Geomagnetism-Aided Indoor Wi-Fi Radio-Map Construction via Smartphone Crowdsourcing

Transcription

1 sensors Article Geomagnetism-Aided Indoor Wi-Fi Radio-Map Construction via Smartphone Crowdsourcg Wen Li 1,2, Dongyan Wei 1, *, Qifeng Lai 1,2, Xianghong Li 1,2 Hong Yuan 1 1 Academy Opto-Electronics, Chese Academy Sciences, Beijg , Cha; wen.li@aoe.ac.cn (W.L.); laiqifeng@aoe.ac.cn (Q.L.); lixianghong@aoe.ac.cn (X.L.); yuanh@aoe.ac.cn (H.Y.) 2 University Chese Academy Sciences, Beijg , Cha * Correspondence: weidongyan@aoe.ac.cn; Tel.: Received: 13 February 2018; Accepted: 25 April 2018; Published: 8 May 2018 Abstract: Wi-Fi radio-map construction is an important phase door fgerprt localization systems. Traditional methods for Wi-Fi radio-map construction have problems beg timeconsumg labor-tensive. In this paper, an door Wi-Fi radio-map construction method is proposed which utilizes crowdsourcg data contributed by smartphone users. We draw door pathway map construct Wi-Fi radio-map without requirg manual site survey, exact floor layout extra frastructure support. The key novelty is that it recognizes road segments from crowdsourcg traces by a cluster based on magnetism sequence similarity constructs an door pathway map with Wi-Fi signal strengths annotated on. Through experiments real world door areas, method is proved to have good performance on magnetism similarity calculation, road segment clusterg pathway map construction. The Wi-Fi radio maps constructed by crowdsourcg data are validated to provide competitive door localization accuracy. Keywords: door localization; Wi-Fi fgerprt; crowdsourcg data; magnetic field; radio-map construction 1. Introduction Location-based service (LBS) is some most important content that provides convenient precise services for users, such as navigation for pedestrians or cars, mobile payment, taxi fdg, bicycle sharg, telligent guidg, loss prevention so on. The global navigation satellite system (GNSS) can provide positiong services most outdoor environments, however door environment, such as a big shoppg mall, underground parkg museums, or positiong techniques should be considered due to signal occlusion problem GNSS. Currently, door positiong techniques commonly used consumer applications maly clude Wi-Fi signal strength fgerprt methods [1,2], range measurement methods usg wireless signal [3,4], geomagnetic field matchg methods [5,6], dead reckong (DR) methods based on smartphone-mounted micro electro mechanical system (MEMS) [7,8] localization usg context recognition lmarks [9,10]. All mentioned localization methods have ir own advantages disadvantages, but Wi-Fi fgerprt method usually plays ma role door localization, for reason that Wi-Fi has been deployed almost all public places its received signal strength (RSS) has good ability location differentiation with a floor or between distct floors. Fgerprt-based Wi-Fi door localization system always consist two phases: fle radio map construction onle localization by fgerprt matchg. In fle phase, RSS from Wi-Fi access pots (APs) are labeled usg location coordates each reference pot (RP), all RP data are stored toger as a fgerprt database. In onle phase, user s real time RSS measurements are matched to fgerprt database usg an algorithm, position Sensors 2018, 18, 1462; doi: /s

2 Sensors 2018, 18, with most similar RSS measurements is given as fal position solution. To realize fle phase, it is ideal that RSS all detected APs be carefully calibrated to a location grid which completely covers door map, n Wi-Fi radio map can be constructed exactly. However, this method is time-consumg labor-tensive, as it needs repeated measurements on each RP to obta statistical value RSS pressional work to realize exact calibration door coordates. Anor challenge is that constructed radio map would lose stability even become valid some situations like fluctuatg air humidity door architecture changes [11]. In order to solve above problems, some new kd Wi-Fi fgerprt construction techniques have been proposed, cludg data collection with help volunteers [12], simultaneous localization mappg (SLAM) usg Wi-Fi signal strength [13], RSS prediction based on exist fgerprts [14], fgerprt construction usg passive crowdsourcg data [15]. Redp [16] OIL [12] are previously proposed fgerprt-based door localization systems that omit time-consumg trag phase, which volunteer users report ir current locations with room-level accuracy correspondg Wi-Fi signal-strength. The more users that are uploadg fgerprts at different locations, more areas database can cover. Aimg for a more flexible scalable pot design space user-generated Wi-Fi localization system, Molé [17] arranges places a hierarchy stead an accurate map for floor plan labels users fgerprts by semantic locations. These solutions depend on active participation users that results conveniences for user experience unknown measurement noises [18]. Ferris et al. [13] Huang et al. [19] proposed signal-strength-based SLAM techniques. Reference [13] uses a Gaussian Process Latent Variable Model (GPLVM) to determe latent-space locations unlabeled signal strength data. Reference [19] presents a GraphSLAM-like algorithm for signal strength SLAM, which is viable for a broader range environments due to its lack special constrats reduction runtime complexity. WiFi-SLAM serves a promisg solution for problem collection matenance WiFi sensor models for large-scale localization, but it needs user trajectories with some closed loops requires more calculation. HIWL [20] uses K-means to produce discrete signal observation sequences, tra Hidden Markov Model (HMM) parameters by limited topology formation door environments. Through HMM trag, system learns mappg relationship geographical signal distribution, n matches unlabeled fgerprts to correspondg physical locations based on mappg model. UMLI [21] proposes usg nonparametric clusterg methods to classify unlabeled signal observations through two classification layers. By utilizg clusterg method, unlabeled signal data are classified to locations or rooms havg similar RSS, achievg less site survey labelg work. Chang et al. [14] developed a Mimum Inverse Distance (MID) algorithm to build a virtual database with uniformly distributed virtual RPs. The Local Gaussian Process (LGP) is n applied to estimate virtual RPs RSSI values based on crowdsourcg surveyed data. These methods need a set surveyed fgerprts for model trag RSS prediction, so quantity quality labeled data will seriously impact ir accuracy. With popularization smartphones creasg number location-based service (LBS) users, research on passive methods Wi-Fi radio map construction based on crowdsourcg has become a research hot spot currently. Its greatest advantage is that crowdsourcg data can be obtaed passively through user s common behaviors when y use smartphone applications (APP). Meanwhile, Wi-Fi radio map can be formed automatically is easy to update thanks to contuous uploadg user data. WILL [22] is proposed as a wireless door logical localization approach that achieves room level location accuracy without site surveys. By exploitg user motions from mobile phones, dependent radio signatures are previously connected followg certa semantic rules to make a logical floor plan, fally mappg it with a physical floor plan. Wang et al. [23] proposed an door subarea localization scheme which first constructs subarea fgerprts from crowdsourced RSS measurements usg RL-clusterg n matches m to door layouts. They also proposed

