Pedestrian Positioning Using WiFi Fingerprints and A Foot-mounted Inertial Sensor

Transcription

1 Pedestran Postonng Usng WF Fngerprnts and Foot-mounted Inertal Sensor Yang Gu*, Cafa Zhou, ndreas Weser, Zhmn Zhou* Insttute of Geodesy and Photogrammetry ETH Zurch Zurch, Swtzerland {yang.gu, cafa.zhou, *College of Electronc Scence and Engneerng atonal Unversty of Defense Technology Changsha, Hunan, Chna bstract Foot-mounted nertal postonng (FMIP) and fngerprntng based WF ndoor postonng (FWIP) are two promsng solutons for ndoor postonng. However, FMIP suffers from accumulatve postonng errors n the long term whle FWIP nvolves a very labor-ntensve offlne tranng phase. new approach combnng the two solutons s proposed n ths paper, whch can lmt the error growth n FMIP and s free of any offlne ste survey phase. Ths approach s realzed n the framewor of a partcle flter, where each partcle denotes a potental trajectory of the user and s weghted accordng to ts consstency n sgnal strength space. Compared wth the tradtonal Gaussan process based approaches, the proposed one has less computatonal cost and s free from any pror nformaton n the poston doman, such as the postons of access ponts, receved sgnal strengths at certan postons and so on. n experment s carred out to demonstrate the performance of the proposed approach compared to the tradtonal Gaussan process based approach. Keywords ndoor postonng; foot-mounted IMU; WF; fngerprntng; partcle flter; Gaussan process I. ITRODUCTIO fter years of ganng attenton and despte fast development, ndoor postonng s stll a great challenge. Dfferent from outdoor postonng, where Global avgaton Satellte Systems (GSS) fulfll the postonng needs of a broad varety of applcatons, there s no sngle ndoor postonng soluton satsfyng the requrements of most users. Combnng dfferent ndoor postonng solutons and technques seems necessary to obtan the requred accuracy, relablty and coverage. In ths paper, we focus on the combnaton of two complementary and very promsng ndoor postonng solutons: dead-reconng based on a foot-mounted nertal sensor, and absolute postonng usng WF fngerprntng. The core of foot-mounted nertal postonng (FMIP) s an nertal measurement unt (IMU) mounted on the foot of the user and provdng data for calculatng the poston changes of the user [][]. Ths soluton s self-contaned and has several attractve features: () t does not requre any pre-nstalled specal nfrastructure; () t does not requre a database of prevously determned reference data; () t has no coverage lmtatons n theory. Overall, ths soluton s easy to deploy even n an unnown envronment. Zero-velocty updates (ZUPTs),.e., detectng and properly ntroducng short statonary perods of the foot n the postonng algorthm (e.g., n an extended Kalman flter, EKF) can substantally decrease the postonng error growth from cubc n tme to lnear n tme []. evertheless, the errors of FMIP are stll accumulatve and unbounded n the long term. Even f the ntal poston and orentaton are perfectly nown, the errors may exceed the admssble levels n many applcatons. Fngerprntng-based WF ndoor postonng (FWIP) s attractng attenton because WF sgnals and WF enabled moble devces are becomng more and more ubqutously avalable. s a result, no addtonal nfrastructure or hardware s needed for FWIP. Under the assumpton that smlar postons (postons wth low Eucldan dstances from each other) correspond to smlar receved sgnal strengths (RSS) of the WF access ponts (Ps), the RSS values observed at an unnown poston can be compared to the ones stored n a database for nown locatons (fngerprnts). In a smple realzaton the unnown poston s estmated usng the - nearest neghbor () algorthm [4]. The man hurdle does not le n the poston estmaton (estmaton phase), but n the tranng phase n whch the fngerprnts assocated wth nown locatons are collected and stored n the fngerprntng rado map pror to postonng. Usually the tranng phase s slow and labor ntensve []. The effcency for buldng the rado map can be mproved by crowd sourcng [6][7]. However, the approaches avalable so far requre users to share and upload sensor data from ther moble devces durng ths phase and are thus stll labor ntensve. n exstng approach combnng the two ndoor postonng solutons adopts Gaussan processes (GPs) to model the RSS measurements [8][9]. However, the GP based approach has three problematc features: hgh computatonal complexty, nconsstent weght updates, and dffculty n ntalzaton. We therefore propose a new approach nspred by smultaneous localzaton and mappng (SLM) [][] n ths paper. It allows explotng the RSS measurements even f no rado map exsts (yet). The approach s based on a partcle flter, where

