WLAN-Based Pedestrian Tracking Using Particle Filters and Low-Cost MEMS Sensors

Transcription

1 WLAN-Based Pedestran Trackng Usng Partcle Flters and Low-Cost MEMS Sensors Hu Wang, Hennng Lenz, Andre Szabo, Joachm Bamberger, Uwe D. Hanebeck Abstract Indoor postonng systems based on Wreless LAN (WLAN) are beng wdely nvestgated n academa and ndustry. Meanwhle, the emergng low-cost MEMS sensors can also be used as another ndependent postonng source. In ths paper, we propose a pedestran trackng framework based on partcle flters, whch extends the typcal WLAN-based ndoor postonng systems by ntegratng low-cost MEMS elerometer and map nformaton. Our smulaton and real world experments ndcate a remarkable performance mprovement by usng ths fuson framework. Index Terms Indoor Postonng, Pedestran Trackng, Partcle Flter, MEMS P I. INTRODUCTION OSITIONING and navgaton systems have acheved great success n a broad category of so-called locaton-based servces (LBS), such as personnel securty, trackng of assets and people, ntellgent gudance, locaton-aware multmeda servces and many others [-4]. Generally, these systems can be separated nto three groups: satellte based systems, local network based systems and sensor based systems. Satellte systems, such as the well-known GPS or Galleo systems, focus on the outdoor postonng [5, 6]. However, these systems suffer from the attenuaton, reflecton and refracton of buldngs and walls when used ndoors. Another category of postonng systems makes use of exstng communcaton network nfrastructures, such as Wreless LAN (WLAN), Ultra-Wdeband (UWB) or DECT networks [7-]. The receved sgnal strength (), tme of arrval (TOA), tme dfference of arrval (TDOA) and angle of arrval (AOA) are typcally used to nfer the user s locaton. The advantage usng such systems s that they can be deployed both ndoors and outdoors. In addton, they make use of avalable networks and does not need addtonal hardware, thereby keepng the nstallaton and mantenance cost at a low level. But stll, current network-based systems suffer from the nosy characterstcs of wreless channel and mult-path dstorton, leadng to a coarse uracy. The last category of systems uses Manuscrpt receved December 9, 7 Hu Wang, Hennng Lenz, Andre Szabo, and Joachm Bamberger are wth Semens AG, Corporate Technology, Informaton and Communcatons, CT IC 4, Germany ({hu.wang.ext, hennng.lenz, andre.szabo, joachm.bamberger}@semens.com). Uwe D. Hanebeck, s wth Intellgent Sensor-Actuator-Systems Laboratory, Insttute of Computer Scence and Engneerng, Unverstät Karlsruhe (TH), Germany (uwe.hanebeck@eee.org). varous dedcated sensors. These sensors ether sense the absolute locaton related nformaton, such as magnetc sensors, laser sensors, ultrasonc and nfrared sensors, or sense the change of locaton related nformaton, such as nertal sensors or barometrc sensors [5,,, 4]. Snce nertal sensors can only provde relatve nformaton, they are often combned wth other postonng systems. For nstance, the GPS/INS soluton uses GPS as a supervsor to correct the umulatve errors of nertal sensors, and on the other hand, nertal navgaton systems (INS) also mprove the performance of GPS, especally n tunnel or other scenaros where GPS sgnals are temporally blocked [5, 3]. Tradtonal nertal navgaton systems are bg and expensve, whch lmts ther ntegraton wth ndoor navgaton systems. However, the emergng MEMS technology makes low-cost and small sze nertal sensors a realty [6]. One example are MEMS elerometers, whch are avalable at a prce lower than dollar today and have successfully been ntegrated nto moble devces [5]. In ths paper, we propose a fuson framework based on partcle flters. Dfferent from other expensve IMU asssted systems [3, 4], our framework ntegrates the typcal WLAN pedestran postonng system wth only a low cost elerometer and map nformaton, as shown n Fg.. The remander of the paper s organzed as follows. In Secton II, we brefly ntroduce the -based WLAN postonng system. In Secton III, we analyze the useful nformaton from MEMS elerometer. Our partcle flterng algorthm s proposed n Secton IV. We also dscuss other flters for the purpose of comparson n ths secton. Expermental results based on both smulaton and real world test data are gven n Secton V. Fnally, Secton VI concludes the paper. II. POSITIONING ALGORITHM BASED ON MEASUREMENTS In network based localzaton systems, s most often used as the nput of the postonng algorthm because t s much easer to obtan than the tme or the angle nformaton. The popular localzaton algorthm for the based systems s the so-called pattern matchng or K-nearest neghbors (KNN) algorthm [7]. Ths algorthm ncludes the followng two steps:. In the offlne step, the receved power vectors from several ess ponts (APs) at calbraton ponts are measured

