Academic Editors: Lyudmila Mihaylova and Byung-Gyu Kim Received: 21 January 2016; Accepted: 14 March 2016; Published: 16 March 2016

Transcription

1 sensors Artcle Scalable Indoor Localzaton va Moble Crowdsourcng and Gaussan Process Qang Chang, Qun L *, Zesen Sh, We Chen and Wepng Wang College of Informaton Systems and Management, Natonal Unversty of Defense Technology, Changsha , Chna; changqang@nudt.edu.cn (Q.C.); nudtshzesen@126.com (Z.S.); wechen@nudt.edu.cn (W.C.); wang.wp2010@gmal.com (W.W.) * Correspondence: lqun@nudt.edu.cn; Tel.: Academc Edtors: Lyudmla Mhaylova and Byung-Gyu Km Receved: 21 January 2016; Accepted: 14 March 2016; Publshed: 16 March 2016 Abstract: Indoor localzaton usng Receved Sgnal Strength Indcaton (RSSI) fngerprntng has been extensvely studed for decades. The postonng accuracy s hghly dependent on the densty of the sgnal database. In areas wthout calbraton data, however, ths algorthm breaks down. Buldng and updatng a dense sgnal database s labor ntensve, expensve, and even mpossble n some areas. Researchers are contnually searchng for better algorthms to create and update dense databases more effcently. In ths paper, we propose a scalable ndoor postonng algorthm that works both n surveyed and unsurveyed areas. We frst propose Mnmum Inverse Dstance (MID) algorthm to buld a vrtual database wth unformly dstrbuted vrtual Reference Ponts (RP). The area covered by the vrtual RPs can be larger than the surveyed area. A Local Gaussan Process (LGP) s then appled to estmate the vrtual RPs RSSI values based on the crowdsourced tranng data. Fnally, we mprove the Bayesan algorthm to estmate the user s locaton usng the vrtual database. All the parameters are optmzed by smulatons, and the new algorthm s tested on real-case scenaros. The results show that the new algorthm mproves the accuracy by 25.5% n the surveyed area, wth an average postonng error below 2.2 m for 80% of the cases. Moreover, the proposed algorthm can localze the users n the neghborng unsurveyed area. Keywords: WLAN; ndoor localzaton; rado map; moble crowdsourcng; gaussan process; Bayesan algorthm 1. Introducton The dffculty of determnng the locaton of moble users wthn buldngs has been extensvely studed for decades, due to potental applcatons n the moble networkng envronment [1]. Wth the wde avalablty of WLAN networks, wreless localzaton usng Receved Sgnal Strength Indcaton (RSSI) fngerprntng [2] has attracted a lot of attenton. Fngerprnt ndoor postonng conssts of two phases: tranng and localzaton [3]. Durng the tranng phase, a database of locaton-fngerprnt mappng s constructed. In the localzaton phase, the users send locaton queres wth the current RSS fngerprnts to the locaton server; the server then retreves the sgnal database and returns the matched locatons. The accuracy of fngerprntng technques s hghly dependent on the densty of the sgnal database. Buldng and mantanng a hgh-densty database are not easy, however, for two reasons. Frstly, buldng a hgh-densty fngerprnt database s labor ntensve, expensve, and even mpossble n some cases. Takng a 50 m 50 m floor as an example, f we want to buld a fngerprnt database wth a 1 m sample dstance, we would have to collect 2500 samples. For each sample, we need to measure several tmes to get relable results. Sometme t s mpossble to collect sgnal fngerprnts from certan locatons, because of the complex local envronment. Sensors 2016, 16, 381; do: /s