2 each partcle represents a potental trajectory of the user. The partcles are weghted accordng to ther consstency n the RSS space,.e. by assessng the smlarty of the respectve IMU-based and fngerprntng-based poston. s opposed to the exstng approach based on GP we predct the poston usng RSS values rather than predctng the RSS values usng postons. We consder ths more approprate because the errors of the RSS measurements are vrtually ndependent of tme whle the ones of the IMU-based postons grow qucly wth tme. Indeed we wll show that the proposed approach acheves better performance than the GP-based approach, and has further advantages. The structure of ths paper s as follows. The partcle flter used n our approach s dfferent from a standard partcle flter. Its fundamentals are ntroduced n Secton II. In Secton III, the GP-based approach and ts dsadvantages are dscussed, and the proposed weght update strategy s descrbed. The applcaton s demonstrated n Secton IV analyzng data from an ndoor/outdoor experment. II. FUDMETLS OF PRTICLE FILTER Partcle flters are wdely used for non-gaussan and nonlnear flterng []. Fundamentals of partcle flterng can be found n e.g., [] and [4]. In our applcaton we assume that there s no rado map. So, a sngle RSS observaton cannot be used to update weghts of partcles representng postons, because the lelhood of the RSS observaton cannot be calculated. Therefore, some adaptatons are made to the partcle flter. They are nspred by the SLM technque, n partcular by loop-closure [].. Structure of partcles In many partcle flter based postonng approaches, see e.g. [], each partcle represents a canddate of the state vector representng the poston and headng of the user at a partcular tme. We wll only consder two-dmensonal postons heren and subsequently use pos = {, x y} to denote a poston, and θ to denote the headng. s the dea of loop-closure s appled n our mplementaton, the hstory of the state vector s needed as well. Therefore, the partcles are extended to represent not only the latest poston but also the hstory of postons. Each partcle thus denotes a potental trajectory of the user. Fg. shows the chosen structure of the partcles assumng that the hstory taen nto account extends epochs bac n tme from the current one, and that the ensemble comprses partcles. For all expressons relatng to partcles heren, e.g., pos, the superscrpt denotes the partcle ndex and the subscrpt denotes the tme ndex. t each tme represented wthn the partcles, the user s at a certan, possbly dfferent, locaton, and the RSS values observed at that tme are stored n a lst (also ndcated n Fg. ). s these observatons are gven, they are not part of the partcles but ept n a separate lst.. Partcle propagaton In our mplementaton, we assume that FMIP ncludng ZUPTs s avalable as an encapsulated soluton such that the j foot-mounted sensor or the computer processng ts data outputs a new estmate of poston or poston ncrement each tme a step s detected by the sensor. Snce such algorthms have been publshed prevously, e.g. [], we wll not further elaborate on FMIP here. Instead we assume that the partcles are updated wth each detected step, and that ths update s based on the poston ncrements derved from the FMIP output parameterzed as estmated step length ΔL and headng Δ θ. The process of partcle propagaton s vsualzed n Fg. whch shows three nstances wth three partcles, assumng the ntal poston and headng are nown beforehand (blue trangle and arrow). The th partcle s propagated from tme to tme by appendng a canddate poston pos to the ntal poston pos : where cosθ pos = pos + ( Δ L+ δ L ) () snθ θ = θ +Δ θ + δθ () Δ L and Δ θ are the measurements output by the FMIP system (or drectly derved therefrom). δ L and δθ are obtaned usng a random number generator and represent possble correctons for the FMIP measurement nose. These are the contrbutons creatng dfferent partcles startng from the same ntal poston, orentaton and measurements, see Fg. a. The canddate nose correctons are drawn from the (assumed or nown) probablty dstrbutons of the FMIP system s step length nose and headng change nose,.e., δl ~ ( ) p ε Δ L () δθ ~ ( ) p ε Δ θ (4) Smlarly, the propagaton from epoch to conssts n appendng a canddate poston pos to the postons pos,..., pos, where pos pos pos pos pos RSS pos RSS RSS Fg. The structure of the partcles, and the observaton lst. Each partcle represents a potental trajectory of the user at + tmes.

