sia.com Abstract The pedestria iertial avigatio systems are geerally based o Pedestria Dead Recoig (PDR) algorithm. Cosiderig the physiological characteristics of pedestria movemet, we use the cyclical characteristics ad statistics of acceleratio waveform ad features which are associated with the walig speed to estimate the stride legth. Due to the radomess of the pedestria had-held habit, the step evets caot always be detected by usig the periods of zero velocity updates (ZUPTs). Furthermore, the sigal patters of the sesor could differ sigificatly depedig o the carryig modes ad the user s had motio. Hece, the step detectio ad the associated adaptive step legth model usig a hadheld device equipped with accelerometer is required to obtai high-accurate measuremets. To achieve this goal, a compositioal algorithm of empirical formula ad Bac-propagatio eural etwor by usig hadheld devices is proposed to estimate the step legth, as well as achieve the accuracy of step detectio higher tha 98%. Furthermore, the proposed oit step detectio ad adaptive step legth estimatio algorithm ca help much i the developmet of Pedestria Navigatio Devices (PNDs) based o the hadheld iertial sesors. Idex Terms Pedestria iertial avigatio; hadheld devices; step detectio; step legth estimatio; accelerometer I. INTRODUCTION Nowadays, the most of the hadheld devices have bee itegrated with the gyroscope, accelerometer, magetometer, ad barometer to provide the data eeded for pedestria avigatio sesors. With the developmet of Micro Electro Mechaical Systems (MEMS) techique ad its wide applicatios i smart phoes ad may other hadheld devices, the demad for avigatig the pedestria by usig a had-held mobile device has remarably icreased over the last few years, especially i GPS deied scearios []. The widespread dissemiatio of smartphoes has prompted a great success of locatio-based services, lie the emergecy relief map for idoor itelliget avigatio [2]-[4]. Real-time measuremet of the process of movig the body motio parameters ad the calculate the displacemet iformatio is a commo approach to realize the idoor positioig, how to obtai huma motio parameters of Mauscript received March 2, 205; revised July 20, 205. Correspodig author slili202@sia.com. doi:0.2720/cm which became the first problem to be solved. To obtai the accurate, as well as real-time huma motio parameters, the MEMS sesors are ofte selected to collect the iertial parameters. The proposed pedestria avigatio algorithm is based o Pedestria Dead Recoig (PDR) which cosists of step detectio, stride legth estimatio, ad headig estimatio [5]. The MEMS sesor data which are obtaied by usig acceleratio, agular velocities, ad magetic parameters, are used to reveal the displacemet movemet of the target. The step legth estimatio algorithm by usig the MEMS sesors is always recogized as a difficult problem. I step legth estimatio, a large umber of previous literatures idicated that the carryig habit of MEMS sesors is the ey to the precisio of measuremets [6-8]. Although early i 972 the use of accelerometer was proposed to aalyze the process of movig huma poit of view, the step legth estimatio algorithm was ot util recetly that a few years before someoe will study the process of movig the body based o accelerometers ad gyroscopes equipped o the torso, thighs, legs, feet, ad hads. With the help of the parameters of MEMS sesors, we ca easily recogize the huma actios, calculate the road displacemet, ad fid the travel directio. Whe the MEMS sesors are fixed o the body tru, the accuracy is low ad the cost of MEMS sesors is high [9]. Whe the sesors are fixed o the thigh, sice this place does ot tae advatage of the body's ormal movig, MEMS sesors will affect the body's ormal travel traectory, the performace of actio recogitio is well, whereas the accuracy of step legth estimatio is low [0]. Whe the sesors are fixed o the calf, the accuracy of estimatig the travel speed ad travel displacemet is higher tha other methods, obtaied by the particularity of the traectory of the calf i the process of movig, whereas this approach requires the strict process of movig approximatio iverted pedulum motio []. Whe the MEMS sesors are fixed o the foot, the step legth is calculated based o the switch sesor, pressure sesor, groud reactio force, ad mobile mode of foot [2]. I this case, although the accuracy of measuremets is sigificatly high, the strict test coditios ad high cost of equipmet restrict its wide applicatios.