2 Sensors 2016, 16, of 19 Secondly, mantanng a large sgnal database s expensve. As the envronment changes over tme due to furnture or sgnal sources beng moved, the fngerprnts dverge from those n the database. Ths means that the entre area needs to be re-surveyed n order to update the database. As ndoor envronments often change, the database would requre frequent updates, whch would be tme-consumng and expensve. Even though fngerprnt ndoor localzaton has many advantages, and some commercal products have been developed on ths technology, such as Google Maps [4], WFSlam [5], and so on, challenges stll exst n ts applcaton. In area wthout calbraton data, however, ths algorthm breaks down. Real-world deployment of such postonng systems often suffers the problem of sparsely avalable sgnal data. For example, Google has collected floor plans for over 10,000 locatons. However, only a few of these rado maps are avalable for postonng. For these problems n fngerprntng, researchers are contnually searchng for better algorthms to create and update dense databases more effcently. The popularzaton of smartphones makes moble crowdsourcng fngerprnt localzaton more practcal. However, desgnng a sustanable ncentve mechansm of crowdsourcng remans a challenge. In ths paper, we propose a scalable ndoor postonng algorthm va moble crowdsourcng and Gaussan Process. The basc dea behnd our proposed algorthm s smple: we frst propose a Mnmum Inverse Dstance (MID) algorthm to buld a vrtual database wth unformly dstrbuted vrtual Reference Ponts (RP). The area covered by the vrtual RPs can be larger than the surveyed area. A Local Gaussan Process (LGP) s then appled to estmate the vrtual RP s RSSI values based on the crowdsourced tranng data. Fnally, we mprove the Bayesan algorthm to estmate the user s locaton usng the vrtual database. All the parameters are optmzed by smulatons, and the new algorthm s tested on real-case scenaros. In summary, we make the followng major contrbutons: (1) We propose a MID algorthm to buld a vrtual database wth unformly dstrbuted vrtual RPs. The area covered by the vrtual RPs can be larger than the surveyed area. (2) The Local Gaussan Process (LGP) s appled to estmate the vrtual RPs RSSI values based on the crowdsourced tranng data. (3) Bayesan algorthm s mproved to estmate the user s locaton usng the vrtual database. (4) We optmze all the parameters n the proposed algorthm by smulatons. (5) An Androd app s developed to test the proposed algorthm on real-case scenaros. The rest of the paper s organzed as follows: Secton 2 dscusses related work on buldng and mantanng a dense fngerprnt database. Secton 3 descrbes the detals of the proposed algorthm. Secton 4 optmzes the parameters and evaluates the postonng algorthm, and Secton 5 concludes the paper. 2. Related Works For the challenges of fngerprnt postonng, much tme and effort has been put nto buldng and mantanng a dense fngerprnt database wth less effort [6]. Except for pont by pont measurement, there are manly fve ways to construct and mantan a fngerprnt database. The frst s crowdsourcng [7 11]. The users are also database constructors. The database s updated wth the most recently measured RSS uploaded by the users [12,13]. However, desgnng a sustanable ncentve mechansm of crowdsourcng remans a challenge [14]. The second method s buldng the database wth mathematcal models. The most wdely used model s the Log-Dstance Path Loss (LDPL) [15 18] model. However, the ndoor envronments are so complex that no smple mathematcal model exsts to accurately predct the RSS values. Practcally, LDPL only gves good results close to the AP. Ray-Tracng [19 21] s the thrd method. However, for accurate ray tracng, you need a very detaled descrpton of the envronment such that all the reflectons that eventually characterze the

3 Sensors 2016, 16, of 19 receved sgnal can be smulated. Furthermore, ths approach s very computatonally demandng. Because of these reasons, t s only vable for small setups. The fourth method s Smultaneous Localzaton and Mappng (SLAM) [22,23]. In SLAM, the database s populated on the fly, provded that the users are equpped wth a recever and an IMU. In general, the accuracy of postonng wth ths technque s lower because the database s less accurate. The ffth way s the combnaton of the prevous methods. A few RPs cover a large range of area and are collected or generated by the prevous method. The remanng RP RSS values are estmated mathematcally. Lnear and exponental taper functons are used by [24]; the Motley Keenan model [25] and a sem-supervsed manfold learnng technque [26] are also used by researchers [27]. Lqun L propose Modellet [28] to approxmate the actual rado map by unfyng model-based and fngerprnt-based approaches. However, ther algorthm only works for nodes near the Access Ponts (APs). Gaussan Process (GP) [29] s a non-parametrc model that estmates Gaussan dstrbuton over functons based on the tranng data [30]. GP s sutable for estmatng RSS values [31]. However, GP s computatonal consumng, meanng t s not a satsfactory method of generatng a large scale area s sgnal strength. There are also some other researchers that mproved fngerprntng performance by ntroducng new sensors. For example, IMU [32,33], barometer [34], and so on. However, extra runnng sensors not only consume more battery, but also brng n new errors. Some such algorthms requred the sensors to keep runnng even f the user does not need the postonng servce, whch s not sutable for our daly use. Our study s motvated by these poneer works, but we approached the problem from a dfferent angle and manly focus on a scalable ndoor postonng algorthm that works both n surveyed and unsurveyed areas. We propose a novel algorthm to create WLAN rado map by moble crowdsourcng and Gaussan Process. We frst propose a Mnmum Inverse Dstance (MID) algorthm to buld a vrtual database wth unformly dstrbuted vrtual Reference Ponts (RPs). A Local Gaussan Process (LGP) s then appled to estmate the vrtual RPs RSSI values based on the crowdsourced tranng data. Fnally, we mprove the Bayesan algorthm to estmate the user s locaton usng the vrtual database. We ddn t use the crowdsourced data for postonng drectly, and we ddn t ntroduce other sensors to mprove the performance ether. 3. Materals and Methods 3.1. Problem Settng and Algorthm Overvew We only concentrate on the 2D postonng problem n ths paper. Assumng the target area s denoted as P, the area of P s S(m 2 ). There are a W-F APs n the target area. In crowdsourced fngerprnt postonng, the rado map s created by users. The RSS values n dfferent RPs from dfferent sgnal sources are measured and uploaded to the database together wth the coordnates. The coordnates come from another postonng system, such as GNSS, or specfed by the users. Assumng we have bult a sgnal database DB Crowd by crowdsourcng, and there are n RPs n DB Crowd. The RPs are denoted as RP = {p, F, σ }, = 1, 2,, n, where p = (x, y ) and F = {(Mac j, RSS,j ), j = 1, 2,, a}. σ s the measurement varance. The densty of DB Crowd s denoted as ρ Crowd = n/s. The problem n fngerprnt localzaton s estmatng the user s current coordnate p t at tme t based on the measurement F t and the database DB Crowd. The densty of DB Crowd wll be dfferent from regon to regon. As a result, the postonng accuracy wll be dfferent for the area. If we want a contnuous postonng performance, we need a database wth unformly dstrbuted reference ponts. There also mght be certan areas wthout RPs, e.g., because of the complex local envronment or not covered due to some other reasons. Ths method breaks down.