3 and cosθ pos = pos + ( Δ L + δ L ) () snθ δθ θ = θ +Δ θ + δθ (6) pos Ths means that we have an ensemble of partcles, each of whch represents a potental trajectory of the user from tme to tme, where each of these partcles can then be wrtten as Δθ ΔL Δθ (a) pos pos δ L pos pos pos pos pos pos P = [ pos, pos, pos,..., pos ] (7) n agreement wth Fg.. Three such partcles are vsualzed n Fg. for epochs, and. C. Observaton approxmaton We have chosen to update the partcles and thus obtan a new poston estmate each tme the FMIP sensor detects a step (step-wse update). Snce the FMIP sensor may be a blac-box sensor operated ndependently from the WF sgnal strength sensors, and snce step duraton may vary whle RSS measurements may tae place at regular tme ntervals, the RSS observatons wll usually not be synchronzed wth partcle update, see Fg.. There are several possbltes how to synchronze the measurements computatonally. In order to allow real-tme processng wthout watng for future measurements, extrapolaton of the RSS values based on regresson or predcton based on tme seres analyss would be vable optons. For smplcty, we just chose the most recent RSS readng before the step here, and assume that the tme nterval and poston change between ths RSS measurement and the step s neglgble. If, for a partcular access pont or for all of them, no RSS observaton s obtaned between the prevous step and the current one, the correspondng value(s) are ndcated as not avalable n the lst of RSS observatons. pos pos Δθ (b) Fg. lgnment of the observed RSS and the poston data. In our mplementaton RSS measurements come from the sensors of a WF enabled smart phone and the tme s not synchronzed wth the steps. The step-wse poston data comes from the foot module. The RSS observaton made closest to the tme of the current step s consdered as current observaton (n the ellpse). pos Δθ pos pos pos (c) Fg. Three potental trajectores (three partcles) at tme epoch t= (a), t= (b), and t= (c). III. WEIGHT UPDTE STRTEGIES Wthn a partcle flter, each partcle s assocated wth a weght. Partcles wth a hgh weght are more lely to represent the true values than partcles wth a low weght. In a standard partcle flter, the weghts are calculated from the lelhood of the observatons actually avalable. In the GP based approaches, GP regresson s carred out to predct the dstrbuton of the RSS n the current locaton by tang the RSS observatons of nearby postons as tranng samples. Then the weght of each partcle can be calculated from the lelhood of the RSS observatons derved from the dstrbuton predcted usng the coordnates wthn the partcle.