2 Raw Acceleraton n X Applcatons.5 Walls, Doors Locaton Dstance Map Partcle Flters Accelerometer Tme (s) Raw Acceleraton n Y.5 Locaton Pattern Matchng Tme (s) Raw Acceleraton n Z WLAN Fg.. Structure of Indoor Trackng Framework - 3 Tme (s) 4 5 and recorded as the fngerprnts of the calbraton ponts.. In the onlne step, the receved power vector s then compared wth the fngerprnt of calbraton ponts usng the dstance metrc n Equaton (). The K calbraton ponts whch have the closest dstances wth the receved power vector are fnally chosen and averaged as the fnal estmaton. Q d( x ) = P m P ( x), () Q q = q q where P m q s the measured power from ess pont q, P q (x) s the q th element of the fngerprnt at the calbraton pont x. Q s the number of APs. III. MEMS ACCELEROMETER AND MOVEMENT MODEL The elerometer s a devce for measurng the eleraton of movng objects. Thanks to the fast development of MEMS technology, the small and cheap MEMS elerometers are already avalable [6]. Fg. gves an example of the raw measurement of a stay-walkng-stay behavor usng the commercal Freescale MMA76Q 3-axs elerometer. Theoretcally, the movng speed and dstance can be obtaned by ntegratng the eleraton sgnal. But for ndoor pedestran walkng, the eleraton s small, so t can hardly be separated from sensor nose, offset drft, and tlt varaton. An alternatve approach s to detect the walkng steps. Whle people walk, the vertcal eleraton fluctuates perodcally due to the moton mechansm. Ths perodcal sgnal stands for the steps people walked, as shown n Fg. 3. So we need to dentfy the steps and step sze to obtan the walkng dstance D = Step _ Sze Num _ Steps. () In our paper, we use a smple zero-crossng algorthm to detect the number of steps. We know that the vertcal eleraton sgnal crosses the zero lne twce every step. Hence, we can count the number of zero crossng ponts and dvde t by two, dervng the number of walked steps Num_Steps. The step sze s calculated by an emprcal equaton proposed by engneers from Analog Devce [], as shown n Equaton (3). Step _ Sze 4 A A C, (3) max mn where A max and A mn are the maxmum and mnmum eleraton n one step, respectvely; C s a constant Acceleraton (g) Acceleraton (g) Acceleraton (g) A cce le ra to n (g ) Fg.. Raw Measurement of Acceleraton (The offset g n z-axs s already compensated) Fltered Acceleraton n Z-axs (Flter Length=.5s) Tme (s) Fg. 3. Fltered Acceleraton n Z-axs (The offset g n z-axs s already compensated) value, whch can be obtaned from walkng tranng. Some more urate, but also more complex models for calculatng the number of step and step sze can be found n the lterature [7, ]. In Secton V, we wll see that our flterng algorthm s not senstve to the estmaton error of walkng dstance, whch favors the use of a smple model for the dstance estmaton. IV. FILTERING ALGORITHMS In ndoor postonng systems, the fluctuaton of measurements leads to a coarse estmaton uracy. When the moble devce needs to be localzed contnuously, the flterng can help to smooth the trajectory and to reduce the estmaton error. A Kalman flter s commonly used n trackng applcatons. The drawback of Kalman Flter s also obvous. Its man assumpton,.e. the lnear model, s hardly fulflled n real lfe. The Extended Kalman Flter (EKF) and Unscented Kalman Flter (UKF) are proposed to solve the non-lnear estmaton problem by lnearzng all the non-lnear models. But they are only relable for systems whch are almost lnear. Dstrbuted nformaton lke the map nformaton s mpossble to be ntegrated for trackng by EKF or UKF. As an alternatve to Kalman flter and ts dervatves, partcle flters are attractng more and more attenton recently []. Partcle