4 Sensors 2016, 16, of 19 In ths paper, we propose a novel algorthm to create a vrtual WLAN rado map by moble crowdsourcng and Gaussan Process for scalable ndoor postonng. Ths vrtual rado map s denoted as DB (v). DB (v) contans m RPs, so that the densty of the vrtual database s ρ (v) = m/s. The th RP n DB (v) s RP (v). RP (v) = {p (v), F (v), σ (v) }, where p (v) = (x (v), y (v) ) and F (v) = {(Mac j, RSS (v),j ), j = 1, 2,, a}. RSS (v),j varance of the measurement. RSS (v),j s AP j s RSSI measured at RP, and σ (v) s the s estmated usng our proposed Local Gaussan Process (LGP) based on DB Crowd. The user makes use of DB (v) for postonng. Fgure 1 shows the framework of the proposed algorthm. Fgure 1. Framework of the proposed algorthm. RSS: Receved Sgnal Strength; LGP: Local Gaussan Process. After collectng RSS values from surroundng APs, f the user gets the current coordnate by other methods, he can upload the fngerprnt contanng the coordnate and the RSS values to the server. The server wll add the fngerprnt to DB Crowd, and update DB (v) usng LGP. If the user wants to estmate current locaton, he can send the postonng requrement, ncludng the RSS measurement, to the server. The server wll estmate the coordnate usng the proposed Bayesan algorthm based on DB (v) and then send the result to the user. In the next secton, we frst bult a dense vrtual database by ntroducng unformly dstrbuted vrtual RPs n the area, and then we propose the Local Gaussan Process (LGP) to estmate the vrtual RPs RSSI values and the varance. We mproved the Bayesan algorthm to estmate the user s locaton usng the vrtual database Buldng the Dense Vrtual Database As stated earler, the fngerprnts n the vrtual database should be selected as unformly as possble over the target area. m s the number of RPs n DB (v). However, for general values of m, t s not straghtforward to unformly dstrbute the RPs over the area. Therefore, we propose a low-complexty algorthm to select the postons of the RPs: the Mnmum Inverse Dstance (MID) algorthm. In ths algorthm, the selecton of the postons of the RPs s based on a vrtual sample database DB Sample, whch s constructed by placng a square grd n the target area wth grd sze λ, where the postons of the vrtual RPs are selected as the corners of the squares n the grd. Assumng the target area has sze x max y max, the number of vrtual postons equals x max /λ y max /λ. The m postons of the RPs for vrtual database DB (v) are selected out of the sample database DB Sample. We ntalze the algorthm by randomly choosng one vrtual poston RP e from DB Sample :

5 Sensors 2016, 16, of 19 DB (v) = {RP e }. The other m 1 postons are pcked from the vrtual database DB Sample based on the measure n Equaton (1): 1 Ds = (x j x j ) 2 + (y y j ) 2 (1) where (x, y ) s the coordnate of the canddate poston DB Sample and (x j, y j ) are the coordnates of the RP postons already present n the database DB (v). The vrtual poston that mnmzes Ds s selected and added to the database DB (v). Because the measure functon Ds s nversely proportonal to the Eucldean dstances between the canddate RP and the RPs n the database DB (v), canddate postons that are far from the already selected RP postons are favored, whle canddate postons near already selected RP postons are fltered out. As a result, the dstances between the RPs wll be maxmzed and the RPs n DB (v) wll be dstrbuted unformly and expand to the very edges of the target area. We call ths algorthm as Mnmum Inverse Dstance (MID) algorthm. Detals of MID are shown n Algorthm 1. Algorthm 1 Requre the target area P, the dstance λ between neghbor vrtual RPs n DB sample the number m of RPs we want to select. Ensure select RPs every λ meters n P to buld DB sample Ensure randomly select RP e from DB sample, DB (v) = {RP e } Whle( DB (v) = m) For all(rp DB sample ) Calculate Ds usng Equaton (1) End all RP = arg mn Ds RP DB sample DB (v) RP EndWhle To llustrate MID, we consder an area P of 19.5 m 48.5 m and λ = 0.5 m. Fgure 2 shows the postons of the RPs n DB (v) when m = 100 and 200 RPs are selected out of the vrtual sample database DB Sample. Further, Fgure 2 shows the postons of the RPs when the RPs are selected randomly from DB Sample. (a) (b) (c) (d) Fgure 2. Postons of the Reference Ponts (RPs) (a) Mnmum Inverse Dstance (MID), m = 100; (b) randomly, m = 100; (c) MID, m = 200; (d) randomly, m = 200.