4 . Tradtonal GP based weght update strategy GP can estmate dstrbutons over functons based on tranng data [6]. It s sutable for modelng sgnal strength measurements. The advantages are as follows: Wth several tranng samples, a GP can predct the RSS at arbtrary postons. It provdes a predctve dstrbuton whch s sutable for assessng the qualty of the predcted RSS values and for calculatng the lelhood of the RSS measurements. GP can cope well wth nonlnearty, whch s benefcal for RSS-based ndoor postonng because the relaton between RSS and postons s hghly nonlnear due to the complexty of ndoor envronment. It s usually assumed that the RSS of dfferent Ps are ndependent and thus GPs for the RSS of each P can be estmated separately. Detals for GP regresson have already been descrbed by other authors such as [6] and [7], so they are spped here. We only use a numerc example of GP regresson (see Fg. 4) to hghlght some ey aspects. In ths example, raw sgnal strength measurements of one P are acqured at ndvdual locatons (Fg. 4a) by a user walng around a certan area. The postons and RSS values are provded by the foot-mounted IMU module and by the moble devce descrbed n sec. IV, respectvely. The synchronzaton s carred out le depcted n Fg.. s the total walng tme s short n ths case, the poston errors are consdered nsgnfcant. Wth a GP, the Gaussan predctve dstrbuton of sgnal strength at arbtrary postons n the area can be derved. The predcted mean and varance are shown n Fgs. 4(b) and 4(c), respectvely. ot surprsngly, the areas wth few samples, prmarly near the borders of the covered area, have larger varance. When applyng ths concept to partcle flters and postonng, the predctve dstrbuton s not needed at each poston n the area but only at the current partcle s poston RSS -6 (dm) -7-8 X (m) (a) Y (m) 4 (b) 4. Lmtatons of the GP based approaches lthough GPs are sutable for modelng sgnal strength measurements, the exstng GP based approaches have three lmtatons. The computatonal cost s too large. t each flterng epoch, the number of GPs to be traned s the number of partcles multpled by the number of Ps (as above, the RSS of dfferent Ps are assumed ndependent). The number of tranng samples for each of these GPs comprses all nearby postons and the related RSS values. It ncreases wth tme. If the user wals around n a small area, the newly collected samples are all nearby tranng samples and the number of tranng samples grows even faster. GPs are by default zero mean processes. So they can only be used here wth a proper estmaton of the mean values of the RSS, whch are non-zero. There are manly three mean offset models: () constant mean (can lead to ncorrect predctons at areas wth few Predcted varance X (m) (c) tranng samples); () model of sgnal strength decreasng lnearly wth dstance from the P [9]: Y (m) Fg. 4 (a) Raw sgnal strength measurements for one P; (b) predcted mean and (c) varance for the entre area obtaned from the traned GP. mean = p pp + d (8)

5 where s propagaton slope, d s the sgnal strength at the P, p s the current poston and p P s the P s poston; () the log-dstance model [8]: mean = s q p p P (9) where s s the sgnal strength measured at m from the P, q s the attenuaton factor, p and pp are as above. oth the second and the thrd model need addtonal nformaton such as the postons of all Ps and some sgnal strength measurements at certan postons wth nown dstances from the Ps. Implementng ths s very labor-ntensve, especally when the number of Ps s large, and the models may not be suffcent approxmatons to the true stuaton n complex ndoor envronment. The weght update of the partcles s nconsstent. Fg., shows a constructed example wth three partcles, each denotng a possble trajectory. The trajectores dffer because of the uncertantes due to nertal drfts. The marers denote postons (accordng to the partcles) at whch RSS measurements are avalable. ll postons wth RSS measurements wthn a certan predefned radus (see crcles n Fg. ) are consdered tranng samples of the GP for the RSS at the center of the crcle. ll other postons are excluded because they are too far away from the current poston. The reason for excludng samples outsde a certan radus s to lower computatonal cost for onlne GP applcatons, see [8], whch s also nown as sparse approxmaton of full GP. In ths partcular example, the number of tranng samples for the three partcles are, and, respectvely. Therefore, the lelhood calculated from the GPs s not consstent for the three partcles. Ths can Fg. Smple example to show that dfferent partcles have dfferent numbers of tranng samples and thus lelhoods calculated therefrom are not drectly comparable. There are three partcles, each partcle denotes a possble trajectory. The marers denote postons are whch RSS measurements are avalable. If a poston wth RSS measurement s