Received signal strength based localization for large space indoor environments

Transcription

1 Research Article Received sigal stregth based localizatio for large space idoor eviromets Iteratioal Joural of Distributed Sesor Networks 2017, Vol. 13(1) Ó The Author(s) 2017 DOI: / jourals.sagepub.com/home/ijds Xigwag Wag 1, Xiaohui Wei 1,2, Yuayua Liu 1 ad Shag Gao 1 Abstract WiFi-based idoor localizatio has attracted recet research attetio. Large space layout is a special ad more complex idoor eviromet. Most existig idoor localizatio methods lead to poor accuracy ad may of them are ot suitable for large space eviromets. I this article, we propose a ovel approach for idoor localizatio ad avigatio. I our approach, the expesive traiig is avoided by utilizig the cocept of pre-scheduled path ad automatically mappig the WiFi figerprits to it. For olie tracig, we utilize historical sesor data to delieate users trajectory ad calculate the similarity to all possible paths o the map, the the system chooses the most similar oe as the result. The proposed work is evaluated ad compared with previous methods. The results show that our approach improves accuracy by 80%. Keywords Idoor localizatio, large space eviromet Date received: 5 July 2016; accepted: 2 December 2016 Academic Editor: Gag Wag Itroductio I recet years, with the developmet of ubiquitous computig ad mobile computig, there is a growig use of locatio-based services (LBS). As the precoditio of idoor LBS, mobile idoor localizatio attracts icreasig iterests. Although the accuracy of previous methods ca reach to the cetimeter level usig ultra widebad (UWB), 1,2 ifrared ad radio frequecy (RF), 3,4 beaco, 5 ad multi-ateas, 6 those systems eed to deploy extra facilities, such as UWB sers ad receivers. Give that may buildigs are equipped with WiFi access poits (APs), WiFi-based localizatio system becomes widely acceptable by users. However, WiFi-based localizatio is particularly challegig sice the radio sigal is ofte affected by some exteral factors, such as reflectio, refractio, multi-path, shadow fadig, scatterig, ad temporal dyamics. 7 9 I a large space idoor eviromet, these effects lead to poor accuracy if previous idoor localizatio methods are used for large space eviromets. Curretly, large space idoor layout (such as super market ad shoppig malls) is commo i compaies due to the eed for large space utilizatio ad flexible decoratio. However, the large space also causes icomprehesive positio cogitio whe a ufamiliar visitor eters. For may large space idoor eviromets, ufamiliar visitors geerally desiderate avigatio or localizatio service to help them perceive surroudigs. Therefore, solvig the localizatio problem i large space idoor eviromets is of sigificat value. 1 College of Computer Sciece ad Techology, Jili Uiversity, Chagchu, Chia 2 Key Laboratory of Symbolic Computatio ad Kowledge Egieerig of Miistry of Educatio, Jili Uiversity, Chagchu, Chia Correspodig author: Shag Gao, College of Computer Sciece ad Techology, Jili Uiversity, 2699, Qiaji Street, Chagchu , Jili, Chia. shaggao@jlu.edu.c Creative Commos CC-BY: This article is distributed uder the terms of the Creative Commos Attributio 3.0 Licese ( which permits ay use, reproductio ad distributio of the work without further permissio provided the origial work is attributed as specified o the SAGE ad Ope Access pages ( opeaccess.htm).