3 Sensors 2018, 18, an onle localization algorithm to deal with device diversity issue. Both WILL Wang proposed methods divide user data to some clusters by RSS similarity match m to subareas a floor plan map. They can only provide room level localization rar than contuous positiong when a user walks door environment. Or systems use DR to compute user trajectories furrmore label fgerprts door map pathway, which can provide a contuous localization door corridors (roads). Zee [24] use ertial sensors present mobile phone to track m by a motion estimator (e.g., step counter, headg fset stride length estimator) an door environment, implements an augmented particle filter both usg floor map showg pathways (e.g., hallways) barriers (e.g., walls) Wi-Fi scans to acquire crowdsourcg users position. RACC [25] identifies door anchors (doors) as reference positions whole radio-map, which doors RSS fgerprts can be identified accordg to motion detection when users walk through doors annotated with ir correspondg physical locations by an adjacent recursive matchg method. RCILS [26] detects people s activities trajectories door environment matches m to a semantic graph door map usg HMM. Then RSS collected along trajectories can be labeled with location formation. The air pressure detected by barometer is used for elevator/stairs detection. RCILS also propose a trajectory fgerprt-based method onle localization phase, which performs better when longer trajectory wdow is used sequence matchg. Zee, RACC RCILS can provide an accurate location solution about 1~2 m, but y need an exact floor layout. PiLoc [15] divides a user s sgle trajectory to disjot path segments (turns long straight les) by detectg steps turns, utilized movement displacement (distance direction) as well as associated Wi-Fi signal to match path segments. Then PiLoc merges clustered path segments annotated with displacement signal strength formation to derive a floor plan walkg paths annotated with radio signal strengths. It does not require manual calibration, prior knowledge frastructure support. A comparison fgerprt localization methods without site survey via passive crowdsourcg data is shown Table 1. Table 1. Comparison fgerprt localization methods without site surveys via passive crowdsourcg data. Method Floor Plan Assistant Sensors Reported Accuracy WILL [22] with Acc. Average 86% (room-level) Wang [23] with None 95% (subarea-level) Zee [24] with Acc., gyro., comp. 1.2 m (%), 2.3 m (80%) RACC [25] with Acc., gyro., comp. 1.7 m (%), 2.2 m (80%) (fgerprt density: 1 m) 2.9 m (%), 4.3 m (80%) (fgerprt density: 2 m) RCILS [26] with Acc., gyro., mag., bar. Median error ~1.6 m PiLoc [15] without Acc., gyro., comp. Average 1.5 m In addition, localization based on geomagnetic field has attracted attention door localization area for fact it does not need frastructure support its stability compared to Wi-Fi signals. GROPING [27] utilizes magnetic fgerprtg collected by crowdsensg users construct a floor map from an arbitrary set walkg trajectories. Map explorer records magnetic fields usg smartphones tags road junctions manually to help GROPING partition trajectories to segments. The similarity magnetic tensity sequences is used to fer overlappg segments among trajectories stick m toger. Reference [28] presents a SLAM algorithm based on measurements ambient magnetic field strength (MagSLAM) for pedestrians with foot-mounted sensors. Reference [29] considers magnetic field SLAM exploration usg a mobile robot with a magnetometer wheel encoders. Different from above methods, we propose this paper a geomagnetism-aided door radio-map construction method via passive smartphone crowdsourcg. The proposed method don t need exact floor layouts, but rar utilizes crowdsourcg traces to form pathway map a floor plan with merged Wi-Fi radio signal strengths annotated on it. It recognizes road segments from crowdsourcg traces by a cluster based on magnetism sequence similarity, which can be calculated

4 Sensors 2018, 18, exactly by a proposed feature matchg algorithm even though walkg speeds may be different for each user. The rest paper is organized as follows: Section 2 describes opportunity challenge this problem gives an algorithm overview. The algorithm details experimental results are respectively given Sections 3 4. Fally, conclusions are presented Section Problem Algorithm Overview 2.1. Opportunity Challenge Currently, sensors mounted smartphones are abundant, ir performance is better. The sensors maly utilized door localization are accelerometers, gyroscopes, magnetometers, electronic compasses, barometers Wi-Fi, which provide acceleration, angular velocity, magnetic field, orientation, barometric pressure Wi-Fi RSS. Most sensors measurements can be uploaded by users via smartphone APPs that provide payment, navigation, map or shop formation services door environments, called crowdsourcg data. Based on se data, Wi-Fi radio map door environment can be constructed. The ma components for door radio map construction via crowdsourcg data are users trajectory trackg Wi-Fi fgerprt labelg to accurate locations. In followg content, we discuss opportunities challenges on resources techniques available our problem. It maly covers pedestrian dead reckong (PDR) fgerprt localization Pedestrian Dead Reckong PDR is a technique which estimates relative locations follow tracks a pedestrian via step detection, stride length estimation headg determation. It is widely used door localization systems with or without crowdsourcg, for its autonomy pedestrian localization. In a smartphone-based PDR system, accelerometer, gyroscope magnetometer embedded with smartphone are generally utilized to realize PDR algorithm. 3-axis acceleration can be used to detect walkg steps estimate stride length. Besides, 3-axis angular velocity magnetic field data are usually fused to determe headg pedestrians. There are some key challenges this technique, which are addressed as follows [8,30]: The unconstraed human motions smartphone postures make it complex to capture user s motion modes, detect steps estimate accurate walkg orientation. Long/short term drift accelerometer gyroscope, which perform worse due to low-cost IMU sensors embedded smartphones, as well as magnetic disturbances result accurate stride length estimation headg determation. As a result above-mentioned two issues, PDR localization output calculated by Equation (1) would not converge sce its lacks an efficacious reference source: { x t+1 = x t + L t+1 s φ t+1 y t+1 = y t + L t+1 cos φ t+1 (1) Consequently, it is hard to use PDR directly for users trajectory trackg by crowdsourcg data. However, it still can benefit for distance estimation approximately a limited area Fgerprt The Wi-Fi fgerprt on a location pot is a vector RSS from all scanned Wi-Fi APs at a same time. For different locations door areas, detected Wi-Fi RSS vectors are correspondgly different, due to diversity signal attenuation caused by different ranges, wall blocks multipath from each APs to smartphone. Meanwhile, Wi-Fi RSS vectors are

5 Sensors 2018, 2018, 18, 18, 1462 x FOR PEER REVIEW similar for adjacent locations. The location correlation Wi-Fi fgerprt makes it available similar door for positiong. adjacent locations. Similarly, The location Bluetooth correlation fgerprt Wi-Fi fgerprt magnetic makes field fgerprt it available can door also be positiong. used Similarly, door localization Bluetooth based fgerprt on same prciple magnetic as field Wi-Fi fgerprt fgerprts, can also be y used are all available door localization crowdsourcg, based on so we same will talk prciple about as m Wi-Fi toger fgerprts, compare y ir are all advantages available crowdsourcg, disadvantages. sofor we will reasons talk about that m Bluetooth toger fgerprt comparehas ir almost advantages same features disadvantages. as Wi-Fi For fgerprt reasons that y are Bluetooth all based fgerprt on wireless has almost electromagnetic same features signal as similar Wi-Fi fgerprt frequency as (2.4 y GHz), are all based Bluetooth on launchers wireless electromagnetic are always few signal most public similar door frequency environments (2.4 GHz), for ir Bluetooth lack launchers ternet are access always functions few compared most publicwith door Wi-Fi, environments so this for section ir lack we will ternet focus access on discussion functions compared Wi-Fi fgerprts with Wi-Fi, so magnetic this section fields, we will furrmore focus on discussion show Wi-Fi opportunities fgerprts challenges magnetic fields, usg m furrmore for door show localization. opportunities challenges usg m for door localization. (1) (1) Fgerprt Fgerprt Stability Stability Stability Stability comparisons comparisons between between Wi-Fi Wi-Fi magnetic magnetic fgerprts fgerprts have been have given been given some works. some Here works. we adopt Here we stability adopt dex stability proposed dex proposed [27] to judge [27] stability to judge between stability Wi-Fibetween RSS magnetic Wi-Fi RSS field tensity. magnetic Stability field tensity. dex is Stability mean-to-stard dex is mean-to-stard deviation ratio deviation tensity, ratio like Signal-to-Noise tensity, like Radio Signal-to-Noise (SNR). TheRadio Wi-Fi(SNR). RSS The a settled Wi-Fi AP RSS a settled magnitude AP magnetic magnitude field are magnetic detected field atare a same detected location a pot same location compared pot usg compared stabilityusg dex. We detect stability sixdex. location We pots detect six anlocation fice room pots corridor an fice (stayg room for 5corridor m on each (stayg pot), for 5 m calculate on each pot), stability dex calculate Wi-Fi stability magnetic dex field Wi-Fi signals. Figure magnetic 1 shows field signals. result. Figure It is seen 1 shows that magnetic result. It is field seen isthat obviously magnetic more stable field than is obviously Wi-Fi more RSS. stable than Wi-Fi RSS Magnetic field Wi-Fi RSS Value Magnitude magnetic field Wi-Fi RSS one AP Stability dex Time (sample count) Test locations Figure 1. Comparison stability between Wi-Fi magnetic field at a simple location: Time Figure 1. Comparison stability between Wi-Fi magnetic field at a simple location: Time sequences sequences for for magnitude magnitude magnetic magnetic field field Wi-Fi Wi-Fi RSS RSS one one AP AP measured measured on on location location 1 1 at at same same time; time; Stability Stability dex dex comparison comparison between between Wi-Fi Wi-Fi magnetic magnetic field field for for six six test test locations. locations. In addition, it is known that 2.4 GHz Wi-Fi signal is easily absorbed by human body, In addition, it is known that 2.4 GHz Wi-Fi signal is easily absorbed by human body, which leads to obvious changes RSS with or without ambient crowds. Figure 2 shows which leads to obvious changes RSS with or without ambient crowds. Figure 2 shows comparison comparison Wi-Fi RSS magnetic field when a pedestrian walks along a corridor two Wi-Fi RSS magnetic field when a pedestrian walks along a corridor two opposite directions. opposite directions. The magnetic field shows good consistence with corridor different The magnetic field shows good consistence with corridor different directions, but on contrary, directions, but on contrary, Wi-Fi RSS is changg. Wi-Fi RSS is changg. (2) (2) Location Differentiation Ability Ability The The measured magnetic field is is 3-axis magnetic tensity, tensity on each axisis is dependenton on pose pose smartphone, so so resultant tensity tensityis is usually usually used used to to dicate dicate magnetic magnetic fgerprt. Therefore, Therefore, for for a sgle a sgle location location pot pot magnetic magnetic fgerprt fgerprt is a isscalar, a scalar, but but Wi-Fi Wi-Fi fgerprt is isa arss vector whose dimensions will crease with number ambient APs. APs. As As shown shown Figure Figure 3a, 3a, magnetic magnetic tensity tensity is same is same some location some pots location pots one corridor one ( corridor resultant ( magnetic resultant field magnetic tensities field are tensities all µtare atall location μt pots at location 1, 2, 3pots 4), 1, but 2, 3 Wi-Fi 4), but RSS Wi-Fi RSS vectors (seven APs are detected corridor) ate se location pots are different, as shown Figure 3b.