wthn a crcle, t s consdered one of the tranng samples of the GP, otherwse t s excluded from GP tranng. be partally mtgated by eepng partcles wth low lelhood [9], however, ths ntroduces the problem of falsely eepng wrong partcles. C. RSS dstance based weght update s mentoned above, we am at an algorthm that does not requre a rado map and thus we cannot calculate the lelhood of the RSS observatons because we do not have expected RSS values to whch the actual measurements could be compared. However, wth the general assumpton that smlar RSS values correspond to smlar postons, we can calculate weghts of the partcles by comparng the current RSS values to those obtaned at earler tmes and stored n the observaton lst. Ths s smlar to the dea of loop-closure, where correlatons between observatons can be used to calbrate the estmated postons. Ths dea also yelds an algorthm whch s computatonally less demandng than the GP-based approach. Fnally, the new approach only requres searchng nearby RSS values n the RSS space, thus avodng the search for nearby postons n the coordnate space affected by errors of poston estmaton whch grow rapdly wth tme. In the new approach, the weghts of the partcles are updated accordng to the consstency n the RSS space. smlarty metrc s requred for fndng smlar RSS observatons and subsequently assessng consstency. We accomplsh ths usng a normalzed Eucldean dstance for two RSS vectors RSS and RSS, where: () () () ( ) RSS = [ RSS, RSS, RSS,..., RSS ] () () () ( ) [,,,..., () RSS = RSS RSS RSS RSS ] The superscrpts n the vectors denote the P to whch the respectve sgnal strength refers. Some specal precautons are needed f RSS and RSS contan RSS values from dfferent Ps, for example, f the sgnal strength of a certan P s avalable n RSS but not n RSS. Wthn ths paper we have chosen to set such mssng RSS values to - dm assumng that the respectve sgnal s just bured wthn nose and the actual sgnal strength s very low. (Ths s a woraround and wll further be nvestgated n the future.) The normalzed Eucldean dstance between two RSS vectors of dmenson s then defned as follows: ds( RSS, RSS ) = j = ( RSS RSS ) ( j) ( j) () Fg. 6 shows the dstance comparsons n sgnal space and coordnate space for an experment where a certan closed path was waled three tmes. The horzontal axs denotes the epoch ndex of the collected RSS samples, and the vertcal axes denote the normalzed Eucldean dstance n RSS space (left axs, blue dashed lne) and the Eucldean dstance n coordnate space (rght axs, red lne). ll the dstances are dstances from the ffteth sample. The marers (samples and 6) denote observatons made at almost the same place as the ffteth sample. oth, coordnates and RSS values do not reach exactly the same values agan when ths place s revsted. However,

6 the drft n poston s much larger, and the local mnmum dstance does not correspond to the actual revstng of the ste showng the mpact of accumulatve error growth of the IMU-based postons output by the FMIP system. Dstance n RSS (d) 4 4 Sample number Fg. 6 Dstances w.r.t. th sample n RSS space (blue) and coordnate space (red) durng a repeated closed-loop wal; marers denotng observatons made at approxmately the same place as the th sample. fter fndng smlar RSS values n the RSS space, we can use the spatal correlatons of the RSS to chec the estmated postons. Fg. 7 shows the relaton between the dstances n the two spaces for three dfferent real world data sets: one was acqured outdoors around a buldng (Fg 7, top), one n the corrdors of a buldng (Fg. 7, center) and the thrd one (Fg. 7, bottom) n dfferent rooms wthn n the buldng. Each data set was acqured durng a wal wth total walng tme less than mnutes, such that the poston estmaton errors are assumed nsgnfcant. Whle we cannot establsh a functonal relaton between the dstances, the fgures do suggest that thresholds can be defned n the two domans such that the dstance n coordnate space s normally under d POSthres ( m, n our case) f the normalzed dstance n RSS space s below d RSSthres (8 d, Dstance n coordnate (m) Dstance n coordnate (m) Dstance n RSS (d) Fg. 7 Three samples sets of the dstance n RSS space and n coordnate space. See text for dscusson. n our case). We use ths nformaton to form a constraned partcle flter where postons wth smlar RSS (.e. dstance n RSS space below the threshold) can be used to constran the current poston estmaton. The weght update process based on smlar RSS observatons has three steps: ) Fndng smlar RSS. Iterate over the observaton lst to fnd the RSS vectors whose normalzed dstance from the current RSS vector s less than d RSSthres. ormally, we do not want to nclude the observatons that are near n tme or have been collected wthout walng n between, because they are not helpful for the loop-closure process. In our mplementaton, we only compare