2 2 Iteratioal Joural of Distributed Sesor Networks I most buildigs, sigals may ecouter a cosiderable drop whe passig through a wall. 10 Owig to the fact that the received sigal stregth (RSS) values of the same AP are sigificatly differet i differet rooms, ad the diversity of RSS ca be used to distiguish differet rooms. I large space idoor eviromets, such approach is ot possible because of lackig of walls. Compared with other idoor coditios, idoor localizatio is more ecessary for large space eviromets. I geeral buildigs, rooms are labeled by iterrelated room id/ame (e.g. cotiuous umbers). A perso ca idetify his locatio by the label whe he is i the corridor, as log as the room is ot too large to tell the exact locatio. For large space buildigs, there ofte exists obstructios (such as cotaiers, bookshelves, ad people), thus it is difficult to tell the locatio for a ew visitor. I may idoor localizatio systems, there is a simplificatio that the collected WiFi figerprit database is static. The geerated data set will be used forever. However, i the real world, the WiFi sigal stregth will chage over temperatures, 11 devices, 8 ad eve the huma body that ca also absorb sigals. 12 Therefore, the RSS value varies with differet temperatures, huma traffic, ad devices. The static database caot adapt the fickle RSS values ad will lead to a huge positioig error. To achieve a high-accuracy localizatio, the figerprit database should be updated frequetly. However, updatig the figerprit database is very costly. There are also a lot of idoor positioig systems without traiig. For istace, Bisio et al. 13 geerate the database through fiite-differece time-domai (FDTD) simulatios of the electromagetic propagatio that eeds to measure the dielectric properties of all the materials i the idoor eviromet. Redpi 14 is also a traiig-less idoor localizatio system which relies heavily o users iteractio. WILL is used to map WiFi figerprits to rooms i a wall-partitioed idoor eviromet oly, but ot fittig large space areas. 10 Hece, a highaccuracy idoor localizatio without traiig is ecessary for large space eviromets. I this study, we obtai users motio by aalyzig the sesor raw data from mobile phoes. By mappig the motio to a map, we successfully remove the labelig process of traditioal approaches. To achieve competitive localizatio accuracy, we leverage the trajectory mappig ad figerprit set matchig. As a result, our approach is ot desired for labelig measured data with correspodig locatios ad get a good localizatio accuracy. Our cotributios ca be summarized as follows: 1. We preset a low-cost idoor localizatio system by avoidig the data collectio phase by makig pre-scheduled paths. Whe collectors walk alog the path, the system automatically collects WiFi figerprits ad the maps them to the floor pla. 2. We propose a high-accuracy idoor localizatio algorithm for large space eviromets. The localizatio i this algorithm is computed by a trajectory mappig method. The trajectory is formed through measurig the iertial measuremet uit (IMU). 3. We implemet a demo system to evaluate the performace of our method. Our results show a substatial improvemet i accuracy. The rest of this article is orgaized as follows. I sectio Related work, we preset the basic techiques of estimatio of positio usig a WiFi device. We itroduce our system desig ad preset the detailed algorithm i sectio System desig. I sectio Simulatio, we describe the system implemetatio ad report evaluatio results. Fially, sectio Coclusio ad future work cocludes the article with future directios. Related work Previous WiFi-based idoor localizatio mechaisms (Figure 1) are geerally divided ito two categories: figerpritig based ad model based. The figerpritig-based approach cotais two stages, offlie stage ad olie stage. I the offlie stage, the RSS collector eeds to take a mobile device ad walk through the buildig to mark locatios ad collect RSS values. The, store RSS values ad correspodig coordiates ito figerprit database. I the olie stage, the mobile device collects the real-time RSS values ad matches them to the RSS values stored i the figerprit database ad the determies the Figure 1. Taxoomy of idoor localizatio systems.