6 Sensors 2018, 18, vectors (seven APs are detected corridor) ate se location pots are different, as shown Figure 3b. Sensors 2018, 18, x FOR PEER REVIEW 6 38 Sensors 2018, 18, x FOR PEER REVIEW 6 38 Resultant Resultant magnetic magnetic field tensity field tensity Resultant Resultant magnetic magnetic field tensity field tensity (ut) (ut) Forward direction 1 Opposite direction Forward direction Time (sample count) Time (sample count) Time (sample count) Time (sample count) Figure 2. Comparison stability between Wi-Fi magnetic field a corridor: Time Figure 2. Comparison stability between Wi-Fi magnetic field a corridor: Time sequences sequences for magnitude magnetic field generated a same corridor usg forward for Figure magnitude 2. Comparison magnetic stability field generated between Wi-Fi a same magnetic corridor usg field forward a corridor: opposite Time opposite directions; Time sequences for Wi-Fi RSS one AP generated same corridor directions; sequences for Time magnitude sequences for Wi-Fi magnetic RSS one field AP generated generated a same same corridor corridor usg usg forward forward usg forward opposite directions. The sequences generated opposite directions have been opposite opposite directions; directions. The Time sequences sequences generated for Wi-Fi opposite RSS one directions AP generated have been reversed same corridor se reversed se two figures. two usg figures. forward opposite directions. The sequences generated opposite directions have been reversed se two figures Opposite direction Forward direction Time (sample count) Time (sample count) AP ID Figure 3. Comparison ability location differentiation between magnetic field Wi-Fi RSS: Figure Sequence 3. Comparison resultant magnetic ability field location tensity differentiation a corridor, between at location magnetic pots field 1, 2, 3 Wi-Fi 4, where RSS: Figure 3. Comparison ability location differentiation between magnetic field Wi-Fi Sequence tensities are resultant same; magnetic Difference field RSS tensity vectors at a location corridor, pots at location 1, 2, 3 pots 4. 1, 2, 3 4, where RSS: Sequence resultant magnetic field tensity a corridor, at location pots 1, 2, 3 4, tensities are same; Difference RSS vectors at location pots 1, 2, 3 4. where tensities are same; Difference RSS vectors at location pots 1, 2, 3 4. On or h, magnetic fgerprt performs better differentiation among corridors (or roads On or door h, parkg) magnetic than Wi-Fi, fgerprt even when performs measured better differentiation opposite direction among (shown corridors (or Figure On roads 2). Figure or door h, 4 shows parkg) magnetic than comparison Wi-Fi, fgerprt even magnetism when performs measured sequences better differentiation measured opposite direction among same corridors (shown corridor (or Figure roads different 2). Figure door corridors. 4 parkg) shows It is than obvious comparison Wi-Fi, that even when magnetism measured sequences show measured opposite highly direction similar same shapes (shown corridor Figure same different 2). corridor Figure corridors. 4 shows low similarity It is comparison obvious different that magnetism magnetism corridors, sequences sequences so it is useful measured show for highly crowdsourcg similar same corridor shapes data to be different same divided corridor corridors. to different It low is corridors obvious similarity that or clustered magnetism different to corridors, sequences same one. so show it This useful highly is for similar prciple crowdsourcg shapes for our data proposed same to be corridor divided method. to Sce low different similarity similar corridors shape different or clustered magnetic corridors, to sequences so same it is useful one. same This for crowdsourcg corridor is prciple is based data for on to our be proposed divided location to method. correlation different Sce corridors similar magnetic or clustered shape field; to magnetic when same one. sequences magnetic This is field same prciple time corridor sequences for is our based proposed are on obtaed method. location by Sce correlation crowdsourcg similar shape users magnetic with magnetic different field; sequences walkg when speeds same magnetic corridor (most field is based time time, on sequences users location walkg are correlation obtaed speeds are by crowdsourcg different, magnetic field; hard users when to with estimate magnetic different accurately field walkg time usg speeds sequences crowdsourcg (most are obtaed data), time, by magnetism crowdsourcg users walkg sequences users speeds would with are different different, show an walkg uncerta hard speeds zoomg to estimate (most state accurately compared time, users usg with walkg crowdsourcg true speeds space scale data), are different, between magnetism two hard sequences sample to estimate pots. would accurately show In an summary, uncerta usg crowdsourcg zoomg Wi-Fi state fgerprt data), compared magnetism has with a better sequences true performance space would scale show between sgle an uncerta location two sample zoomg differentiation pots. state compared while In summary, with magnetic true field space Wi-Fi shows scale fgerprt between better has stability two a better sample performance pots. ability corridor sgle division location when differentiation used while sequence. magnetic Thus, a geomagnetism-aided field shows better stability method is ability designed corridor to construct division when door used Wi-Fi sequence. radio-map via Thus, smartphone a geomagnetism-aided crowdsourcg method this paper. is designed to construct door Wi-Fi radio-map via smartphone crowdsourcg this paper. RSS RSS RSS (dbm) RSS (dbm) Forward direction 1 Opposite direction Forward Forward direction direction 1 2 Opposite direction Forward direction 2 Location pot 1 Location pot 2 Location pot 13 Location pot 24 Location pot 3 Location pot AP ID