6 Sensors 2016, 16, of 19 As can be observed, the proposed algorthm s able to select any number of RPs spatally unform over the target area. After the postons of the RPs n database DB (v) are selected wth MID, the RSS values and the varance for these RPs need to be determned. To ths end, we compare the postons of the RPs n DB (v) wth those n DB Crowd. Whenever one or more RPs n DB Crowd are wthn a dstance ε of a RP RP n DB Crowd, we wll replace the poston of the RP n DB (v) wth the poston of the nearest RP n DB Crowd, together wth ts RSS values and the varance on the measurement. If no RPs n DB Crowd are wthn a dstance ε of a RP RP n DB Crowd, the Local Gaussan Process (LGP) algorthm wll be used to estmate the RSS values and ther varance n RP. The resultng vrtual database DB (v) s determned by three parameters: the number m of RPs n DB (v), the dstance λ between RPs n the vrtual sample database, and the radus ε wthn whch nearby tranng RPs are looked for. The number m of RPs s defned by the postonng accuracy. The dstance λ determnes not only the spatal unformty of the resultng RPs, but also the complexty of the algorthm: by reducng λ, the RPs wll be placed more unformly over the area P, but the complexty of MID ncreases as the number of vrtual RPs to be searched ncreases n an nverse proporton to the quad-rate of λ. Fnally, the radus ε wll also have an nfluence on the postonng accuracy. When the radus s small, the resultng database DB (v) wll have a more unform placement of RPs, but the probablty of fndng a nearby tranng RP decreases, such that the RSS of more RPs needs to be determned usng the LGP algorthm. On the other hand, when the selected radus s large, the resultng database DB (v) wll be less spatally unform, but more tranng RPs wll be present n DB (v). In Secton 4, we wll optmze them before postonng Local Gaussan Process The Local Gaussan Process (LGP) algorthm s used to reduce the computatonal complexty of the Gaussan Process (GP) algorthm, whch s used to predct unknown RSS values at postons that are not n the tranng database [29]. In ths secton, we frst revew the GP algorthm. Ths algorthm starts from the property that RSS values at surroundng postons are correlated. Because of ths correlaton, t s possble to descrbe the RSS at postons where the RSS s not known as functon of the RSS at postons where the RSS value s measured. The GP algorthm uses the Gaussan kernel to descrbe ths correlaton. As a result, the correlaton matrx between the nosy RSS values RSS at postons c = {x, y }, = 1,..., n, measured durng the tranng phase, can be wrtten as: covρ = Q + S (2) where ρ() = RSS, Q,j = k(c, c j ), and S = dag{σ 2 } s the dagonal matrx of the varances of the measured RSS values RSS. Further, k(c, c j ) s the Gaussan kernel functon: k(c, c j ) = σ 2 f exp( 1 2l 2 c c j 2 ) (3) where σ 2 f and l are the sgnal varance and length scale, respectvely, determnng the correlaton wth the RSS values at surroundng postons. The parameters σ 2 f, and l can be estmated usng hyper-parameter estmaton [5]. Ths covarance matrx can be used to predct the RSS value RSS at an arbtrary poston c = {x, y }. The posteror dstrbuton of the RSS value at any poston s modeled as a Gaussan random varable,.e., (RSS c ) = N (RSS ; µ, σ ), 2 where µ and σ 2 are gven by: µ = k T (Q + S) 1 ρ (4) σ 2 = k(c, c ) k T (Q + S) 1 k + σ 2 n (5) wth σ 2 n s the measurement varance, k () = k(c, c ), = 1,..., n. The estmate of the RSS value at poston c = {x, y } equals RSS = µ and the uncertanty on the estmated RSS s σ 2.

7 Sensors 2016, 16, of 19 For a large area contanng several hundred RPs, computng the RSS values wth Equatons (4) and Equaton (5) s computatonally demandng because of the nverson of the large covarance matrx Equaton (2). However, n an ndoor envronment, we may assume that RPs at a large dstance from the poston where we want to estmate the RSS value are blocked by several walls and other objects. Hence, the covarance k(, ) between the RSS values of those far away RPs and the RSS values at the consdered poston wll be approxmately zero. As a result, t s a reasonable assumpton that only tranng RPs close to the consdered poston wll contrbute to the RSS value at the consdered poston. The LGP algorthm restrcts the tranng RPs that contrbute to the RSS value at poston c to a tranng set TS, settng k(x, x ) = 0 f x TS. Assumng the number of RPs n TS equals L, the LGP algorthm smplfes Equatons (4) and (5) by only consderng the L nearest to RPs. That s, k and ρ reduce to a L 1 vector, and covρ Equaton (2) to a L L matrx. Compared to the complexty O(n 3 ) when all n RPs n the tranng database are used, the LGP algorthm has complexty O(nL) to select the L nearest RPs and O(L 3 ) to nvert the reduced-sze covarance matrx Equaton (2). To llustrate the LGP algorthm, we consder the RSS rado map of a WF access pont n an ndoor envronment. The true rado map s created usng the WnProp tool from AWE Communcatons [35], denoted as DB. The area s a 19.5 m 48.5 m rectangle, contanng 18 rooms n the same floor. The true rado map contans 3318 unformly dstrbuted RPs. We select 100 RPs from DB, whch covers part of the target area. Fgure 3 shows the true rado maps and the dstrbuton of the selected RPs. (a) (b) Fgure 3. True rado map and the dstrbuton of RPs. (a) True Rado map of the whole target area; (b) Dstrbuton of Reference Ponts. We apply the proposed LGP to create the rado map for the target area. Part of the un-surveyed areas are ncluded. There are some algorthms can be appled to buld the rado map rapdly presented n Secton 2, such as crowdsourcng, ray-tracng, SLAM, and mathematcal models. We dd not supply enough comparson wth all of these technques because dfferent algorthms rely on dfferent equpment and nput. It s not straghtforward to make comparsons between dfferent algorthms n dfferent condtons. Our study manly focuses on the mathematcal model. As a result, we only make comparsons between the wdely used mathematcal models, ncludng Gaussan Process (GP) and Log-Dstance Path Model (LDPL). Fgure 4 s the smulaton result. Durng the smulaton, we set λ = 0.5, L = 4, m = 800, and ε = 0.5. In the Log-Dstance Path Model (LDPL) [36], where the parameters of the LDPL model are estmated based on the tranng data, the uncertanty of RP s defned as follows: D f f = F F (6) where RSS,j and RSS,j are estmated and true RSS values at RP j, respectvely.