3 Wag et al. 3 locatio of the user. Most of these methods utilize RF sigals. Radio detectio ad ragig (RADAR) 15 is a early system usig this techique. Horus 16 improves upo RADAR by employig a stochastic descriptio of the RSS-locatio relatioships ad usig a maximum likelihood based method to estimate locatios. However, this techique faces a great deficiecy that it is pretty costly to collect ad label the traiig data i a large scale buildig. The model-based method applies a geometrical way to work out locatios, ad the iformatio used i the locatio calculatio cotais RF propagatio distaces ad all AP locatios. These approaches assume the sigal stregth is cosistet with a specific model (such as log-distace path loss model). Due to the effects of multi-path ad shadow fadig, the WiFi stregth is quite oisy ad highly deps upo eviromet. Although some previous works have bee itroduced, for istace, Wag et al. 17 preset a curve right based idoor localizatio approach to costruct a fitted RSSdistace fuctio for each trasmitter, PiPoit, 18 Cricket, 5 ad VOR, 19 there is always a large error for this kid of method. There are may studies preseted to improve the accuracy of figerprit-based idoor localizatio. Sice smartphoes have bee equipped with a umber of sesors, leveragig iertial sesors to improve localizatio accuracy is gradually possible. Based o the iertial sesor data, we are able to kow ad record users movemets, such as sittig, walkig, ad ruig The combiatio of IMU ad the WiFi RSS is itroduced by Yag et al., 24 ad Zhag et al. 25,26 make a fusio of WiFi RSS, IMU, ad map iformatio to get a better accuracy. Also, the filter techique is widely used to improve accuracy, such as Che et al. 27 ad Eveou ad Marx. 28 utilize Kalma filter with WiFi RSS ad IMU for precisio localizatio. Sheg et al. 29 recogize that RSS measuremet poits caot be collected desely i large ope idoor eviromets. However, they do ot deal with the complexity i large space eviromets. Differet from the previous works, our idoor localizatio approach is a combiatio of WiFi RSS, IMU, ad map iformatio ad adapts the large space layout (also fits for geeral eviromet) without the expesive traiig. Thus, users will ot be ivolved i data collectio. System desig Motivatio The most costly ad error-proe stage i the RSS-based system is the offlie figerprit database maual collectio. Because of the time varyig characteristic of WiFi sigal (as show i Figure 2), the labeled data are ofte Figure 2. RSS value chages over time. the average value of may samples at the same positio. 30 For orietatio aware sceario, the labeled data at kow locatios should be collected toward differet orietatios. 31 Assumig that oce the collectio ad labelig job for a collector takes a miute, the distace amog referece poits is 2 m. For a buildig which has five floors ad each floor is 200 m m, there will be at least 416 h of collectio work to traiig a figerprit database, which is evidetly a huge labor time. Therefore, the RSS-based idoor localizatio method without or with a little survey is more efficiet ad iterestig. Because of the expesive cost, whe the figerprit database is geerated, it is rarely updated, which caot fit the chage caused by variable eviromets (temperature, huma desity, devices, etc.), ad will lead to low localizatio accuracy. For the large space layout buildig, owig to lackig of walls, the cosiderable drop while passig through a wall is missig. This makes it more challegig for the large space idoor localizatio system. Takig the above ito cosideratio, we preset a idoor localizatio approach for accurate positioig ad avigatio for large space idoor eviromets. System architecture I this work, as show i Figure 3, the localizatio approach cosists of four compoets: coarse trajectory formig (CTF), figerprit mappig (FM), trackig service (TS), ad WiFi figerprit database. I this sectio, we preset high-level architecture of our method.

4 4 Iteratioal Joural of Distributed Sesor Networks Figure 3. System architecture. There is little value to localize a user at a idepet time poit, but the trajectory with time property is valuable for both users ad orgaizatios who wat to aalyze user behavior. Cosequetly, the temporal ad spatial attributes of user s localizatio are essetial for a idoor localizatio system. I this view, we should solve trackig problem istead of localizatio problem, ad the trackig task is ot a simple combiatio of idepet localizatio tasks i a cosecutive time poit. Due to the radomess of huma movemet, the well-kow Kalma filter that is well used i a liear situatio is ot appropriate for idoor trackig. I this work, we record a fixed size of historical iformatio for trackig user trajectory. CTF is the foudatio of FM ad TS. Durig the movemet, collectors/users do ot eed to collect data o purpose, just carry mobile devices (such as cell phoe ad tablet) ad tur o WiFi switch, the system will auto-collect WiFi sigal stregth, accelerometer sesor data, ad magetometer sesor data with timestamp. The, the compoet formig a coarse trajectory ca be costructed by the sesor data. Defiitio 1. Pre-schedule path. A pre-schedule path is a path that a specified collector will walk alog as the admiistrator pre-plaed. FM is used by collectors who oly move aroud the buildig (this role ca be carried out by