2 Joural of Commuicatios Vol. 0, No. 7, July 205 Compared to the previously discussed approaches, a ovel oit step detectio ad adaptive step legth model usig a hadheld device oly with the accelerometer is required to achieve high accuracy measuremets. I this paper, the compositioal algorithm of empirical formula ad Bac-propagatio eural etwor usig a smartphoe is preseted to estimate step legth. The rest of this paper is structured as follows. Sectio II presets the gait model of pedestria. Sectio III shows the steps of the step detectio algorithm by usig hadheld devices i detail. The discussio o the step legth estimatio method is addressed i Sectio IV. Extesive experimetal results are provided i Sectio V. Fially, Sectio VI cocludes the paper. II. GAIT MODEL OF PEDESTRIAN Walig is the most commo ad frequet movemet of the pedestria. Whe the pedestria is walig, the body ceter of gravity chages costatly i the horizotal directio, as well as i the vertical directio. The developmet of moder measuremet techique helps to coduct the dyamic quatitative aalysis with respect to the various parts of the body. The various parts of the body, lie the feet, legs, ad waist produce a correspodig movemet durig walig as the acceleratio ad agular velocity chage. Each gait cycle ca be divided ito two phases [3]: the stace phase ad swig phase, as show i Fig.. Iitial stace phase The first swig phase The secod swig phase Ed stace phase III. STEP DETECTION ALGORITHM Accordig to the characteristics of pedestria walig, the output waveform of the tri-axial accelerometer chages periodically while the pedestria is walig. O this basis, we rely o the cyclicity ad eigevalues of tri-axial acceleratio to detect the gait. The output wave form of the tri-axial acceleratio is calculated by where a x, Acc Value a a a () a y, ad _ x y z a z represet the output wave form i the X, Y, ad Z directios of the accelerometer, respectively. The output wave form of the tri-axial accelerometer always produces multiple peas, which most probably lead to the mistae idetificatio of the pedometer. By usig the digital low pass filter to modify the output wave form of the tri-axial accelerometer, we ca obtai the fie-tued pea curve ad cosequetly detect the peas accurately based o the calculatio of the umber of steps. We adopt the Hammig widow fuctio with digital low-pass filter to tri-axial accelerometer. The widow legth of filter is 0. The filterig results are show i Fig. 2. Acc-Value(m/s 2 ) Raw filterig Time(s) Fig. 2. Compariso betwee the raw output wave form ad the output wave form after filterig Fig.. Physical model of pedestria movemet The stace phase is the period occupyig about 62% of the gait cycle time whe the feet touch the groud. Uder the ormal walig coditio, the feet are touchig the groud the whole time about 24% of the gait cycle time. The swig phase which cosists of the first swig phase ad secod swig phase is the period occupyig about 38% of the gait cycle time whe the feet are i the air. Specifically, the first swig phase begis whe the stace phase eds, while the gravity ceter of the body moves up ad is the located at the frot foot. The gravity ceter of the body is located at the bac foot i the secod swig phase, ad moves dow at the ed of the secod swig phase. Sice the hadheld device is held i the swigig had, the output wave form of the tri-axial accelerometer geerates icorrect peas, as show i Fig. 3. Acc-Value(m/s 2 ) Icorrect Pea Time(s) Fig. 3. Output wave form of the tri-axial accelerometer after filterig 52