8 Sensors 2016, 16, of 19 (a) LGP RSS value(dbm) (b) GP RSS value (dbm) (c) LDPL RSS value (dbm) (d) LGP RSS uncertanty (dbm) (e) GP RSS uncertanty (dbm) (f) LDPL RSS uncertanty (dbm) Fgure 4. The estmated RSS values and the uncertanty. LGPL: Log-Dstance Path Model. As can be observed, the rado maps for GP and LGP are smlar to the true rado map. The LDPL model, whch s known to fal at postons far from the sgnal source, resembles the true rado map less, comparatvely. We also compute the varance over all RPs. The varance s defned n Equaton (7). σ = m =0 D f f 2 /m (7) We evaluate the average uncertanty for dfferent areas, whch are Surveyed Area (SA), Unsurveyed Area (UA) and the Target Area (TA, TA = SA UA). Table 1 llustrates the smulaton results. Table 1. varance for dfferent algorthms n dfferent areas (dbm) SA: Surveyed Area; UA: Unsurveyed Area; TA: Target Area. Algorthm SA UA TA GP LGP LDPL From Table 1, we can see that GP has the lowest varance n the target area, whch s about 5.77 dbm, followed by LGP wth an average of 5.88 dbm. The hghest varance comes from LDPL, whch s 7.43 dbm. In the surveyed area, all the three algorthms perform better than n the unsurveyed area. In all cases, GP performs the best over the three algorthms. L s the number of tranng RPs used for estmatng the RSS values for a gven vrtual node. A large L ntroduces more tranng data, and a more accurate result s obtaned. However, the tme for estmatng the RSS values wll be ncreased. In ths secton, we explore the queston of how to fnd a good balance between the varance and the tme for buldng the vrtual database. Durng the smulaton, we set λ = 0.5, ε = 0.5, and m = 800. Fgure 5 shows the result. In ths smulaton, L ncreases from 2 to 20. In Fgure 5a, we can see that the varance decreases as L ncreases. Fgure 5b shows the tme complexty ncrease wth L. If we want to keep a good balance between tme complexty and varance, we can set L = 7.

9 Sensors 2016, 16, of 19 (a) (b) Fgure 5. Varance and Tme complexty vary wth dfferent L. (a) Varance of the estmaton; (b) Tme for buldng the vrtual database. For a more accurate result, we evaluate the three algorthms wth dfferent denstes of DB Crowd. In the followng smulaton, we set ρ Crowd varyng from 0.02 to 1, and the tranng RPs were selected randomly from DB. For each value of ρ Crowd, we smulated 2000 tmes wth λ = 0.5, ε = 0.5, m = 800, and L = 7. Fgure 6 shows the results. Tme refers to the tme for buldng the vrtual database. (a) (b) Fgure 6. Varance and Tme complexty vary wth dfferent ρ Crowd. (a) Varance of the estmaton; (b) Tme for buldng the vrtual database. In Fgure 6a, GP performs the best, followed by LGP, and LDPL performs the worst. However, the dfferences between GP and LGP are small. In Fgure 6b, LDPL has the lowest tme complexty, followed by LGP and GP. In summary, LGP keeps a good balance between varance and tme complexty Improved Bayesan Algorthm Gven measurement F t at tme t and DB (v), the objectve n fngerprnt localzaton s to estmate the user s real-tme coordnate p t at tme t. The Bayesan localzaton algorthm s sutable for a user contrbuton-based localzaton system for moble devces [8]. The standard Bayesan localzaton algorthm wll calculate all the RPs posteror probablty, and maxmum them to estmate the coordnates. If the fngerprnt database