security guards, cleaig staff, etc.). These collectors eed to wader alog the pre-scheduled path ad walk aroud the buildig periodically. Figure 4 shows a example of pre-scheduled path for libraria i Library of Jili Uiversity. The coarse trajectory geerated i this walkig will be mapped oto the pre-scheduled path. The, the correspodig WiFi figerprits i the trajectory are mapped oto the floor pla. Evetually, every poit i the floor pla ows a figerprit. The database will be updated whe the ew data belogig to a existig pre-scheduled path come. TS is utilized by users who wat to employ the localizatio service. The system collects the WiFi sigal stregth with sesor data ad the stores these data temporarily. By historical sesor data, the system ca form the user s trajectory ad the cosult the database to obtai the most possible path. Figerprit database is the fudametal compoet for FM ad TS. It stores the output of FM that are figerprits with correspodig coordiates ad is the iput of TS. Updatig figerprit database is triggered by FM ad TS. I our approach, traiig work is greatly simplified by removig the locatio labelig. Collectors oly eed to carry their mobile devices ad walk alog the prescheduled paths. The, the figerprit database will be auto-geerated. We use trackig to replace localizig to achieve temporal ad spatial cosecutiveess. Sice our approach achieves a good localizatio accuracy i a more complex large space idoor eviromet, it will also fit for more geeral scearios. CTF WiFi RSS values, accelerometer sesor data, ad magetometer sesor data are collected by collectors mobile devices. The record ca be represeted as R t = hf, A, Mi, where t is the timestamp, F idicates the WiFi figerprit vector, A is the accelerometer data, ad M deotes the magetometer value. Assume there are APs i the buildig, the the WiFi figerprit vector ca be defied as F = ½ f 1, f 2,..., f Š ð1þ where f i (0\i ) is the RSS value of ith AP. We ca get the legth of user s trajectory by the accelerometer raw data with timestamp. However, high-performace sesors are prohibitively expesive, ad due to the existig oise from sesor raw data, error accumulatio is also large. 32 Fortuately, we ca adopt the time-labeled accelerometer raw data to cout steps. The, the steps ca be utilized to estimate the walkig distace. 33 We cosider the case that user s trajectory T ca be separated ito a set of lies flg. The directio L d of 6¼ Li + 1 d. each lie is differet from its adjacet lies, L i d The trajectory ca be formed by aalyzig sesor raw data. First, we covert the accelerometer data fag to cotiuous steps S ad the mark the orietatio Sd i of each step through processig the magetometer data fmg. Fially, the steps fsg ca be coected together to get the coarse trajectory T. Sice the directios of steps are obtaied by magetometer sesor data ad there may be a agle a

5 Wag et al. 5 Figure 4. A example of pre-scheduled path for libraria i JLU library. betwee the mobile devices i had ad facig directio, the measured directio M i may ot exactly match the walkig orietatio Sd i. Thus, a correctio agle a should be added to the measuremet. The value of correctio ca be obtaied by pre-measure or learig i the stage of figerprits collectio. The CTF algorithm is preseted for formig the coarse trajectory. The iput i CTF algorithm is the origial records of sesor data, ad output is the coarse trajectory of users. There are two for loops i CTF. The outer loop processes each record, ad the ier loop trasforms the raw accelerometer data to steps ad deals with the steps i each record. Therefore, the algorithm ca be doe i O() time, is the total step umber. Let S i = \l i, Sd i. deote the ith step, where l i is the legth of ith step. Usig CTF, the coarse trajectory T = fs i g is geerated. However, l i is ukow. Mappig figerprits The coarse trajectory caot be directly used for localizatio because the compoet l i of S i is ot clear. Differet people have differet step legths, so we caot assig a costat value to l i. We eed to figer out the accurate legth of each lie i the trajectory. Sice the coarse trajectory from a collector is a trackig of pre-scheduled path, each lie from this trajectory ca be mapped to a real lie i the floor pla. Accordig to the Sd i compoet, we ca separate the steps of the coarse trajectory ito differet cotiuous step sets i which the steps compose to a straight lie. Let ½x s, y s Š ad ½x e, y e Š deote the startig coordiate ad ig coordiate of a real liear path i the map which is mapped from the trajectory. Assumig a user walks alog this lie with a fixed step legth, the the legth of each step i this lie is qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (x e x s ) 2 +(y e y s ) 2 ð2þ where is the step umber i this lie. The, the coordiate of startig poit for ith step is h x s +(i 1) 3 x e x s, y s +(i 1) 3 y e y s ad the coordiate of ig poit for ith step is i ð3þ