3 Joural of Commuicatios Vol. 0, No. 7, July 205 To solve this problem, we set a threshold to elimiate the errors ivolved i step coutig, as show i (2). T Acc _ Value g where T is the time iterval betwee two adacet peas, g is the output value of the acceleratio. ad are the thresholds for the time ad peas respectively. The values of ad were obtaied accordig to the sample frequecy ad data aalyses ad test results. IV. STEP LENGTH ESTIMATION ALGORITHM Alog with the developmet of the pedestria dead recoig algorithm, the step legth estimatio algorithm becomes more ad more favored. Up to ow, the previous studies maily focused o the situatios that the sesors are equipped i the user s phoig or textig had without cosiderig the hadheld sesors. The existed ad most represetative simple liear model [4], huma movemet model [5], empirical model ad eural etwor model [6] have paid little attetio to the improvemet of the accuracy of step legth estimatio. To fix this gap, a ovel step legth estimatio approach is proposed by usig the compositioal algorithm of empirical formula ad etwor. A. Empirical Formula Based Modelig Based o the relatios betwee the output wave form of the tri-axial accelerometer ad step legth [7], we have SL K 4 Accmax Accmi (2) (3) where SL is the step legth, Acc max ad Accmi stad for the maximum ad miimum output wave form of a tri-axial accelerometer i each step respectively. K is the calibratio factor which is obtaied by the ratio of the real ad estimated referece traectory distaces, as show i formula (4). d real K= (4) d estimated Based o formula (4), the step legths of differet pedestrias are estimated by adustig the values of K. B. BP Neural Networ Based Modelig etwor is ow as a multilayer feed forward eural etwor which is featured with sigal prior to trasmissio ad error bac propagatio [8]. The iput sigal from the iput layer through the hide layer is processed scale by scale util the output layer i the forward pass. Each layer of euros state affects oly the ext layer of euros state. If the output layer is ot expected output, it will be trasferred bac propagatio. Accordig to the forecast error adustmet of etwor weights ad thresholds, BP eural etwor predicts the output more ad more close to the desired output. Fig. 4 shows the structure of a simple BP eural etwor. X X 2 X Iput Layer i Fig. 4. Structure of etwor Hide Layer Y Output Layer I Fig. 4, X ( X, X 2,,X ) T, Y ( Y, Y2, Y ) T m are the iput ad output vectors. i ad are the weights betwee the iput ad hide layers ad betwee the hide ad output layers respectively. By settig ad as the thresholds of the hidde ad output layers, we have ' ' X f i Xi, Y f X i i (5) For simplicity, we set, X,, ad ' X Y m. The, (5) is coverted ito ' ' i i, i i (6) X f X Y f X By assumig that the umber of traiig samples is p, ad the correspodig expected ad actual output are p t p p p (,2,, ) ad Y, the error is the sum of each output uit error represeted by the formula (7). E t Y (7) m p p 2 p ( ) 2 0 Hece, the traiig error with respect to the traiig set equals to f V h E t Y (8) p m p p 2 all ( ) 2 p 0 Iput Hide layer Output Fig. 5. Structure of etwor for step legth estimatio We assume that the walig frequecy of the pedestria is f, amout of acceleratio chage is V, ad height of SL 522