10 Sensors 2016, 16, of 19 contans a great number of RPs, computng all the RPs posteror probablty would be tme consumng. In ths paper, we frst select K nearest RPs from the vrtual database based on the metrc defned n Equaton (8). a d t, = ( RSS t,s RSS,s q ) 1/q (8) s=1 These K RPs have the smallest d t,s among the others n DB (v). A standard Bayesan localzaton algorthm was used to estmate the user s real-tme coordnates based on the selected RPs. The posteror probablty of beng n one of the selected RPs locatons s gven by Equaton (9): P(p F t ) = P(p ) P(F t p ) m j=1 P(p j) P(F t p j ) (9) where P() represents the probablty densty functon, P(p ) s the pror probablty of the user s locaton, and P(F t p ) s the lkelhood of observng a set of sgnal strength measurements F t at locaton p. p s assumed to be unformly dstrbuted. For smplcty, we assume that each sgnal strength RSS,j1 s condtonally ndependent of every other RSS,j2 for j1 = j2. So, we have: P(F t p ) = a j=1 P(RSS t,j p ), = 1, 2,..., K (10) For modelng the condtonal probablty P(RSS t,j p ), we frst show the measurement results from a specfed AP at a statonary locaton n Fgure 7. (a) (b) Fgure 7. RSSI data and Gaussan Ft. (a) RSSI values measured at a statonary locaton; (b) PDF and Gaussan Ft. Fgure 7 mples that we can model the condtonal probablty P(RSS t,j p ) as a Gaussan dstrbuton: P(RSS t,j p ) = 1 2πσ e (RSS t,j RSS,j )2 2σ 2 (11) The users have to estmate the RSS varance σ 2 n before uploadng the measurement. For the vrtual RPs, the varance s gven by Equaton (5). Fnally, we estmate the user s coordnates usng Equaton (12): p t = k p ˆP(F t p ) (12) =1

11 Sensors 2016, 16, of 19 where ˆP(F t p ) s the normalzed condtonal probablty gven by Equaton (13): ˆP(F t p ) = P(F t p ) k j=1 P(F t p j ) (13) 4. Results and Dscusson There are some parameters n the proposed algorthm, ncludng λ n MID, ε n LGP, m the number of RPs n vrtual database, and K n the mproved Bayesan. All of these parameters determne the complexty and postonng accuracy of the proposed algorthm. We frst optmze these parameters by smulatons, and then we evaluate the proposed algorthm by a real-case scenaro experment. In the followng secton, root mean square error (RMSE) s defned n Equaton (14): RMSE = W =1 [(x x ) + (x x )] W where (x, y ) and ( x, ŷ ) are the true and estmated coordnates of the user and W s the number of postonng cases Optmze the Parameters n the Algorthm (14) λ The dstance λ determnes not only the spatal unformty of the resultng RPs, but also the complexty of the algorthm: by reducng λ, the RPs wll be placed more unformly over the area, but the complexty of MID ncreases as the number of vrtual RPs to be searched ncreases n nverse proporton to the quad-rate of λ. In ths smulaton, we buld dfferent DB (v) based on dfferent DB Sample for postonng. The tranng database are randomly selected from DB, contanng 80 RPs. We apply the LGP for estmatng the vrtual RPs RSS values. The mproved Bayesan algorthm s appled for postonng. The other parameters are set as follows: ε = 0.5, L = 7, m = 80, and K = 3; λ s set to ncrease from 0.1 to 3.3. Results from 3000 postonng cases are shown n Fgure 8. (a) (b) Fgure 8. Root mean square error (RMSE) and tme for buldng the vrtual database vary wth dfferent λ. (a) RMSE.; (b) tme for buldng the vrtual database.

12 Sensors 2016, 16, of 19 Fgure 8a shows that RMSE doesn t change sgnfcantly wth λ. Fgure 8b shows that the tme decreases when λ ncreases. The results from Fgure 8 tell us that we can use as large a λ as possble to reduce the tme for buldng the vrtual database ε The radus ε has an nfluence on the postonng accuracy. When the radus s small, the resultng database DB (v) wll have a more unform placement of the RPs, but the probablty of fndng a nearby tranng RP decreases, such that the RSS of more RPs need to be determned usng the LGP algorthm. On the other hand, when the selected radus s large, the resultng database DB (v) wll be less spatally unform, but more tranng RPs wll be present n DB (v). Smlar wth the prevous settng, we apply the LGP for estmatng the vrtual RPs RSS values, and the mproved Bayesan algorthm for postonng. The other parameters are set as follows: λ = 3.3, L = 7, m = 80, and K = 3. We buld DB (v) based on the crowdsourcng database, whch contans 80 RPs and s randomly selected from DB. ε s set to ncrease from 0 to 2. Results from 3000 postonng cases are shown n Fgure 9. (a) (b) Fgure 9. Percentage of tranng data and RMSE vary wth dfferent ε. (a) Percentage of tranng data; (b) RMSE. Fgure 9a shows that the tranng RPs percentage ncrease as ε ncreases. Fgure 9b shows that more tranng data doesn t mprove the performance, because DB (v) s less spatally unform K K s the number of nodes used for postonng. In ths smulaton, we want to fnd the best K for estmaton. We apply the mproved Bayesan algorthm for postonng. We buld DB (v) based on the crowdsourcng database, whch contans 80 RPs and s randomly selected from DB. We set K to ncrease from 1 to 10. The other parameters are set as follows: λ = 3.3, L = 7, m = 80, and ε = 0.5. Results from 3000 postonng cases are shown n Fgure 10. The result from Fgure 10a shows that usng 4 or 5 RPs for postonng performs the best. And Fgure 10b shows that the tme for postonng s not senstve to K.