7 Sensors 2018, 18, In summary, Wi-Fi fgerprt has a better performance sgle location differentiation while magnetic field shows better stability ability corridor division when used sequence. Thus, a geomagnetism-aided method is designed to construct door Wi-Fi radio-map via smartphone crowdsourcg this paper. Sensors 2018, 18, x FOR PEER REVIEW 7 38 Smood resultant magnetic feild tensity (ut) 70 Trace 1 on corridor 1 65 Trace 2 on corridor Time (sample count) Smood resultant magnetic feild tensity (ut) 80 Trace on corridor 1 Trace on corridor 2 70 Trace on corridor 3 Trace on corridor Time (sample count) Figure 4. Comparison magnetism sequences measured same corridor different Figure 4. Comparison corridors: Smood magnetism magnetism sequences sequences measured generated same same corridor corridor; different Smood corridors: Smood magnetism sequences sequences generated generated different corridors. same corridor; Smood magnetism sequences generated different corridors Problem Settg 2.2. Problem Settg In this paper, we only concentrate on 2D door localization problem. The crowdsourcg data collected by smartphone users are utilized to construct a Wi-Fi radio map automatically. In thiscrowdsourcg paper, we only data concentrate mentioned here on generally 2D door clude localization acceleration, angular problem. velocity, Themagnetic crowdsourcg field, orientation Wi-Fi RSS provided respectively by accelerometer, gyroscope, data collected by smartphone users are utilized to construct a Wi-Fi radio map automatically. magnetometer, electronic compass Wi-Fi connector mounted on a user s smartphone. These Crowdsourcg data are data generated mentioned uploaded here generally by crowdsourcg clude acceleration, users when y angular are walkg velocity, around magnetic field, orientationdoor Wi-Fi environment, RSS provided meanwhile, respectively recorded by time accelerometer, identification stamp. gyroscope, Assumg magnetometer, that electronic compass se data are contuous Wi-Fi connector time for mounted each user, on we a user s call m smartphone. movg traces These users, data which are generated are denoted as T. Each movg trace T is recorded as: uploaded by crowdsourcg users when y are walkg around door environment, meanwhile, recorded by time identification T = { Ori, Acc, stamp. Gyro, Mag Assumg, F, t} that se data are contuous (2) time for each user, Ori is weuser s call m movg orientation movg valued traces users, [0,3 which ) are is denoted readg asfrom T. Each movg trace T is recorded electronic as: compass. However, due to magnetic field anomalies door environments unconstraed smartphone T poses = {Ori, crowdsourcg Acc, Gyro, users, Mag, it F, is t} essential to estimate user s (2) headg usg acceleration, angular velocity magnetic field by some better algorithm rar Ori is than user s usg readgs movgdirectly orientation from valued electronic compass. [0, 3The ) which headg isestimation readg method from raised electronic [30] is a kd solution for orientation problem. Acc is 3-axis acceleration, denoted as compass. However, due to magnetic field anomalies door environments unconstraed ( Accx, Accy, Acc z). Gyro is 3-axis angular velocity, denoted as ( Gyrox, Gyroy, Gyro z). Mag is smartphone poses crowdsourcg users, it is essential to estimate user s headg usg 3-axis magnetic field tensity, denoted as ( Magx, Mag y, Mag z). F is Wi-Fi fgerprt, clude acceleration, angular velocity magnetic field by some better algorithm rar than usg readgs AP Mac RSS, denoted as{ ( Macm, RSSm), m = 1,2,..., M}, here M is total number Wi-Fi directly from electronic compass. The headg estimation method raised [30] is a kd solution APs scanned by smartphone t is time identification. for orientation problem. Acc is 3-axis acceleration, denoted as (Acc Sce door localization generally happens corridors (or roads door x, Acc parkg) y, Acc z ). Gyro is which 3-axis angular lead velocity, to rooms (or denoted function sections) as (Gyro x, Gyro entries y, Gyro a floor z ).(like Mag stairs is 3-axis elevators); magnetic our method, field tensity, denoted as (Mag door x, Mag map y is, hled Mag z ). as Fa ispathway Wi-Fi graph fgerprt, dicated clude by topology. AP As shown Mac Figure RSS, 5, denoted as {(Mac a pathway graph door plan, edges represent all pathways that users can walk from m, RSS m ), m = 1, 2,..., M}, here M is total number Wi-Fi APs scanned by smartphone one place to anor; vertexes represent turng corners endgs pathways. t is time identification. The door graph is denoted as Map this paper, which is described as: Sce door localization generally happens corridors (or roads door parkg) which lead to Map = { V, E} (3) rooms (or function sections) entries a floor (like stairs elevators); our method, door map is hledv asis a pathway set coordates graph all dicated vertexes by topology. graph, denoted As shown as {( Coor mfigure ), m = 1, 2,..., 5, M } a. pathway graph In door this paper, plan, we use 2D edges coordates represent to describe all V pathways, so, vector that V users can can also walk be denoted fromas one place to anor; { ( xm, y m), mvertexes = 1,2,..., M} represent. Here M is turng total number corners vertexes. E endgs is a matrix pathways. to represent The door graph is denoted as Map this paper, which is described as: Map = {V, E} (3)

8 Sensors 2018, 18, V is a set coordates all vertexes graph, denoted as {(Coor m ), m = 1, 2,..., M}. In this paper, we use 2D coordates to describe V, so, vector V can also be denoted as Sensors 2018, 18, x FOR PEER REVIEW 8 38 {(x m, y m ), m = 1, 2,..., M}. Here M is total number vertexes. E is a matrix to represent length each edge between two vertexes, denoted as { (d p,q ), p = 1, 2,..., M, q = 1, 2,..., M } length each edge between two vertexes, denoted as {( d, here d p,q is pq, ), p = 1,2,..., M, q = 1,2,..., M}, here d pq, Euclidean distance between p-th q-th vertex. is Euclidean distance between p-th q-th vertex. Sensors 2018, 18, x FOR PEER REVIEW 8 38 = =, here d, length each edge between two vertexes, denoted as {( dpq, ), p 1, 2,..., M, q 1, 2,..., M} is Euclidean distance between p-th q-th vertex. pq Edge Vertex Figure 5. The door map is hled as a pathway graph this paper: a floor plan an Figure 5. The door map is hled as a pathway graph this paper: a floor plan an underground underground parkg, blue le is pathway; pathway graph left floor plan, parkg, edges represent blue leroads is pathway; vertexes pathway represent graph connections between left floorroads. plan, edges represent roads vertexes represent connections between roads. In order to construct an door pathway graph by crowdsourcg user s Edge movg traces our algorithm, user s trace will be broken down to some distct road segments Vertex In order to construct an door pathway graph by crowdsourcg user s movg like edges traces a our map. A road segment trace is a contuous trace with turng connection or pathway endg algorithm, Figure user s 5. trace The door willmap be broken is hled down as a pathway to some graph distct this paper: road segments a floor plan like an edges a only on its underground start or end parkg, pots. The blue road le is segment pathway; R is pathway denoted graph as: left floor plan, map. A road segment trace is a contuous trace with turng connection or pathway endg only edges represent roads vertexes represent connections between roads. on its start or end pots. The road segment R = { Rori, ROri is, denoted Acc, Gyroas:, Mag, F, t} (4) In order to construct an door pathway graph by crowdsourcg user s movg traces our Rori is mean value Ori road segment trace, it is a scalar identifyg algorithm, user s trace R will = be {Rori, broken Ori, down Acc, to Gyro, some distct Mag, road F, t} segments like edges a (4) displacement map. A road orientation segment trace is road a contuous segment, trace valued with [0 turng, 3 connection ). And or or pathway elements endg R are Rori defed is only as on same its mean start as or value end T. The pots. connection Ori The road segment between road segment R two is denoted road trace, segments as: it is is denoted a scalar as identifyg I, which is displacement recorded as: orientation roadr = segment, { Rori, Ori, valued Acc, Gyro, Mag [0,, F3, t} ). And or elements (4) R are defed as same Rori as T. is The mean connection value between Ori I = { two Rroad i, Rroad j, Typesegments, Angle trace, } is denoted it is a scalar as I, identifyg which is recorded (5) as: displacement orientation road segment, It represents connection between I = { valued [0,3 Rroad segment R i R. Type is connection type i, R j, Type, Angle } ). And or elements R are j (5) defed as same as T. The connection between two road segments is denoted as I, which is cludg four kds as shown Figure 6, which is defed as: recorded as: It represents connection between road segment R 1, start connect i R to j. Type is connection type cludg I = { R j start i, R j, Type, Angle} (5) four kds as shown Figure 6, which is defed as: 2, Ri start connect to Rj end It represents connection Type between = road segment R i R. Type is connection type j (6) 1, 3, R Ri end to Rj start cludg four kds as shown Figure 6, which i start is connect defed as: to R j start 2, 4, R Ri end to j end Type = 1, i Rstart to R j end i connect to Rj start (6) 3, 2, R i Rend to R j start i start connect to Rj end I R 2 Type = 4, R 2 3, R i end I (6) Ri connect to to RjRstart j end 4, Ri end connect to Rj end R 1 I R 2 R 2 R 1 I R 1 R 1 R 1 R 1 Figure 6. Four kds connection type defed this paper. R represents a road segment, I represents a connection. I I R 2 R 2 R 1 R 1 Figure 6. Four kds connection type defed this paper. R represents a road segment, I Figure 6. Four kds connection type defed this paper. R represents a road segment, I represents a connection. represents a connection. R 2 R 2 I I