4 Joural of Commuicatios Vol. 0, No. 7, July 205 the pedestria is h. The, the o-liear relatios from f, V, ad h to SL which are characterized by etwor (see Fig. 5) is otated as SL= ( f, V, h) Step umber Step detectio Step legth estimatio Raw Data Pre-proccesig Step detectio Evet extractio (max/mi) Step legth model Step frequecy etwor Calibrated coefficiet K (9) I (9), V is obtaied by the variace i the acceleratio mode value of a step. The flowchart of BP eural etwor based modelig for step legth estimatio cosists of the modules of etwor costructio, traiig, ad predictio, as show i Fig. 5. It has associative memory ad ability to predict by traiig the etwor before etwor predictio. Step estimatio algorithm based o etwor modelig, icludig etwor costructio, BP eural etwor traiig ad etwor predictio, the algorithm processes show i Fig. 6. height Fig. 7. Flowchart of the proposed compositioal algorithm I the costructed etwor, there are 2, l, ad odes i the iput, hidde, ad output layers respectively, as show i Fig. 8. The value of l is determied based o the criteria show below. l l ( m ) a N suitable BP eural etwor to build etwor traiig etwor iitializatio Ed where, l, ad m are the umber of euros i the iput, hidde, ad output layers respectively. a is a costat i the rage of [0, 0]. Through the actual etwor traiig, the system o the umber of hidde layer odes is 5, l =5. Based o etwor, the oliear equatio modelig of the calibratio factor K is established, which impacted by height ad step frequecy, as show i Fig. 8. etwor traiig Y etwor predictio (0) l log 2 etwor costructio System Modelig Step legth f Test Data K etwor predictio h Fig. 6. Flowchart of etwor based modelig for step legth estimatio C. Compositio of Empirical Formula ad BP Neural Networ Fig. 8. Structure of etwor for step estimatio Due to the differet height, attitude, ad walig frequecies of the pedestria, the step legths could vary greatly. Therefore, a efficiet calibratio factor K i the empirical formula to be used to estimate the step legths is difficult to be obtaied. I etwor, the accuracy of estimatig the step legths caot be guarateed sice the model estimate of the step legth is ot accurate. I this paper, the step legth is estimated by usig the compositioal algorithm of empirical formula ad etwor. As the calibratio factor of the experiece model does ot require statistical user practical step, which ca be estimated by etwor model ad the usig the experiece formula obtaied the step legth. By aalyzig the obtaied, the calibratio factor K experieces the greatest impact by height ad step frequecy of pedestria, taig ito accout the o-liear relatioship betwee them, usig etwor to predict the real-time values for the calibratio factor K. Fig. 7 shows the flowchart of the proposed compositioal algorithm. Output layer Hide layer Iput layer 523 (a) (b) (c) Fig. 9. (a) Photo of the tri-axial accelerometer (b) Photo of a smartphoe equipped with the tri-axial accelerometers (c) Photo of a user holdig the smartphoe V. EXPERIMENTAL RESULTS A. Hardware Descriptio We select the tri-axial accelerometer, LIS303DLHC, equipped i a HUAWEI smartphoe for the testig. This tri-axial accelerometer is featured with the measuremet rage of ±2g, where g is the gravity acceleratio. The calibratio is coducted to tri-axial accelerometer. The tri-axial accelerometer is the sample rate of 50Hz.

Joural of Commuicatios Vol. 0, No. 7, July 205 B. Performace Evaluatio The experimetal data are tae by 5 male ad 5 female voluteers with the height varyig betwee 58 cm ad 86 cm. As show i Fig.

5 Joural of Commuicatios Vol. 0, No. 7, July 205 B. Performace Evaluatio The experimetal data are tae by 5 male ad 5 female voluteers with the height varyig betwee 58 cm ad 86 cm. As show i Fig. 0, each voluteer holdig a smart phoe wals alog a straight path with the legth of 05 m, as well as records the umber of steps three times, each time with differet costat walig velocities, amely as the fast velocity, slow velocity, ad ormal velocity. compares the errors of step legth estimatio by usig the proposed compositioal algorithm ad the covetioal empirical formula based ad etwor based algorithms. The vertical axis idicates the relative errors betwee the real ad estimated path legths. The whiser legth is limited i the.5 iterquartile rages. The + labels outliers i betwee the.5 ad 3 iterquartile rage. Obviously, the relative error of the proposed compositioal algorithm is smaller tha the oes achieved by the covetioal algorithms Relative Errors 0. 0 Fig. 0. A voluteer with a smartphoe walig alog a straight path Table I shows the results of step detectio. The 5 male ad 5 female voluteers are otated as M,, M5 ad F,, F5 respectively. TABLE I: STEP DETECTION ALGORITHM PERFORMANCE FOR THE CONTROLLED DATA COLLECTION Voluteers Height (cm) Real umber of steps Estimated umber of steps F F F F F M M M M M Mea / Estimated path legths (m) BP empirical formula compositioal algorithm IDs of experimets Fig.. Results of the estimated path legths Fig. shows the estimated path legth with respect to each experimet. To illustrate this result clearer, Fig BP Empirical Formula Compositio Algorithm Fig. 2. Compariso of the errors of step legth estimatio VI. CONCLUSIONS I this paper, we have paid sigificat attetio to the accelerometer based oit step detectio ad step legth estimatio, as well as gait aalysis. The experimetal results with respect to 5 male ad 5 female voluteers demostrate that the tri-axial accelerometer based step detectio achieves the percetage of correct step detectio over 99.4%. Furthermore, the proposed step legth estimatio algorithm helps much i decreasig the relative errors of the pedestria avigatio. I future, we will cotiue to discuss the situatio that the pedestria wals with swigig hads. This directio opes may ew research optios towards the free-iertial tracig of the pedestria with hadheld iertial sesors, which have bee widely applied i smart phoes owadays. ACKNOWLEDGMENT This wor was supported i part by the Natioal Natural Sciece Foudatio of Chia uder Grat ad Grat 62749, The Iteratioal Joit Research Ceter techology platform ad base costructio (cstc204ghz0038), Key Laboratory of Optoelectroic Devices ad Systems of Miistry of Educatio ad Guagdog Provice ad i part by the Program for Chagiag Scholars ad Iovative Research Team i Uiversity (IRT299), Natioal Natural Sciece Foudatio of Chia (63026), Special Fud of Chogqig Key Laboratory (CSTC), Fudametal ad Frotier Research Proect of Chogqig (cstc203cya40032, cstc203cya40034, cstc203cya4004), Scietific ad Techological Research Program of Chogqig Muicipal 524