6 6 Iteratioal Joural of Distributed Sesor Networks Algorithm 1: Coarse trajectory formig (CTF). Iput: fr t g Output: trajectory Iitial trajectory to ull; p=1; j=1; for R k do trasform fa k g to cotiuous steps fs 0 g; SS 0 ; i=p; for S i d do if S i d 6¼ Si 1 d the L j fs p,..., S i 1 g; TL j ; j ++ ; p=i; L j fs p,..., S max g; TL j ; Algorithm 2: Figerprit mappig (FM). Iput: fr t g, path Output: D T = CTF(fR t g); for L j 2 T do = js i 2 L j j; calculate pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the step legth i this lie as (x l = e x s) 2 +(y e y s) 2 ; for R i 2 L j do C i = x s + i3 xe xs, y s + i3 ye ys ; h x s + i 3 x e x s, y s + i 3 y e y s i ð4þ The, the coordiate of WiFi sigal s figerprit ca be obtaied by its correspodig record. The mappig relatioship of figerprit ad coordiate ca be stored i database as D i = \F i, C i., where F i idicates the WiFi figerprit vector ad C i is the correspodig coordiate i the floor pla. Sice the RSS value varies with exteral factors (huma desity, temperature, etc.), to achieve a accurate localizatio result, the figerprit database should be updated with the chage of eviromet. Because the mappig figerprit operatio occurs as log as the collectors wader aroud periodically, the update is triggered frequetly. Whe the TS is available for users, the query data are ot oly used for localizatio but also updates the figerprit database. Therefore, the figerprit database is suitable for eviromets. Figure 5. A example of similar pre-scheduled paths. The followig FM algorithm is preseted for mappig the WiFi sigal figerprits to the coordiate of the floor pla. I FM, the iput is the pre-scheduled path with its coordiate, the collected records of WiFi figerprits, ad sesor data, ad the output is the map set of figerprit ad coordiate. If there are some similar pre-scheduled paths (as show i Figure 5, the shapes of these paths are same but part of the legth of lies are differet), the approach caot distiguish from the correct mappig. Therefore, the pre-scheduled path should be oe of the iputs of FM. There are two for loops i this algorithm; from lie 2 to lie 6, that is, the outer loop ad each loop processes oe virtual lie from the trajectory. The ier loop, from lie 5 to lie 6, deals with oe sigle virtual lie, ad each loop hadles oe record i R t. Therefore, FM is a O( 3 m) complexity time algorithm, where is the records umber ad m idicates the maximum step umber of virtual lies. TS Differet from the traditioal ways, figerprits obtaied from FM are ot the average value of multiple measuremets. To overcome this shortcomig about iaccurate figerprits, we leverage the trajectory matchig to fetch all similar path sets. The, we adopt the figerprits matchig to fid out the most possible path from the path set. The TS stores a fixed size of historical records R t. The record set is cotiuously updated. Whe historical records of WiFi figerprits are reewed, the ew virtual trajectory of this user ca be geerated by CTF algorithm. I our idoor localizatio approach, the positioig problem ca be settled by meas of mappig a virtual trajectory to a path i the floor pla. Assumig users walk i a costat step legth, the possible legth is from l mi to l max. The, the virtual coarse trajectory formed by algorithm CTF ca be trasformed to a possible trajectory set T = ft i g through settig the step legth from l mi to l max. For each t i from T there are a set of possible mappig trajectories i the floor pla. Let f^t i g deote the

7 Wag et al. 7 set. The, each WiFi sigal figerprit F j from historical records correspods to a figerprit ^F j from the database. We ca use iterpolatio techique to geerate the missig figerprit which is correspodig to F j. The, the trackig mappig problem ca be described as follows argmi bti ( ) X j = 1 d(f j, bf j ) F j 2 t i, bf j 2 bt i ð5þ where d(f j, ^F j ) is the differece fuctio of two vectors. Simply, we ca use the Euclidea distace. Essetially, TS i our approach is a graph mappig problem. The figerprits are the odes, ad edges are the geographical liks with orietatio attribute. The problem ca be described as mappig a sub-graph to the whole graph ad tell which is the correspodig ewest ode. The graph mappig problem is NP-hard. Thus, there are may possibilities for a specific trajectory ad the calculatio of likelihood is costly. Therefore, we eed to arrow dow the umber of possible trajectories. Here, a cluster techique is preseted to classify the WiFi figerprits. Cosiderig the ature of sigal propagatio that the closer to the sigal source is the greater RSS will achieve. Therefore, for the figerprits surroudig