9 Sensors 2018, 18, x FOR PEER REVIEW 9 38 Sensors 2018, 18, Angle is rotation angle between two road segments R i R connection I, j defed Angle as is angle rotation rotated angle from between vector two R road segments R i R j connection I, defed as i to vector R. The value Angle is ( 180,180 ), j negative angle for rotated clockwise from vector rotation R i to vector positive R j. for The anticlockwise value Angle rotation. is ( 180 Figure, 7180 shows ), negative an example for clockwise connection rotation between positive road segments. for anticlockwise It s obvious rotation. that re Figure are 7four shows road ansegments example ( R connection 1, R 2, R3 between road segments. It s obvious that re are four road segments (R 1, R 2, R 3 R 4 ) three R 4 ) three connections ( I 1, I2 I 3 ) this movg trace. The connections will be connections (I 1, I 2 I 3 ) this movg trace. The connections will be denoted respectively as denoted respectively I 1 = {R 1, R 2, 3, 90 as I1 = { R1, R2,3, 90 }, I 2 = {R 2, R 3, 3, 90 }, I2 = { R2, R3,3,90 } } I 3 {R 3, R 4, 3, 90 I3 = { R3, R4,3, 90 }. }. R 1 I 1 R 2 I 3 I 2 R 3 R 4 Figure Figure Example Example connections connections between between road segments. road segments. The redthe le is red a user le trace is a user an underground trace an parkg. underground R parkg. I are respectively R I are roadrespectively segments connections road segments this trace. connections this trace. Fally, Fally, it it is expected is expected that that through through proposed proposed method method topology topology door map door (pathway map graph) (pathway is acquired graph) is by acquired crowdsourcg by crowdsourcg user traces, user traces, Wi-Fi fgerprts Wi-Fi fgerprts are labeled are on labeled map. on The constructed map. The constructed Wi-Fi fgerprt Wi-Fi fgerprt database is database represented is represented as: as: ( x1, y1), F1 (x ( x2, y 1, y 2), 1 ), F F 1 2 FD (x FD = 2, y 2 ), F ( xn, yn), F (x N N, y N ), F N F RSS RSS RSS AP1 AP2 APM n = ( n, n,..., n ) F n = (RSS AP 1 n, RSS AP 2,..., RSS AP M (7) (7) where N is total number RPs. M is number available Wi-Fi APs area. where N is total number RPs. M is number available Wi-Fi APs area Algorithm Overview 2.3. Algorithm Overview Through discussion on opportunities challenges smartphone-based door localization, Through a method discussion ongeomagnetism-aided opportunities door challenges radio-map smartphone-based construction door via smartphone localization, acrowdsourcg method geomagnetism-aided proposed this door paper. radio-map In this construction method, viaacceleration, smartphone crowdsourcg angular velocity, is proposed orientation, this Wi-Fi paper. RSS In thismagnetic method, field acceleration, from crowdsourcg angular velocity, data orientation, are utilized Wi-Fi to realize RSS magnetic algorithm. field The from architecture crowdsourcg our data method are utilized is shown to realize Figure 8, algorithm. which cludes The architecture five parts: trace our method segmentation, is shown geomagnetism-based Figure 8, which cludes similarity five parts: calculation, trace segmentation, road segment geomagnetism-based clusterg, similarity topology calculation, construction road segment fal radio clusterg, map construction. topology construction fal radio map construction. First all, turng detection usg angular velocity is implemented for users traces, long long traces traces will will be segmented be segmented to some to short some ones short which ones are which generated are generated distct corridors distct (or corridors roads), (or called roads), called segment road traces. segment traces. n n )

10 Sensors 2018, 18, x 1462 FOR PEER REVIEW Sce re are usually more than one user trace generated a corridor (road) crowdsourcg Sce redata, are usually we design morea than clusterg one user method trace generated here to make a corridor se road (road) segment crowdsourcg traces from different data, we users designmatch a clusterg toger method cluster here tom make to se some road distct segment corridors. traces from In order different to realize users clusterg, match toger a kd cluster matchg mmethod to some for distct road segment corridors. traces In order is designed to realizeby clusterg, calculatg a kd similarity matchg magnetism method for sequences road segment se, tracesbased is designed on by stable calculatg shape similarity magnetic field magnetism one corridor sequences (road). se, As based discussed on stable Section shape 2.1, to deal magnetic with field uncerta one corridor zoomg (road). As magnetism discussed sequences Section for 2.1, different to deal with user traces, uncerta magnetism zoomg features magnetism are extracted sequences firstly, for different n user based traces, on m magnetism one sequence features is zoomed are extracted to a same firstly, distance nscale basedas on anor m one one sequence consequently, is zoomed to a similarity same distance two scale road assegment anortraces one is calculated consequently, exactly. similarity two road segment traces is calculated exactly. Crowdsourcg user traces User 1 User 2 User 3 Crowdsourcg Data Acceleration Oritiention Wi-Fi RSS Angular Velocity Magnetic Field Road segment traces Turng Detection Road Segment Trace Generation Trace Segmentaion Road segment clusters Cluster1 Cluster2 Cluster3 Cluster5 Cluster4 Magnetism Feature Extraction Magnetism Sequence Zoomg Similarity Calculation Geomagnetism Based Similarity Calculation Preprocessg Before Clusterg Road Trace Clusterg Road Segment Clusterg Pathway map Road Length Estimatg Connection Estimatg Topology Construction Topology Modification Wi-Fi reference pots RP Generation RSS Mergg on RP Radio Map Construction Figure 8. Overview geomagnetism-aided door Wi-Fi radio map construction method via smartphone crowdsourcg. Supported by magnetism similarity, road segment traces are clustered to some collections with highly magnetic similarity. The clusterg algorithmis is designed based on Density-Based Spatial Clusterg Application with Noise (DBSCAN) algorithm, usg a kd magnetism similarity neighborhood. In In addition, a a preprocessg step step is implemented is implemented before before clusterg clusterg to make to make magnetism magnetism sequences sequences be generated be generated based based on on same orientation. same orientation. Furrmore, length road segments connections between between m m are are estimated, estimated, n n topology topology map ismap constructed. is constructed. To dealto with deal with topology topology mistakes caused mistakes bycaused accurate by accurate connection connection angles angles road lengths, road lengths, topology modification topology modification is carried outis tocarried get a fal out pathway to get a fal graph. pathway Fally, graph. crowdsourcg Fally, crowdsourcg Wi-Fi RSSs are carefully Wi-Fi RSSs labeled are carefully by location labeled coordates, by location coordates, merged toger merged on generated toger on Wi-Fi RPs generated along Wi-Fi constructed RPs along pathway constructed graph. pathway Thus, graph. fal Wi-Fi Thus, radio fal map Wi-Fi (fgerprt radio map database) (fgerprt is constructed database) onis constructed floor. on floor. 3. Algorithm Details