13 Sensors 2016, 16, of 19 (a) (b) Fgure 10. Tme for postonng and RMSE vary wth K. (a) RMSE; (b) Tme for postonng m m s the number of RPs n the vrtual database DB. More RPs mght result n a more accurate postonng result, but also needs more tme for queryng n the database. In ths secton, we want to fnd the best sze of the vrtual database. In ths smulaton, we set m to ncrease from 40 to 800, and the tranng database contans 80 randomly dstrbuted RPs selected from DB. The other parameters are set as follows: λ = 1, L = 7, K = 5, and ε = 0.5; For each value of m, the results come from 3000 postonng cases. Fgure 11 shows the result. (a) (b) Fgure 11. Tme for postonng and RMSE wth varyng m. (a) RMSE; (b) Tme for postonng. Fgure 11a shows that when m s about the same as the number of tranng RPs, the two methods perform the same. However, as m ncreases, the proposed algorthm performs better. When m = 800, the RMSE s 1.63 m compared wth 2.12 m usng the tranng database. The proposed algorthm mproves the accuracy by about 23.2%. Fgure 11b shows that when m = 117, t performs the same as usng tranng database, and the proposed algorthm needs more tme for postonng Real-Case Scenaro Experment For testng the new algorthm n real world, we developed an Androd app. The ndoor rado map s buld n a crowdsourcng way. The user can locate themselves, and they can also upload the fngerprnt data to the locaton server. Fgure 12 s the user nterface of the app.

14 Sensors 2016, 16, of 19 Fgure 12. User nterface of the app. In Fgure 12, the map s the floor layout of our Lab, coverng an area of about 1928 m 2. Clckng the central button wll send postonng requrement. Long pressng the nterface wll change the map of the ndoor envronment. Double clckng the nterface wll specfy a user s current locaton. The user can clck the rght button to send the current RSS measurement and the specfed coordnate to the tranng database. We frst bult a tranng database coverng part of the target area. The database contans 71 RPs. We wll test the new algorthm n the surveyed area and n dfferent unsurveyed areas. Fgure 13 s the dstrbuton of the ntal data. Fgure 13. Dstrbuton of ntal data. We frst estmate the user s coordnate usng vrtual database and tranng database n the surveyed areas. The parameters are set as follows: λ = 1, L = 7, K = 5, ε = 0.5. The densty of the vrtual database s 1. Fgure 14 shows the results from 3000 postonng cases.

15 Sensors 2016, 16, of P e rc e n ta g e (% ) In ta l V rtu a l E rro r(m ) Fgure 14. Postonng result usng ntal database and vrtual database n the surveyed area. Fgure 14 shows that the proposed algorthm performs better. The average localzaton error s 2.47 m usng the ntal database, whle t s 1.84 m usng the vrtual database. The new algorthm mproves the accuracy by 25.5%, wth an average postonng error below 2.2 m for 80% of the cases, whle the vrtual database s 3.1 m. We make comparson to the standard Bayesan algorthm. Both the new algorthm and the standard algorthm apply the vrtual database for postonng. The parameters are set as follows: λ = 1, L = 7, K = 5, ε = 0.5. The densty of the vrtual database s 1. Fgure 15 shows the results from 3000 postonng cases P e rc e n ta g e (% ) Im p ro v e d B a y e s a n S ta n d a rd B a y e s a n E rro r(m ) Fgure 15. Postonng result usng dfferent algorthm. Fgure 15 shows that the new algorthm performs better. The average localzaton error s 1.84 m usng the new algorthm, whle the standard s 1.93 m. The new algorthm mproves the accuracy by 4.66%, wth an average postonng error below 2.2 m for 80% of the cases, whle the standard algorthm s 2.3 m. We evaluate the algorthm n the unsurveyed area. The unsurveyed area s separated nto several sub-areas accordng to the dstance to the surveyed area. We compare the postonng accuracy n these sub-areas. Fgure 16 shows the expermental results. Fgure 16 llustrates that the RMSE ncreases as the dstance to the surveyed area grows. If the users are less than 10 m away from the surveyed area, the average postonng error s 5.75 m. Ths postonng result s not accurate enough, but sometmes t s useful, especally for areas wthout ste survey.