3 3 flters are based on Monte-Carlo samplng and thus can deal wth non-lnear and non-gaussan estmaton problems. Usng Partcle flters addtonal nformaton lke walkng dstance and map nformaton can be straghtforwardly ntegrated. Ths holds although the map nformaton s non-lnear and dstrbuted n space and although the walkng dstance characterzes only one part of the movement behavor,.e., nformaton on the orentaton s mssng. In the followng, we wll brefly ntroduce the Kalman flter model as a reference for comparson. Then we focus on the partcle flter model as well as ts ntegraton wth elerometer and map nformaton. A. Kalman Flter Kalman flter models a dscrete-tme controlled process usng the followng lnear stochastc dfference equatons for state x( and measurement z(: x = Ax( k ) + Bu( + n( k ) (4) z = Hx( + v( (5) Here, the matrces, A, B, H defnes the lnear transton and measurement processes, whle the random vector n and v represent the process and measurement nose respectvely. They are assumed to be ndependent, whte, and wth normal dstrbutons p(n)~n(, Q), (6) p(v)~n(, R). (7) Here, Q and R are covarance matrces of state error and measurement error, respectvely. For the based systems, we defne the parameters as follows: x( = y( x, A =, v x v y a x x n = ( ) Δ, z = a k, y y t e x H =, v =, e y where x and y are the poston n x-axs and y-axs; v x and v y are the speed n x-axs and y-axs; a x and a y are the eleraton whch s regarded as nose; z s the estmated poston from measurements. And v can be seen as the error of -based postonng algorthms. Then the estmated state xˆ can be calculated usng the followng predcton and correcton steps [5, ]: x ˆ = Axˆ( k ), (8) P ( = AP(k ) A T + Q, (9) T T K( k ) = P H ( HP H + R), () x ˆ( = xˆ + K( ( z( Hxˆ ), () P = ( I K( H) P, () where P - ( s the covarance matrx correspondng to the predcted state and P( s the covarance matrx correspondng to the estmated state that already ncludes the recent measurement. B. Partcle Flters () General Algorthm Dfferent from the Kalman flter, the partcle flters drectly estmate the posteror probablty densty functon (pdf) of the state x( gven the past observatons Z( usng the followng equaton []: N = ( x( ) p( x( Z( ) w δ x, (3) where x ( s the -th samplng pont or partcle of the posteror probablty. w ( s the weght of the partcle. The bggest advantage of the partcle flter s that t can solve non-lnear and non-gaussan estmaton problems. Many forms of partcle flters are avalable n the lterature []. Here we consder the commonly used Sequental-Importance- Resamplng (SIR) partcle flter. Ths flter comprses of the followng steps []: a) Intalzaton: Samplng N partcles {x (), = N} ordng to the ntal pdf p(x()). b) Predcton Samplng: For each partcle x (, get a new partcle x (k+) from the transton pdf p(x(k+) x (). c) Importance Samplng: For each new partcle x (k+), calculate w (k+)= p(z(k+) x (k+)). d) Normalzaton and Resamplng: The weghts are normalzed and fnally re-sampled. In the resamplng step, partcles wth low weght are deleted and partcles wth hgh weght are duplcated such that each partcle has the same weght. A detaled descrpton of the resamplng algorthm can be found n []. From the above descrpton, we see that for partcle flters, the transton densty functon p(x(k+) x() and the update densty functon p(z(k+) x(k+)) should be known to such an extent that enables to do predcton samplng and calculaton of weghts (see below). But, n general, the pdfs are not requred to be Gaussan. () Partcle Flter for only Measurement For comparson wth the descrbed Kalman flter, we apply a partcle flter also usng only measurements. For each old partcle x (=[x ( y ( v x( v y(] T, a new partcle x (k+) can be obtaned from the followng transton functon: x ( k + ) x y ( k + ) y a x = + + ( ) ( ) Δ, v x ( k ) v x k a k y t v y ( k + ) v y (4) where t s assumed that the movement of a person s governed by nerta whch s supermposed by Gaussan