11 Sensors 2018, 18, Algorithm Details Sensors 2018, 18, x FOR PEER REVIEW Trace Segmentation In this paper, only only 2D 2D door door localization problem problem is is considered. considered. Considerg Considerg features features pathway pathway graph, graph, we segment we segment a user s trace a user s through trace turn through detection. turn Thedetection. variation The orientations variation can orientations obviously show can obviously turng behavior show turng user, but behavior considerg user, headg but errors considerg caused by magnetic headg errors field anomalies caused by magnetic door environments field anomalies unconstraed door environments smartphone poses, unconstraed readgsmartphone changes poses, gyroscope readg are used changes to detect user s gyroscope turng stead. are used Figure to detect 9 shows user s a user s turng walkg stead. tracefigure 9 vertical shows a component user s walkg angular trace velocity. vertical When component pedestrian walks straight, angular velocity. values When angular velocity pedestrian oscillate walks up straight, down values around zero. angular On velocity contrary, oscillate when up pedestrian down around turnszero. left or On right, contrary, absolute when value pedestrian angular velocities turns left will or right, rise to a peak absolute n value decle angular to normal, velocities correspondg will rise to with a peak turnn start decle fish. to normal, The change correspondg would bewith obvious turn for quickly start turng fish. The gentle change for would a slow be turn. obvious Moreover, for it quickly shows turng that angular gentle velocities for a will slow goturn. negative Moreover, for clockwise it shows turng that positive angular velocities for anticlockwise will go negative turng. for clockwise turng positive for anticlockwise turng Angular velocity (Z-axis) (rad/s) Time (sample count) Figure Figure User s User s walkg walkg trace trace angular angular velocities velocities measured measured by by a smartphone a smartphone gyroscope: gyroscope: walkg walkg trace trace an an underground underground parkg parkg with with three turns; three turns; angular velocities angular (vertical velocities component) (vertical component) smartphone measured smartphone with measured walkg with trace. walkg trace. As discussed above, this paper, we use angular velocity readgs from gyroscope to As discussed above, this paper, we use angular velocity readgs from gyroscope to detect turns, calculate turng angles fally segment user s traces. Before turn detection, detect turns, calculate turng angles fally segment user s traces. Before turn detection, vertical component angular velocity is calculated by gravitational acceleration coordate vertical component angular velocity is calculated by gravitational acceleration coordate transformation. For dealg with measurement noise, angular velocity will be smood transformation. For dealg with measurement noise, angular velocity will be smood usg a usg a movg average filter before turn detection. Three rules are made as follows to realize movg average filter before turn detection. Three rules are made as follows to realize turng detection turng detection turng angle estimation: turng angle estimation: The peaks angular velocities are detected when followg conditions are satisfied. Here The peaks Turn is a positive angular constant. velocities The position are detected each when peak is recorded followg usg conditions sample are count satisfied. n: Here Th Turn is a positive constant. The position each peak is recorded usg sample count n: Gyro( n) > ThTurn, Gyro( n) > Gyro( n 1), Gyro( n) > Gyro( n + 1) n, P = or Gyro( n) < - ThTurn, Gyro( n) < Gyro( n 1), Gyro( n) < Gyro( n + 1) (8) null Gyro(n), else > Th n, Turn, Gyro(n) > Gyro(n 1), Gyro(n) > Gyro(n + 1) P = or Gyro(n) < Th Turn, Gyro(n) < Gyro(n 1), Gyro(n) < Gyro(n + 1) (8) The start null, turn nelse 1 is settled as first pot ascendg from zero to peak, end turn n2 is settled as last declg pot from peak to zero. The start user trace turn nis 1 issegmented settled as by first detected pot ascendg peaks to from some zero road to segments, peak, denoted end as turn { R}, ni 2 = is 1, 2,..., settled num( asp ) + 1last. num( declg P ) is pot number from peak peaks to zero. detected. The orientation each i road segment Rori is mean value data Ori this road; rotation angle turng Angle is tegration from Gyro( n 1) to Gyro( n 2 ), shown followg equations:

12 Sensors 2018, 18, The user trace is segmented by detected peaks to some road segments, denoted as {R i }, i = 1, 2,..., num(p) + 1. num(p) is number peaks detected. The orientation each road segment Rori is mean value data Ori this road; rotation angle turng Angle is tegration from Gyro(n 1 ) to Gyro(n 2 ), shown followg equations: Sensors 2018, 18, x FOR PEER REVIEW Rori Rori Ri = Ri P(i) = Ori( n) (9) Ori(n) (9) n=p(i 1) n2 2 Angle = Angle = Gyro Gyro dn (10) n1 dn (10) n 1 Figure 10 shows turn detection result when settg Th Turn =. There are three turns Figure detected 10 shows this trace turn T. Then, detection we segment result when user settg trace ThT Turn to = four road. There segment are three traces turns R 1, R 2, detected R this trace T. Then, we segment user trace T to four road segment traces R 1, 3 R 4, three connections, which are denoted respectively by I 1 = { R 1, R 2,3, R 2, R 3 R 4, three connections, which are denoted respectively by I 1 = {R 1, R 2, 3, }, }, I2 = { R2, R3,3,95.5 I 2 = {R 2, R 3, 3, 95.5 } I3 = { R3, R4,3, 80.4 } I 3 = {R 3, R 4, 3, 80.4 }. To deal with smartphone pose changes (false }. To deal with smartphone pose changes (false detection) detection) gentle gentle turns (undetected) turns (undetected) user, user, turn detection turn result detection would result be checked would be aga checked aga by user headgs. If fset by user headgs. If fset Rori between two Rori between two separate road segment traces are separate road segment traces are close to detected close turng to angle, detected it is turng proved that angle, re it is is proved a real turn. that If re orientation is a real turn. change If happens orientation side change one road happens segment side trace, one road trug segment detection trace, algorithm trug will detection be re-implement algorithm usg will an be angular re-implement velocity usg an angular velocity with a lower with a lower Th Turn. Of course, erroneous Th road Turn. Of course, erroneous road segments can also be segments can also be elimated by failg magnetic field matchg elimated by failg followg magnetic process. field matchg followg process. Pi () n= Pi ( 1) n 100 R 1 I 1 R 2 I 3 Angular velocity (Z-axis) (rad/s) - 0 I 2 R 3 R Time (sample count) Figure 10. Turn detection results usg angular velocity: vertical component angular Figure 10. Turn detection results usg angular velocity: vertical component angular velocities velocities (smood) test trace detected start pot, peak end pot each turn; (smood) test trace detected start pot, peak end pot each turn; four four segmented road traces three connections between m. segmented road traces three connections between m Geomagnetism-Based Similarity Calculation 3.2. Geomagnetism-Based Similarity Calculation As discussed Section 2.1, geomagnetism sequence road segment obtaed As discussed Section 2.1, geomagnetism sequence road segment obtaed above process will be utilized to calculate similarity between two road segment traces our above process will be utilized to calculate similarity between two road segment traces our proposed method. To deal with different scales sequences, [6] used a Dynamic Time Warpg proposed method. To deal with different scales sequences, [6] used a Dynamic Time Warpg (DTW) algorithm for sequence similarity computation, but DTW algorithms need a large amount (DTW) algorithm for sequence similarity computation, but DTW algorithms need a large amount calculation, so this section, we propose a novel method for similarity calculation usg calculation, so this section, we propose a novel method for similarity calculation usg geomagnetism geomagnetism features. The details geomagnetism-based similarity calculation will be described features. The details geomagnetism-based similarity calculation will be described below, consistg below, consistg magnetism feature extraction, sequence zoomg based on matched feature magnetism feature extraction, sequence zoomg based on matched feature pots, fal pots, fal similarity calculation. similarity calculation Feature Extraction The geomagnetism measurements from a smartphone are 3-axis magnetism tensities (one readg for each axis). Considerg uncerta pose smartphones, which causes measurg coordate system changes, before we extract magnetism features from a data sequence, vector module magnetic field is calculated firstly as resultant magnetism tensity. The resultant