ad Studet Research Traiig Program of CQUPT (A203-64). REFERENCES [] M. Susi, V. Reaudi, ad G. Lachapelle, Motio mode recogitio ad step detectio algorithms for mobile phoe users, Sesors, vol. 3, pp.

, Iertial sesor-based idoor pedestria localizatio with miimum 802.5. 4a cofiguratio, IEEE Tras. o Idustrial Iformatics, vol. 7, pp. 455-466, May 20. [4] J. Cho ad H.

, Idoor 3D pedestria tracig algorithm based o PDR usig smartphoe, i Proc. IEEE 2th Iteratioal Cof. Cotrol, Automatio ad Systems, JeJu, 202, pp. 442-445. [6] A. Ali, S. Siddharth, Z. Syed, et al.

Nashville, Teessee, September 7-2, 202. [7] M. Gluec, A. Buhma, ad Y. Maoli, Autocalibratio of MEMS accelerometers, i Proc. Istrumetatio ad Measuremet Techology Cof., Graz, 202, pp. 788-793. [8] D.

6 Joural of Commuicatios Vol. 0, No. 7, July 205 Educatio Commissio (KJ30528), Startup Foudatio for Doctors of CQUPT (A202-33), Sciece Foudatio for Youg Scietists of CQUPT (A202-77), Sciece Foudatio for Youg Scietists of CQUPT (A203-3) ad Studet Research Traiig Program of CQUPT (A203-64). REFERENCES [] M. Susi, V. Reaudi, ad G. Lachapelle, Motio mode recogitio ad step detectio algorithms for mobile phoe users, Sesors, vol. 3, pp , Feb [2] J. Hightower ad G. Borriello, A survey ad taxoomy of locatio systems for ubiquitous computig, IEEE Computer, vol. 34, pp , Aug [3] S. Lee, B. Kim, H. Kim, et al., Iertial sesor-based idoor pedestria localizatio with miimum a cofiguratio, IEEE Tras. o Idustrial Iformatics, vol. 7, pp , May 20. [4] J. Cho ad H. Cha, Life-map: A smartphoe-based cotext provider for locatio-based services, IEEE Pervasive Computig, vol. 0, pp , Feb. 20. [5] B. Shi, J. H. Lee, H. Lee, et al., Idoor 3D pedestria tracig algorithm based o PDR usig smartphoe, i Proc. IEEE 2th Iteratioal Cof. Cotrol, Automatio ad Systems, JeJu, 202, pp [6] A. Ali, S. Siddharth, Z. Syed, et al., A improved persoal dead-recoig algorithm for dyamically chagig smartphoe user modes, preseted at the 25th Iteratioal Techical Meetig of the Satellite Divisio of the Istitute of Navigatio, Nashville, Teessee, September 7-2, 202. [7] M. Gluec, A. Buhma, ad Y. Maoli, Autocalibratio of MEMS accelerometers, i Proc. Istrumetatio ad Measuremet Techology Cof., Graz, 202, pp [8] D. Gusebauer, C. Isert, ad J. Krosche, Self-cotaied idoor positioig o off-the-shelf mobile devices, i Proc. IEEE 200 Iteratioal Cof. Idoor Positioig ad Idoor Navigatio, Zurich, Switzerlad, 200, pp. -9. [9] S. Ayub, X. Zhou, S. Hoary, A. Bahramiasab, ad B. Hoary, Sesor Placemet Modes for Smartphoe based Pedestria Dead Recoig, New Yor: Spriger Netherlads, 202, ch. 4, pp [0] J. Par, Sythesis of atural arm swig motio i huma bipedal walig, Joural of biomechaics, vol. 4, pp , July [] S. H. Shi, C. G. Par, ad J. W. Kim, Adaptive step legth estimatio algorithm usig low-cost MEMS iertial sesors, preseted at the IEEE Sesors Applicatios Symposium, Sa