16 Sensors 2016, 16, of R M S E (m ) D s ta n c e (m ) Fgure 16. Postonng n dfferent unsurveyed areas usng the vrtual database. The proposed algorthm s scalable, whch allows the users to contnually upload ther coordnates to the server to mprove the performance of estmaton. Fgure 17 shows the expermental result. In ths experment, we use the same brand of smartphone for postonng because dfferent devces report network measurement very dfferently [37]. Fgure 17. Improvng the performance of estmaton by crowdsourcng. In Fgure 17, we can see that the proposed algorthm performs better. As the users contnually upload ther coordnates and RSS measurement, the new algorthm s performance can be mproved. 5. Conclusons The wreless fngerprnt technque has the advantages of low deployment cost, supplyng reasonable accuracy, and ease of applcaton to moble devces. As a result, fngerprntng has attracted a lot of attenton. In areas wthout calbraton data, however, ths algorthm breaks down. Constructng a fngerprnt database wth hgh densty fngerprnt samples s labor-ntensve or mpossble n some cases. Researchers are contnually searchng for better algorthms to create and update dense databases more effcently. The popularzaton of smartphones makes moble crowdsourcng fngerprnt localzaton more practcal. However, desgnng a sustanable ncentve mechansm of crowdsourcng remans a challenge. In ths paper, we propose a scalable algorthm to create a WLAN rado map by moble crowdsourcng and Gaussan Process for fngerprnt ndoor localzaton. We frst propose a Mnmum Inverse Dstance (MID) algorthm to buld a vrtual database wth unformly dstrbuted vrtual Reference Ponts (RP). The area covered by the vrtual RPs can be larger than the area covered by the

17 Sensors 2016, 16, of 19 tranng data. A Local Gaussan Process (LGP) s then appled to estmate the vrtual RPs RSSI values based on the crowdsourced tranng data. Fnally, we mprove the Bayesan algorthm to estmate the user s locaton usng the vrtual database. The parameters n the proposed algorthm are optmzed by smulatons and the new algorthm s tested on real-case scenaros. The average localzaton error s 2.47 m usng the ntal database, whle the error n the vrtual database s 1.84 m. The new algorthm mproves the accuracy by 25.5%, wth an average postonng error below 2.2 m for 80% of the cases, whle the vrtual database s 3.1 m. The proposed algorthm also allows the users to contnually upload ther coordnates to the server to mprove the performance of estmaton. Moreover, the proposed algorthm can localze the users n the neghborng unsurveyed area. If the users are less than 10 m away from the surveyed area, the average postonng error s 5.75 m. The proposed algorthm has to rely on a locaton server. If there s no connecton between the server and clents, the user can t upload the postonng requrement. As a result, the clent won t receve hs coordnate, and ths s the problem for all the crowdsourcng fngerprnt ndoor localzaton algorthms. Clent-based archtecture solutons would be more practcal. However, wth the wde avalablty of WLAN networks, connectng to the nternet would be easer. We beleve ths problem wll be solved wth the wde deployment of WF access ponts n the future. Our study requres a strong user collaboraton. If the user wants to contrbute to the fngerprnt database, he should estmate hs locaton wth another postonng system and upload the fngerprnt, contanng the coordnate and the RSS values, to the server. Ths would lead to the problem that the users are not wllng to submt ther measurement. For ths drawback, we can make the clent upload the RSS and locaton to the server automatcally, but the scale of the fngerprnt database wll ncrease rapdly. And we are not sure about the relablty of the uploaded data. In that case, we have to flter out the unrelable data. Moreover, we haven t focused on the devce dversty problem. It s practcally mpossble for all the users to have the same brand of smartphone. Our future work wll concentrate on these two ssues. Acknowledgments: Ths study s supported by the NSFC (Natural Scence Foundaton of Chna) program under Grand No , No Author Contrbutons: Qun L and Wepng Wang conceved and desgned the experments; We Chen performed the experments; Zesen Sh analyzed the data; Qang Chang wrote the paper. Conflcts of Interest: The authors declare no conflct of nterest. References 1. Gerstweler, G.; Vonach, E.; Kaufmann, H. HyMoTrack: A Moble AR Navgaton System for Complex Indoor Envronments. Sensors 2016, 16, do: /s Bahl, P.; Padmanabhan, V.N. Radar: An n-buldng rf-based user locaton and trackng system. In Proceedngs of the Nneteenth Annual Jont Conference of the IEEE Computer and Communcatons Socetes (INFOCOM 2000), Tel Avv, Israel, March 2000; pp Guzman-Quros, R.; Martnez-Sala, A.; Gomez-Tornero, J.L.; Garca-Haro, J. Integraton of Drectonal Antennas n an RSS Fngerprntng-Based Indoor Localzaton System. Sensors 2016, 16, do: /s Google Maps, Google Maps Indoor Avalable onlne: partners/ndoormaps/ (accessed on 23 May 2015). 5. Ferrs, B.; Fox, D.; Lawrence, N. Wf-slam usng Gaussan process latent varable models. IJCAI 2007, 7, Du, Y.; Yang, D.; Xu, C. A Novel Method for Constructng a WIFI Postonng System wth Effcent Manpower. Sensors 2015, 15, Bollger, P. Redpn-adaptve, zero-confguraton ndoor localzaton through user collaboraton. In Proceedngs of the Frst ACM Internatonal Workshop on Moble Entty Localzaton and Trackng n GPS-Less Envronments, New York, NY, USA, 19 September 2008; pp

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