13 Sensors 2018, 18, Feature Extraction The geomagnetism measurements from a smartphone are 3-axis magnetism tensities (one readg for each axis). Considerg uncerta pose smartphones, which causes measurg coordate system changes, before we extract magnetism features from a data sequence, vector module Sensors 2018, 18, x magnetic FOR PEER field REVIEW is calculated firstly as resultant magnetism tensity. The resultant magnetism tensity is acquired by followg equation, only related to position magnetism smartphone: tensity is acquired by followg equation, only related to position smartphone: Mag = Mag 2 x + Magy 2 + Magz 2 (11) We defe peaks troughs from Mag = sequence Magx + Mag resultant y + Magmagnetism z tensities Mag which (11) satisfy settled constrats as magnetism features user trace. To remove noise magnetism We defe sequence peaks extract troughs its from ma shape, sequence we smooth resultant magnetism magnetism vector tensities usg Mag a movg which average satisfy filter settled before constrats feature extraction. as magnetism The magnetism features features are user identified trace. by To remove followg criteria: noise magnetism sequence extract its ma shape, we smooth magnetism vector usg a movg average All filter peaks before troughs feature extraction. are detectedthe frommagnetism sequence Mag features by are followg identified equation, by followg MP criteria: MT are respectively peak cidates trough cidates: All peaks { troughs are detected from sequence Mag by followg equation, MP MP = n, Mag(n) > Mag(n 1) Mag(n) > Mag(n + 1) MT are respectively peak cidates trough cidates: (12) MT = n, Mag(n) < Mag(n 1) Mag(n) < Mag(n + 1) MP = n, Mag( n) > Mag( n 1) Mag( n) > Mag( n + 1) (12) The cidates (both peaks MT = n, Mag troughs ( n) < toger), Mag( n 1) whose Magmagnetism ( n) < Mag( ntensity + 1) difference with one The cidates two terfacg (both peaks cidates troughs is below toger), defed whose threshold magnetism thmagdi tensity f f difference, are removed with from one cidates. two terfacg cidates is below defed threshold thmagdiff, are removed Peaks troughs that satisfy above constrat are fal magnetism features which are from cidates. marked by P T, respectively. At same time, peaks troughs would be ensured to Peaks troughs that satisfy above constrat are fal magnetism features which are appear alternately. marked by P T, respectively. At same time, peaks troughs would be ensured to appear alternately Smood magnetism sequence Peaks Troughs Resultant magnetism tensity (ut) Time (sample count) Resultant magnetism tensity (ut) A E C B D Time (sample count) Figure Figure Example Example for for magnetism magnetism feature feature extraction: extraction: sequence sequence resultant resultant magnetism magnetism tensity tensity generated generated with with a a user user trace; trace; feature feature extraction extraction result. result. Figure 11 shows an example a magnetism feature extraction result. Pots A, C E Figure 11 shows an example a magnetism feature extraction result. Pots A, C E marked marked figure are detected peaks, B D are detected troughs. When we set figure are detected peaks, B D are detected troughs. When we set thmagdi f f as thmagdiff as 1 μt, difference between B A exceeds thmagdiff, but difference between 1 µt, difference between B A exceeds thmagdi f f, but difference between B C doesn t B C doesn t exceed thmagdiff, so trough pot B is not a feature pot we need. On exceed thmagdi f f, so trough pot B is not a feature pot we need. On contrary, peak D is a feature contrary, pot, peak as D is difference a feature pot, between as D difference A as well between as D D E both A as exceed well as D thmagdi E both f f. Consequently, exceed thmagdiff as shown. Consequently, Figure 11, as trough shown B Figure peak 11, C would trough be B removed peak sce C y would don t be removed sce y don t satisfy constrat, but trough D peaks A E are extracted magnetism features, so though abovementioned method, all peaks troughs are extracted as magnetism features that can describe fluctuation resultant magnetism tensity user s trace.

14 Sensors 2018, 18, satisfy constrat, but trough D peaks A E are extracted magnetism features, so though abovementioned method, all peaks troughs are extracted as magnetism features that can describe fluctuation resultant magnetism tensity user s trace Sequence Zoomg In this part, we propose a method to zoom distance scale one magnetism sequence to anor through magnetism features order to match m toger. It cludes four key steps: Step 1: First all, we estimate movement distance from start pot user trace to each magnetic field samplg time usg an empirical stride length. Then two pairs magnetism features from two sequences are selected romly as itial assumed matchg feature pots, if ratio two estimated distances between features each sequence is with a reasonable range pedestrian stride length. Step 2: Secondly, usg distance ratio calculated by itial matchg feature pairs, remag part second sequence is zoomed to same stride length as first one. Step 3: Thirdly, to deal with common case uneven walkg speed one trace, rest feature pots from two sequences are matched toger based on itial matched features. Step 4: Fally, number matched feature pots is counted, if proportion matched features is greater than settled threshold, one time Sequence Zoomg is fished. The details above steps will be respectively depicted followg paragraphs. (1) Initial Feature Matchg We use detected steps stride length to estimate trace length. The acceleration is utilized for step detection. The algorithm for step detection is same as Feature Extraction algorithm presented The detected peaks resultant acceleration which satisfy settled constrat are user steps, amount steps is marked as N step. Or algorithms can also be used to realize step detection, like one described [31]. Stride length L step is set as an empirical value like 0.6 m, so length user trace is estimated by: L = N step L step (13) The trace length L do not need to be exact, as it is only used to provide a rough distance between each magnetism feature, similarity queues magnetism features is ma criterion to estimate wher two traces are generated on same road segment. The procedures features alignment similarity calculation will be proposed followg context. When we get length trace, distances from start pot trace to each magnetism samplg time, denoted as Dis = {Dis 1, Dis 2, Dis 3,..., Dis M }, can be estimated by: Dis i = L i, i = 1, 2, 3,..., M (14) M Here i is i-th count magnetic field readgs, M is total number field data on a road segment trace. We use a lear model here to estimate distance each time, for it is hard to get exact walkg speed users, lear movg model will simplify procedures to acquire a rough distance sequence. In case uneven walkg speed one trace, magnetism features alignment will be implemented Step 3. Considerg two road segment data different users, denoted by R1 R2. The magnetism sequences m are Mag 1 Mag 2, denoted as Mag 1 = { Mag1 1, Mag1 2, Mag M} Mag1 Mag 2 = { Mag 2 1, Mag2 2, Mag } Mag2 N. The data length each sequences are respectively M N. Though above mentioned method, distance sequences correspondg to Mag 1 Mag 2 are obtaed, denoted as Dis 1 = { Dis 1 1, Dis1 2, Dis1 3,..., M} Dis1 Dis 2 = { Dis 2 1, Dis2 2, Dis2 3,..., N} Dis2.

15 Sensors 2018, 18, Then magnetism features are extracted from Mag 1 Mag 2, recorded by P 1, T 1, P 2 T 2 : } P 1 = {P1 1, P1 2, P1 3,..., P1 MP } T 1 = {T1 1, T1 2, T1 3,..., T1 MT } P 2 = {P1 2, P2 2, P2 3,..., (15) P2 NP } T 2 = {T1 2, T2 2, T2 3,..., T2 NT M P M T are respectively total numbers peaks troughs Mag 1. Similarly, N P N T are respectively total numbers peaks troughs Mag 2. At begng Sequence Zoomg, we pick up two couples magnetism features respectively from Mag 1 Mag 2 romly. They are recorded by FP1 1, FP1 2 (a feature pot pair from Mag 1 ) FP1 2, FP2 2 (a feature pot pair from Mag2 ). The followg constrat should be satisfied selection feature pot pairs: (FP 1 1, FP1 2 ) = (P1 a, P 1 b ) or (T1 a, T 1 b ) or (P1 a, T 1 b ) or (T1 a, P 1 b ), a < b (FP 2 1, FP2 2 ) = (P2 c, P 2 d ) or (T2 c, T 2 d ) or (P2 c, T 2 d ) or (T2 c, P 2 d ), c < d (16) The above equation means that feature pot pairs from Mag 1 Mag 2 should have same pattern same order ir queues. For example, when we choose (Pa 1, Tb 1 ) as feature pot couple Mag 1, we should use (Pc 2, Td 2) Mag2 to match with m. The subscripts a, b, c d should meet conditions a < b c < d. If FP1 1 FP2 1 are generated at a same location pot A, at same time, FP1 2 FP2 2 are at a same location pot B, trace distances between FP1 1 FP1 2, as well as FP2 1 FP2 2 would be equal, assumg that walkg paths on road segment are unique for users, so we can obta followg equality: Nstep L 1 1 step = Nstep L 2 2 step = L AB (17) which, Nstep 1 N2 step are respectively number detected steps from location A to B on road segment traces R1 R2. L 1 step L2 step are real stride length users on R1 R2. L AB is actual trace length between location A B. Stride length L step is empirical value that we use to estimate distances from start pot to each magnetic field samplg pot, so it can also be obtaed that: Nstep L 1 step = Dis 1 (FP2 1) Dis1 (FP1 1) (18) Then stride length ratio is reckoned as: ratio L = L2 step L 1 step N 2 step L step = Dis 2 (FP 2 2 ) Dis2 (FP 2 1 ) (19) = N1 step N 2 step = N1 step L step N 2 step L step = Dis1 (FP 1 2 ) Dis1 (FP 1 1 ) Dis 2 (FP 2 2 ) Dis2 (FP 2 1 ) (20) The normal range pedestrian stride lengths is about 0.4 m to 0.8 m, so stride length ratio ratio L should be on range [0.5, 2]. When calculated ratio L is this range, feature pots (FP1 1,FP2 1 ) (FP1 2,FP2 2 ) can be assumed as itial matched feature pots R1 R2. On contrary, if ratio L is out this range, this procedure will be implemented aga for anor pair feature pots, until itial matched pots are found.