4 4 eleraton nose,.e. a x ( and a y ( are sampled from the normal dstrbuton N(, Q). The weghts can be computed usng Equaton (5), whch assumes that the poston estmated by based pattern matchng s Gaussan dstrbuted around the true poston. w ( k + ) = p( z( k + ) x ( k + )) ( x ( k+ ) x ( k+ )) + ( y ( k+ ) y ( k+ )) σ (5) = e πσ (3) Fuson of Measurement and Accelerometer wth a Partcle Flter When an elerometer s used, the extra nformaton, walkng dstance d( between two samples can be obtaned usng the algorthm n Secton III. Ths nformaton cannot be drectly ntegrated wth Kalman flter because t requres a non-lnear predcton functon. The partcle flter helps to overcome ths problem. We use the followng predcton samplng equaton. x x ( k ) + d cosθ x = =, (6) y y ( k ) + d snθ where d ( s sampled from the normal dstrbuton N( d(, σ ), whch has mean of walkng dstance d( and standard devaton σ. Snce θ ( s unknown, we can sample t from a unform dstrbuton unform(~π). The weghts are calculated from the same equaton as equaton (5). Wth Equaton (5) and (6), we manage to fuse the elerometer and measurement usng the partcle flter. (4) Fuson of Measurement, Accelerometer and Map Informaton wth a Partcle Flter Wth a partcle flter, more nformaton than and elerometer can be fused. In partcular, a buldng map s another very useful nformaton source, snce a lot of locatonrelated data can be extracted from the buldng structure nformaton, such as the dstance between floors, the poston of walls, doors or elevators. For the trackng problem, ths nformaton helps to reduce the uncertanty of the walkng trajectory. Usng a partcle flter, the estmaton can be mproved by deletng mpossble partcles,.e. the partcles whch would have crossed a wall. Accordngly, the weghtng functon (5) changes to Equaton (7)., f new partcle crosses walls ( x x ) + ( y y ) w = σ e, otherwse πσ (7) V. EXPERIMENT RESULTS AND ANALYSIS We conducted experments both n smulated and real world tests n order to better evaluate dfferent flterng technques. In ths secton, we wll descrbe the experments and analyze the results. A. Smulaton Tests Our smulaton platform smulates the dstrbuton n our offce envronment usng a Mult-Wall rado propagaton model [5, 6]. Fve APs are avalable n the test floor. The postons of APs are marked wth stars n Fg. 4. Reference ponts are selected unformly wth the resoluton of meter. KNN algorthm s used to make the ntal estmaton. Dfferent flters are then used to smooth the trajectory and reduce the locaton error. For a far comparson, we haven chosen eght dfferent walkng trajectores, as shown n Fg. 4, ncludng walkng straght wth constant velocty (Test ), walkng straght wth varable velocty (Test ), walkng wth 9 turn (Test 3), walkng wth 8 turn (Test 4), walkng wth 45 turn (Test 5), walkng n a crcle (Test 6&7) and walkng randomly (Test 8). The means and standard devatons of estmaton errors n smulaton are shown n dagram. The algorthm parameters can be found n the appendx. From the smulaton, we notce that the partcle flter tself, when only measurements are consdered, performs comparable wth the Kalman flter. After ntegratng the extra nformaton walkng dstance, a sgnfcant mprovement s acheved. A comparable, but slghtly worse result s obtaned, when nstead of the eleraton sgnal only the map nformaton s added to the nformaton. From the smulaton results, we see that the last partcle flter, combnng elerometer and map, s n average more than 4% better than the KNN estmaton and around 3% better than the Kalman flterng, both n the sense of mean and standard devaton of locaton error. We also test the partcle flter algorthm wth respect to the senstvty of the step sze estmaton. Therefore Test 8 has been performed wth dfferent step szes, smulatng a wrong step sze estmaton. Fg. 5 shows the mean error n Test 8 when dfferent step szes are used. We see that -% step sze errors do not cause a too large devaton from the best localzaton uracy. B. Real Walkng Test We also verfed all the algorthms usng real and eleraton measurements. The test envronment s the same as descrbed n the smulaton. The walkng trajectory s the same as the one smulated n Test 8. We use a Lucent Ornoco Gold Card to collect measurements and use the Freescale MMA76Q 3-axs MEMS elerometer to collect the eleraton measurements. The eleraton data s processed by the movement model algorthm and the determned walkng dstance s shown n Fg. 6. We gve the result of dfferent flters n Table I and the cumulatve densty functon n Fg.7. The real world test approves the results found by the smulatons. Usng a flterng algorthm Kalman flter or partcle flter the localzaton uracy can be mproved by about %, n comparson wth the plan -based nearest neghbor localzaton. Further mprovements of about 5% are obtaned, when the partcle flter gets extra nformaton from an eleraton sensor and from a buldng map.