AP k, thekth RSS is bigger tha the others (the distace to AP, k, is shorter tha the distaces to other APs). The, we ca use the idex of the biggest RSS i a figerprit as its category. As a result, the figerprits belogig to category k are closer to AP k tha others, which meas figerprits are geographically separated ito pieces. The cluster of a figerprit F is k if Algorithm 3: Trackig service (TS). Iput: fr t g, D, map Output: trajectory T = CTF(fR t g); c = argmax k ffi t g; for l mi l l max do for all possible trajectory i floor pla do if the cluster of trajectory is c the p = P d(f j, bf j ) F j 2 t i, bf j 2 bt i ; j = 1 8j, f k f j, j, k.0 ð6þ TT k, T k with the maximum T p ; choose the most likely trajectory i T as the trajectory; I this approach, oly a sortig operatio is used to estimate which cluster a figerprit belogs to. Thus, our cluster approach is much less complex tha the oes proposed before (such as the approaches by Frey ad Dueck 34 ad Feg et al. 30,35 ). Sice the cluster fuctio is a determiistic fuctio, the cluster of each WiFi figerprit will ot be chaged after it is measured. To expedite olie trackig, clusterig ca be doe offlie. I our approach, the possible trajectory is filtrated cosiderig whether the last figerprit ad the ig record s figerprit fall ito the same cluster. If they belog to the same cluster, the add the trajectory to the possible trajectory set. Aother way to reduce the potetial trajectories is to arrow dow the gap of l mi to l max. We ca use the historical iformatio of step legth from a same user calculated i TS ad the after executio for a period of time, choose the miimum value as l mi ad the maximum value as l max. The TS algorithm is preseted for localizig the users positios. The iputs of this algorithm are the floor pla of the buildig, the historical records, ad the WiFi figerprit database, ad the output is the trajectory which is correspodig to the historical trackig data. I this algorithm, there is a double-deck loop. The outer loop iteratively fids out the most likely legth of user s steps. The ier loop fetches the most likely trajectory for the give legth of a step. The variable c i TS deotes the cluster of R t. Evetually, TS figures out user s trajectory for the trackig data. It is a O( 3 m) time complexity algorithm, where is the umber of possible legths of a step ad m is the maximum umber of a trajectory i the same cluster. The WiFi figerprits measured by TS are ot oly used to localize mobile devices but also update figerprit database to keep the database latest with the eviromet varyig. Simulatio Simulatio setup All experimets i this article are coducted i part of secod floor i the Library of Jili Uiversity. We deploy 12 APs i the 20 m 3 20 m area. The distributio of clusters geerated by clusterig is demostrated i this sectio. We illustrate how the AP umber, update period, ad historical time effect the positioig accuracy. Ad the stability ad performace are also cosidered i this sectio. Compariso schema I may idoor localizatio approaches, K-earest eighbors (KNN) ad Kalma filter based are two

8 8 Iteratioal Joural of Distributed Sesor Networks classic idoor localizatio approaches ad used i may research works. 27,36 KNN goes through the figerprit database ad picks up k referece poits whose figerprits match best to the real-time oe. Let N k deote the subset picked up by KNN algorithm, ad N k ca be built with a iterative process as follows N k = fargmi Fi 2Od(F, F i )jf i 62 N k 1 g[ N k 1 ð7þ where O represets the etire figerprits database or figerprits set acquired from coarse localizatio stage, ad F is the real-time WiFi figerprit. Kalma filter ca be illustrated as St ðþ= A t St ð 1Þ+ B t Ut ðþ+ W t ð8þ Zt ðþ= H t St ð 1Þ+ V t where process oise W t ad observatio oise V t follow Gaussia distributio, ad they are idepet o each other, amely, W t ; ð0, QÞ, V t ; ð0, RÞ. Q ad R ca be obtaied by experiece, ad they are ivariable with the system chagig T s 0 >< >= T A t = s H t = ð9þ >: >; where T s is the samplig frequecy. With the restrictio of the system ad hardware, i our experimet, the parameter T s is set to 1 s. The predictio for system status is ^S ðþ= t A t^s(t 1) ^P ðþ= t A t^p ðþa t T ð10þ t + Q The correctio for system status is 8 Kt ðþ= ^P ðþh t T t H t^p ðþh t T 1 >< t + R St ðþ= St ð 1Þ+ Kt ðþ Zt ðþ H t^s ðþ t >: Pt ðþ= ði Kt ðþh t Þ^P ðþ t ð11þ The fial positio estimatio is obtaied by the Kalma filter that itegrates system state estimatio with real-time WiFi figerprit. The parameter Z(t) is oly related to the real-time WiFi figerprits ad is idepet o the user s movemet. Localizatio accuracy Sice we choose the strogest RSS idex as the idicator to cluster figerprits, ad the earer the referece poit to the AP, the stroger