RSS values whose tme dfference s larger than seconds and where the accumulated walng dstance between them s larger than meters. gan, these numbers are frst choces whch wored well for the examples heren but wll be further nvestgated n the future. We assume that there are m RSS n the lst satsfyng the condton, namely RSSn, RSSn,..., RSS nm. The dstances n RSS space are drss, n, drss, n,... d RSS, nm and the correspondng postons for the th partcle are pos,,..., n posn pos nm. ) Estmatng the current poston by fngerprntng. Use the weghted algorthm to calculate a fngerprntng estmate of the current poston as: m pos = posn d F () = RSS, n where F s the normalzed factor: m F d () = RSS, n ) Update weght. If the dstance between the estmated poston pos and the partcle s current poston pos s larger than the threshold d then ths partcle s consdered POSthres mpossble. However, to be more robust, the weght s set to be one percent of the orgnal weght. Otherwse, the wegth of the partcles s ept the same as n the prevous epoch. smple example s gven here to show the weght update process for the th partcle n our approach (Fg. 8). The two orange dots denote the postons whch are smlar n sgnal space found n step. The red dot denotes the estmated pos pos d, d pos pos, : = Fg. 8 smple example of weght update process for the th partcle.

7 poston through the weghted algorthm at step. The blue dot denotes the current end poston of the partcle. d, s the dstance between the two postons n coordnate space. IV. EXPERIMET. Expermental Setup We have carred out real measurements to demonstrate the algorthm. Fg. 9 shows a scene durng data acquston. The nertal sensor s mounted on the foot of the user. The sensor s a multple nertal measurement unts (MIMU) platform wth an embedded sngle-chp mcrocomputer []. The collected nertal data are processed n real-tme n the foot module and the calculated postons are transmtted to the hand held exus 6P smart phone through luetooth Low Energy (LE). The poston estmaton from the foot module s avalable stepwsely. To obtan reference coordnates, a local coordnate frame was establshed usng prsms permanently mounted on the celng of the rooms. total staton Leca MS was utlzed to measure the coordnates wthn ths frame. The hand held target s a frame (-D prnted) supportng the smart phone and a 6 mn-prsm traced by the total staton. Durng the experment the poston of the cell phone s measured and traced wth the total staton by the prsm wth hgh accuracy (a few mm) and update rate (about /.7 s). The tracng process s controlled by a laptop runnng MTL. The poston data collected by the total staton are consdered as ground truth wthn ths experment. custom made app on the smartphone was used to collect RSS together wth SSID and MC of the avalable access ponts. These measurements were collected and stored by the applcaton together wth the readngs from the foot-mounted module. The datasets collected by the exus 6P and the laptop were afterwards merged and synchronzed manually n post-processng.. Results s shown n Fg., the total staton (blue trangle) s placed at the corner of two perpendcular corrdors, whch can cover the areas n the blac ellpse. The blue dot denotes the startng poston of the user. s the blac arrows show, the walng trajectores nclude walng outsde and nsde of the buldng. The user has waled the same trajectory for three teratons. From the trajectores n Fg., t s apparent that the new approach and the GP based approach have smaller postonng errors than the raw trajectory drectly derved from the foot module. Ths shows the beneft of supportng the FMIP by sgnal strength measurements. The total walng length s about 8 meters and the total tme duraton s about 4 mnutes. Fg. The settngs nsde the buldng. The total staton (blue trangle) s placed at the corner of two perpendcular corrdors, whch can cover the areas n the blac ellpses. The blue dot denotes the startng poston of the user. s the blac arrows show, the walng trajectores nclude walng outsde and nsde of the buldng. Fg. Comparsons of the raw trajectory, GP based approach and our approach. Fg. 9 The expermental scene. The user has re-vsted the total staton covered area twce. Therefore ground truth provded by the total staton s avalable for the correspondng two parts of the wals and postonng errors can be calculated for these parts. Fg. shows the errors for the frst and second vsts respectvely. We can see that both the GP based approach and our approach mprove the postonng accuracy. However, at the second re-vst, the error of the GP based approach becomes larger. The reasons may be two folds: wrong estmaton of mean value of GP (postons of each P s not nown); and nconsstent weght update as mentoned before. Table I reports the mean errors from the two re-vsts and further corroborates the results shown n Fg..