5 5 VI. CONCLUSIONS In ths paper, we proposed a partcle flter framework to extend the typcal based ndoor postonng systems by usng an MEMS elerometer and map nformaton. The walkng dstance s estmated usng a moton model based on a zero-crossng algorthm, whch avods a large umulatve error nduced by sensor nose. The SIR partcle flter s used to ntegrate the non-lnear nformaton from elerometer and buldng map. Our smulaton and real walkng test ndcates a remarkable mprovement compared to Kalman flterng n the sense of mean and standard devaton of estmaton errors. In addton, ths fuson algorthm s robust wth respect to a wrong step sze estmaton. Snce the estmated postons are not lmted to those obtaned from the -based WLAN postonng systems, our framework can also be used for trackng and fusng n other network based systems, e.g. UWB, DECT or GSM systems, or wth other sensng methods, e.g. TDOA, TOA or AOA () () Standard Devaton (m) (3) (4) 5 5 Test Test Test 3 Test 4 Mean Error (m) Test 5 Test 6 Test 7 Test (5) (6) 5 Test Test K-Nearest-Neghbours Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 usng Kalman Flter usng Partcle Flter Accelerometer usng Partcle Flter +Accelerometer+Map usng Partcle Flter Dagram. Comparson of Standard Devatons and Mean n Smulaton (7) (8) Fg. 4 Smulaton envronment and test routes (Stars represent the APs.)

6 6 Mean Error (m) Rato Between Wrong and True Step Sze Fg. 5 Results Usng Dfferent Step Szes n Smulated Test 8 CDF KNN KF PF PF+Acc PF+Acc+Map 3 4 locaton error [m] Fg. 7 CDF of Locaton Error of Real World Test Step Sze(m) Cumulated Walkng Dstance (m) Estmated Step Sze 5 5 Index of Steps Real Walkng Dstance Estmated Walkng Dstance 5 5 Number of Steps (b) TABLE I RESULTS OF REAL WORLD TEST Mean Error(m) Standard devaton(m) KNN Kalman Flter(KF) Partcle Flter(PF) PF+Accelerometer PF+Accelerometer+Map (a) Fg. 6 Estmated Walkng Dstance from Real Acceleraton Measurements APPENDIX TABLE II PARAMETERS OF ALGORITHMS Smulaton KNN K=7 Kalman Flter Partcle Flter Q = 5 R = (m ) 5 Q = Real World (m ), σ=5m T (m ), PF+Accelerometer σ =.5m, σ=m σ =.5m, σ=.5m PF+Accelerometer+Map σ =.5m, σ=m σ =.5m, σ=.5m REFERENCES [] C.A.Patterson, R.R. Muntz, and C.M. Pancake, Challenges n locatonaware Computng, Pervasve Computng, vol., pp 8-89, Aprl/June 3. [] Mark Weser, Hot Topcs: Ubqutous Computng, IEEE Computer, October 993. [3] Jeffrey Hghtower and Gaetano Borrello, Locaton System for Ubqutous Computng, IEEE computer, [4] Hroak Koshma and Joseph Hoshen, Personal Locator Servces Emerge, IEEE Spectrum, February [5] D. Obradovc, H. Lenz and M. Schupfner, "Sensor Fuson n Semens Car Navgaton System," IEEE Conference on Machne Learnng and Sgnal Processng, São Lus, Brazl, 4. [6] Dxon, T.H., An Introducton to the Global Postonng System and Some Geologcal Applcatons, Revew of Geophyscs, vol. 9, p , May 99. [7] P. Bahl and V. N. Padmanabhan, RADAR: An n-buldng RF-based User Locaton and Trackng system, n proceedngs of IEEE INFOCOM, (3), pp , March. [8] Ingram, S.J. Harmer, D. Qunlan, M., Ultra-Wdeband Indoor Postonng Systems and Ther Use n Emergences, n proceedngs of Poston Locaton and Navgaton Symposum 4 (PLANS 4), pp , Aprl 4. [9] B.B. Parod, H. Lenz, A. Szabo, H. Wang, J. Horn, J. Bamberger and J. Obradovc, Intalzaton and Onlne-Learnng of Maps for

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