the RSS value, the figerprits belogig to the same cluster are geographically adjacet. Moreover, the area of oe cluster is related to the correspodig AP s power. The clusterig result is show i Figure 6. Each colored poit is a figerprit, ad the figerprits with the same color belog to the same cluster. I a complex idoor eviromet, the coverage rage of a sigle AP is limited, ad the weak RSS will lead to a poor result. Thus, we evaluate relatioship betwee the umber of APs ad the localizatio accuracy. Figure 7 shows that the mea errors of systems, respectively, usig KNN, Kalma filter, ad TS sharply drop as the AP umber varies from 3 to 6, ad the the dowtr of mea error decreases slowly. To further study their relatioship, we use the cocept of WiFi desity. Defiitio 2. WiFi desity. WiFi desity for a locatio is the accessible AP umber at this positio. As show i Figure 8, with the stregtheig of WiFi desity, the mea error of the localizatio systems goes dow. As oe AP may ot cover the whole field, the miimum WiFi desity ad the AP umber are ot i liear correlatio. Here, we use a homogeeous deploymet way to maximize the miimum WiFi desity. As the result idicates, the curves almost match the tail of Figure 7. The RSS value is effected by temperature ad huma traffic; thus, the localizatio accuracy is correlative with the freshess of WiFi figerprits. As show i Figure 9, whe the update period is expoetially elargig, the mea errors early liearly icrease. As the time goes o, sice the variatio of temperature ad huma traffic will ot exceed the maximum value, the mea errors declie is almost stable. From Figure 9, we ca see whether the WiFi figerprits update timely, ad the localizatio accuracy ca improve about 10%. The TS stores a fixed umber of historical records, ad the records are used to describe the trajectory of users. Thus, the more records there are, the less particular iformatio ca be used which leads to less matched paths. Sice TS compares the likelihood of the whole historical figerprits with the possible trajectory figerprits stored i database, the loger the fixed umber is, the less ifluece caused by RSS fluctuatig will be. As illustrated i Figure 10, the mea errors go dow as the historical time magifies. Particularly, whe there is oly oe record, the approach degeerates to be KNN. Stability is also a importace attribute for the localizatio approach. Figure 11 shows a 10-mi executio for TS. Let m ti deote the mea error of time t i, the M ti = 1= P t m t i, where is the umber of total time till t i. Here, the mea error is M ti. At the first miute, the mea errors expoetially decrease, which is owig to

9 Wag et al. 9 Figure 6. Cluster of WiFi figerprits at JLU library. Figure 7. AP umber versus mea error, update period 0.5 h. Figure 8. Desity versus mea error, update period 0.5 h. the missig of historical records. The, the mea errors are almost stable as the umber of historical records reaches the predetermied fixed size. Reducig the traiig time is a effective way for service providers to cut their cost. Comparig with the traditioal way, as illustrated i Figure 12, our approach is much less costly i traiig. The traditioal traiig method eeds to label the locatio ad collect the average RSS value which cost about a miute for a referece poit (RP). I our approach, the collector oly eeds to walk by. Although, we do ot use the average RSS value, we still get a high localizatio accuracy because of the trajectory matchig.

10 10 Iteratioal Joural of Distributed Sesor Networks Figure 9. Update period versus mea error, ie APs. Figure 12. Traiig time. Figure 10. Mea error versus historical time. Figure 13. CDF of mea error, update period 0.5 h, ie APs. We further compare our approach with the KNN method ad Kalma Filter method. The KNN is just a coectio of idividual localizatio results. Kalma Filter method uses the Kalma filter i the trackig. The cumulative distributio fuctio (CDF) is show i Figure 13. The results of all methods are Laplace distributed, ad TS has a smaller m ad b, which meas TS achieves a better accuracy. As illustrated i Figure 13, TS improves the accuracy by 80%. Figure 11. Mea error versus executio time, historical time 5s. Coclusio ad future work I this work, we propose a traiig-less idoor localizatio approach by automatically collectig the WiFi RSS ad sesor data ad the mappig the WiFi figerprits to the coordiates i the correspodig prescheduled path. Through calculatig the likelihoods with all possible trajectories formed by historical sesor