8 Postonng error (m) Table II shows the processng tme for the two approaches comprsng the two vsts covered by the total staton. The two approaches both run on the same computer usng MTL. The GP based approach consumes much more tme than our approach. That s because n the GP based approach, at each flterng epoch, many ndependent GPs are traned ndependently and the number of samples n each GP grows larger wth tme. otng that n each GP the computatonal complexty s O ( ), where s the number of samples used for tranng, t s clear that ths approach cannot cope well wth nematc processng and large tranng sets. Mean Error Frst re-vst Second re-vst Sample number TLE I. (a) Sample number ME ERRORS OF TWO RE-VISITS Trajectory Raw trajectory Our approach GP based approach (b) Raw trajectory Our approach GP based approach Fg. Postonng error curves at the frst re-vst (a) and the second revst (b) of the area covered by the total staton. Raw trajectory GP based approach Our approach 9.m.4m 4.m.6m 6.m.4m TLE II. PROCESSIG TIME OF THE TWO PPROCHES Processng tme GP based approach Our approach Frst re-vst 79s 9s Second re-vst 6887s 96s V. COCLUSIOS partcle flter based ndoor postonng approach combnng FMIP and FWIP s proposed n ths paper. Ths approach wors wthout any labor-ntensve ste survey phase, and can greatly suppress postonng error growth (due to nertal drfts of the foot-mounted IMU) wth tme. Compared wth the GP based approaches, the experment shows our approach can have a better performance n terms of both postonng accuracy and processng tme. Our future wor wll contnue n two ways: () the mpact of dfferent choces of parameters (e.g., thresholds n determne smlar RSS) wll be nvestgated; () the approach wll be extended for not only estmatng the postons but also the correspondng rado map. CKOWLEDGMET The Chnese Scholarshp Councl has supported Y.G. durng hs academc vst at ETH and C.Z. durng hs Ph.D. studes at ETH. REFERECES [] J. O. lsson,. K. Gupta, and P. Handel, Foot-mounted nertal navgaton made easy, n IPI 4-4 Internatonal Conference on Indoor Postonng and Indoor avgaton, 4, pp []. R. Jménez, F. Seco, J. C. Preto, and J. Guevara, Indoor pedestran navgaton usng an IS/EKF framewor for yaw drft reducton and a foot-mounted IMU, n 7th Worshop on Postonng, avgaton and Communcaton,, pp. 4. [] E. Foxln, Pedestran tracng wth shoe-mounted nertal sensors, IEEE Comput. Graph. ppl., vol., no. 6, pp. 8 46,. [4] T. agos and Z. aruch, Indoor localzaton by WF, n IEEE 7th Internatonal Conference on Intellgent Computer Communcaton and Processng,, pp [] S. He and S. H. G. Chan, W-F Fngerprnt-ased Indoor Postonng: Recent dvances and Comparsons, IEEE Commun. Surv. Tutorals, vol. 8, no., pp , 6. [6] J. Par et al., Growng an Organc Indoor Locaton System, n Proceedngs of the 8th Internatonal Conference on Moble Systems, pplcatons, and Servces,, pp [7] C. Wu, Z. Yang, Y. Lu, and W. X, WILL: Wreless Indoor Localzaton wthout Ste Survey, IEEE Trans. Parallel Dstrb. Syst., vol. 4, no. 4, pp ,. [8] V. V Kosyanchu,. S. Smrnov, and.. Panyov, avgaton system for a wde range of tass based on IMU aded wth heterogeneous addtonal nformaton, n Internatonal Conference on Indoor Postonng and Indoor avgaton (IPI),, pp. 9.

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