Diego, CA, February -5, [2] W. Y. Shih, L. Y. Che, ad K. C. La, Estimatig walig distace with a smart phoe, preseted at the IEEE 202 Fifth Iteratioal Symposium o Parallel Architectures, Algorithms ad Programmig (PAAP), Taipei, December 66-7, 202. [3] J. Jah, U. Batzer, J. Seitz, et al., Compariso ad evaluatio of acceleratio based step legth estimators for hadheld devices, preseted at the IEEE 200 Iteratioal Cof. Idoor Positioig ad Idoor Navigatio (IPIN), Zurich, September -6, 200. [4] D. Alvarez, R. C. Gozalez, A. Lopez, ad J. C. Alvarez, Compariso of step legth estimators from weareable accelerometer devices, i Proc. IEEE 28th Aual Iteratioal Cof., New Yor, NY, 2006, pp [5] M. Susi, V. Reaudi, ad G. Lachapelle, Quasi-Static Detectio from MEMS Hadheld Devices, preseted at the Proceedigs of the Iteratioal Coferece o Idoor Positioig ad Navigatio (IPIN), Guimarães, Portugal, September 2-23, 20. [6] I. Sog, P. Hädel, J. O. Nilsso, ad J. Rataoo, Zero-velocity detectio A algorithm evaluatio, IEEE Trasactios o Biomedical Egieerig, vol. 57, pp , November 200. [7] L. Pei, J. Liu, R. Guiess, Y. Che, H. Kuusiemi, ad R. Che, Usig LS-SVM based motio recogitio for smartphoe idoor wireless positioig, Sesors, vol. 2, pp , May 202. [8] R. H. Nielse, Theory of the bac-propagatio eural etwors, i Proc. Iteratioal Joit Cof. Neural Networs, Washigto, DC, Jue 593-6, 989. Yu Liu was bor i Chogqig Provice, Chia, i 972. He received the Ph.D. degree from the Chogqig Uiversity of Chia i His research iterests iclude vibratio iertial sesors, optical fiber sesor, iertial avigatio, sesors ad sigal processig. Yapig Che was bor i Chogqig Provice, Chia, i 990. She is ow studyig i Chogqig Uiversity of Posts ad Telecommuicatios of Chia. Her research iterests iclude iertial avigatio, sesors, artificial itelligece, ad sigal processig. Lili Shi was bor i Hea Provice, Chia, i 988. She is ow studyig i Chogqig Uiversity of Posts ad Telecommuicatios of Chia. Her research iterests iclude iertial avigatio, sesors, artificial itelligece, ad sigal processig. Zegsha Tia was bor i Hea Provice, Chia, i 968. He received the Ph.D. degree from Uiversity of Electroic Sciece ad Techology of Chia i His research iterests iclude persoal commuicatios, satellite avigatio, wireless localizatio ad sigal detectio ad estimatio. Mu Zhou was bor i Chogqig Provice, Chia, i 984. He received the Ph.D. degree from the Uiversity of Hog Kog Uiversity of Sciece ad Techology. His research iterests iclude wireless localizatio ad avigatio, atural laguage processig ad artificial itelligece ad satellite commuicatios. Ligxia Li was bor i Hubei Provice, Chia, i 974. She received the Master's degree from Chogqig Uiversity of Posts ad Telecommuicatios. Her research iterests iclude persoal commuicatios, satellite avigatio, wireless localizatio ad sigal detectio ad estimatio. 525

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