11 Wag et al. 11 data ad the choosig the most similar oe as the localizatio result, TS achieves a accurate positioig approach for the large space eviromet which is prevalet i moder buildigs. Sice our approach achieves a good localizatio accuracy i a more complex large space idoor eviromet, it will also fit for more geeral scearios. I this work, we assume users always hold the mobile device i had, but he or she may put it i his pocket ad watch it whe ecessary, which makes the magetometer sesor useless. Therefore, i the future, we will cosider the relatioship of the value of sesor data with the step legth ad the situatio with missig magetometer data. Declaratio of coflictig iterests The author(s) declared o potetial coflicts of iterest with respect to the research, authorship, ad/or publicatio of this article. Fudig The author(s) disclosed receipt of the followig fiacial support for the research, authorship, ad/or publicatio of this article: This work is supported by the Natioal Key Research ad Developmet Program of Chia (Grat Nos 2016YF B ad 2016YFB ), Natioal Natural Sciece Foudatio of Chia (NSFC) (Grat Nos , , ad ), Specialized Research Fud for the Doctoral Program of Higher Educatio ( ), Major Special Research Project of Sciece ad Techology Departmet of Jili Provice ( GX), Key Sciece ad Techology Research Project of Sciece ad Techology Departmet of Jili Provice ( GX), ad EUFP7 Projects EVANS (GA ) ad MONICA (GA ). Refereces 1. Gezici S, Tia Z, Giaakis GB, et al. Localizatio via ultra-widebad radios: a look at positioig aspects for future sesor etworks. IEEE Sigal Proc Mag 2005; 22(4): Prorok A, Tome P ad Alcherio M. Accommodatio of NLOS for ultra-widebad TDOA localizatio i siglead multi-robot systems. I: Proceedigs of the iteratioal coferece o idoor positioig ad idoor avigatio (EPFL-CONF ), Guimara es, September Kolodziej KW ad Hjelm J. Local positioig systems: LBS applicatios ad services. Boca Rato, FL: CRC Press, Liu H, Darabi H, Baerjee P, et al. Survey of wireless idoor positioig techiques ad systems. IEEE T Syst Ma Cy C 2007; 37(6): Priyatha NB, Chakraborty A ad Balakrisha H. The cricket locatio-support system. I: Proceedigs of the 6th aual iteratioal coferece o mobile computig ad etworkig, Bosto, MA, 6 11 August 2000, pp New York: ACM. 6. Xiog J ad Jamieso K. Arraytrack: a fie-graied idoor locatio system. I: Proceedigs of the 10th USE- NIX symposium o etworked systems desig ad implemetatio (NSDI 13), Lombard, IL, 2 5 April 2013, pp Yag J ad Che Y. Idoor localizatio usig improved RSS-based lateratio methods. I: Proceedigs of the global telecommuicatios coferece (GLOBECOM 2009), Hoolulu, HI, 30 November 4 December 2009, pp.1 6. New York: IEEE. 8. Pa SJ, Zheg VW, Yag Q, et al. Trasfer learig for WiFi-based idoor localizatio. I: Proceedigs of the associatio for the advacemet of artificial itelligece (AAAI) workshop, Chicago, IL, July 2008, p.6 9. Yag Z, Zhou Z ad Liu Y. From RSSI to CSI: idoor localizatio via chael respose. ACM Comput Surv (CSUR) 2013; 46(2): Wu C, Yag Z, Liu Y, et al. WILL: wireless idoor localizatio without site survey. IEEE T Parall Distr 2013; 24(4): Yi J, Yag Q ad Ni L. Adaptive temporal radio maps for idoor locatio estimatio. I: Proceedigs of the third IEEE iteratioal coferece o pervasive computig ad commuicatios (PerCom 2005), Kauai Islad, HI, 8 12 March 2005, pp New York: IEEE. 12. Wessapa T ad Rattaadecho P. Numerical aalysis of specific absorptio rate ad heat trasfer i huma head subjected to mobile phoe radiatio: effects of user age ad radiated power. J Heat Trasf 2012; 134(12): Bisio I, Cerruti M, Lavagetto F, et al. A traiigless WiFi figerprit positioig approach over mobile devices. IEEE Ate Wirel Pr 2014; 13: Bolliger P. Redpi-adaptive, zero-cofiguratio idoor localizatio through user collaboratio. I: Proceedigs of the first ACM iteratioal workshop o mobile etity localizatio ad trackig i GPS-less eviromets, Sa Fracisco, CA, September 2008, pp New York: ACM. 15. Bahl P ad Padmaabha VN. Radar: a i-buildig RF-based user locatio ad trackig system. I: Proceedigs of INFOCOM 2000: ieteeth aual joit coferece of the IEEE computer ad commuicatios societies (vol. 2), Tel Aviv, Israel, March 2000, pp New York: IEEE. 16. Youssef M ad Agrawala A. The Horus WLAN locatio determiatio system. I: Proceedigs of the 3rd iteratioal coferece o mobile systems, applicatios, ad services, Seattle, WA, 6 8 Jue 2005, pp New York: ACM. 17. Wag B, Zhou S, Liu W, et al. Idoor localizatio based o curve fittig ad locatio search usig received sigal stregth. IEEE T Id Electro 2015; 62(1): Youssef M, Youssef A, Rieger C, et al. PiPoit: a asychroous time-based locatio determiatio system. I: Proceedigs of the 4th iteratioal coferece o mobile systems, applicatios ad services, Uppsala, Jue 2006, pp New York: ACM. 19. Niculescu D ad Nath B. VOR base statios for idoor positioig. I: Proceedigs of the 10th aual iteratioal coferece o mobile computig ad

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