16 Sensors 2018, 18, (2) Rough Zoomg Based on itial matched feature pots (FP1 1,FP2 1 ), data on Dis2 will be zoomed usg ratio L, Dis 2 (FP1 2) will be translated to Dis1 (FP1 1 ). The new distance sequence is calculated by followg equation: Dis 2 Z(n) = (Dis 2 (n) Dis 2 (FP 2 1 )) ratio L + Dis 1 (FP 1 1 ) (21) here n = 1, 2, 3,..., N. Then we get a new distance sequence Dis 2 Z for R2. Dis 2 Z may have some negative data, for its start pot would not be same as for R1. After rough zoomg above procedure, magnetism feature pots on R2 are basically matched toger with those on R1 if itial matchg pots (FP1 1,FP2 1 ) are correct. Because rough zoomg is an even zoomg only based on scalar ratio L, if users walkg speeds are uneven, which is a very common situation, feature pots will not match well only by rough zoomg. The followg step is designed to deal with this issue. (3) Features Alignment In this step, feature pots R2 are aligned based on current itial matched feature pots ((FP1 1,FP2 1 ) (FP1 2,FP2 2 )) matched with or feature pots R1 usg prciple proximity. Therefore, when itial matched feature pots are really sampled on same location pot, Features Alignment would make or feature pots on R2 R1 match exactly, so that magnetism similarity R1 R2 can be calculated accurately. When itial assumed matchg feature pots are not matched correctly, this procedure will also be carried out fal matchg result will be judged by result Similarity Calculation followg step. We denote assemblage aligned feature pots as AF. Based on itial matched feature pots, itial assemblage AF is shown followg: AF = {AF 1, AF 2 }, AF 1 = (FP 1 1, FP2 1 ), AF 2 = (FP 1 2, FP2 2 ) (22) For peak Pi 2, cidate matchg area R1 is settled at first, which is dicated by (IndexL, IndexR). The edge matchg area is feature pots R1 AF, whose matched feature pots R2 are closest ones respectively to left right side Pi 2. This can be expressed as: IndexL = FP 1 (arg m{pi 2 FPk 2}), FP2 k < P2 i k IndexR = FP 1 (arg m{fpk 2 P2 i }), FP2 k > P2 i k When Pi 2 only has one side neighbor with aligned feature pots, n matchg area will be settled as (1, IndexR) or (IndexL, M). M is data length Mag 1. Then all peaks R1 range (IndexL, IndexR) are traversed to fd matchg pot Pi 2. The matchg pot match(p2 i ) would satisfy two requirements, cludg: The difference between Dis 2 Z(Pi 2) Dis1 (Pk 1 ) is mimum compared with or cidate peaks. For Dis 2 Z have been accorded with Dis 1, difference between m dicates probable location distance between Pi 2 Pk 1, closest pair may have biggest probability to be sampled on a same location. In case some feature pots are undetected, R1 R2 have different trace lengths, we set a distance threshold thalign to restrict difference distance between matchg pots. The thalign this paper is settled as an empirical value. (23)

17 Sensors 2018, 18, The matchg qualification is expressed by followg equation: k = arg m{ Dis 2 Z(Pi 2) Dis1 (Pk 1) } match(pi 2) = P1 k, k Dis 2 Z(Pi 2) Dis1 (Pk 1) < thalign (24) Pk 1 [IndexL, IndexR] The matched peak couples would be added to AF as a new element AF j = (FP 1 j, FP2 j ) = (P1 k, P2 i ), furr used for matchg area choosg new Pi 2 prepared for alignment. For troughs Ti 2, same method is implemented to fd matchg troughs T1 k R1. At same time, matched trough couples will also be added to AF as a new element, recorded by AF j = (FPj 1, FP2 j ) = (T1 k, T2 i ). For matched feature couples should be apparent same order both R1 R2, peaks troughs should appear alternately, element AF (all matched peaks troughs) will be resolved by data order feature pots Mag 1 (or feature pots Mag 2 ). Fally, we obtaed all matched feature couples AF: AF = { } AF j, AFj = (FPj 1, FP2 j ), j = 1, 2,..., J (25) J is total number matched feature couples between R1 R2. Then, based on matched feature pairs AF, Dis 2 Z would be updated usg followg equation: Dis 2 A(n) = (Dis 2 Z(n) Dis 2 Z(FPj 2)) Dis 1 (FPj+1 1 ) Dis1 (FPj 1) Dis 2 Z(FPj+1 2 ) Dis2 Z(FPj 2) + Dis1 (FPj 1), n [FP2 j, FP2 j+1 ], j [1, J 1] Dis 2 Z(n) Dis 2 Z(FP1 2) + Dis1 (FP1 1), n [1, FP2 1 ) (26) Dis 2 Z(n) Dis 2 Z(FPJ 2) + Dis1 (FPJ 1), n (FP2 J, N] It means that all matched feature pots FP 2 j R2 will be aligned to same distance FP 1 j R1 distance or sample pots will be zoomed usg local ratio, estimated by closest two feature pot couples. In start or end part R2, only translation is implemented to Dis 2 Z(n), sce zoomg ratio cannot be estimated only by one pair matched feature pot. Fally, we get updated distance sequence Dis 2 A for R2. (4) Matched Features Amount Judgment In this step we count amount matched feature couples AF, calculate matchg proportion P FP usg followg equation: P FP = J m(m P + M T, N P + N T ) (27) M P M T are respectively total numbers peaks troughs Mag 1. N P N T are respectively total numbers peaks troughs Mag 2. J is total number matched feature pairs between Mag 1 Mag 2. When P FP is greater than settled threshold thfp, one time Sequence Zoomg is fished Similarity Calculation Through method Sequence Zoomg provided above section, distance scales Mag 1 Mag 2 are basically uniform. If feature pots are matched correctly, similarity between Mag 1 Mag 2 can be calculated accurately. In this paper, correlation coefficient two magnetism sequences is identified as similarity two road segment traces R1 R2. Before correlation coefficient calculation, data length Mag 1 Mag 2 would be made to be equal usg origal magnetism data zoomed distance data, based on lear terpolation.

18 Sensors 2018, 18, The equation to calculate new magnetism sequence Mag 2 new, which has same data length with Mag 1, is shown followg: Mag 2 (n + 1) Dis2 A(n+1) Dis 1 (m) Mag 2 Dis 2 A(n+1) Dis 2 A(n) (Mag2 (n + 1) Mag 2 (n)), new(m) = Null Dis 1 (m) [Dis 2 A(n), Dis 2 A(n + 1)], n [1, N 1] Dis 1 (m) < Dis 2 A(1), or Dis 1 (m) > Dis 2 A(N) (28) Symbol Null equation means that it is a null element sequence Mag 2 new, re isn t a valid mamatical result this element. Then we fd dex valid element Mag 2 new, calculate correlation coefficient between Mag 1 Mag 2 new. The dexes start end pot valid element are respectively denoted as m start m end. cc is correlation coefficient between Mag 1 Mag 2 new. They are obtaed by: m start = m(m Mag 2 new (m) = Null) m end = max(m Mag 2 (29) new(m) = Null) cc = mend m end m=m start (Mag 1 (m) Mag 1 )(Mag 2 new(m) Mag 2 new) m end (Mag 1 (m) Mag 1 ) 2 (Mag 2 new(m) Mag 2 new) 2 m=m start m=m start (30) For each time Sequence Zoomg, correlation coefficient cc would be calculated, until all probable itial matched features R1 R2 are tested. Afterwards, maximum all calculated cc between R1 R2 is selected as road segment similarity between R1 R2, denoted as RS(R1, R2). Correspondgly, fal zoomg ratio R2 based on R1 (denoted as Ratio(R 2, R 1 )) is calculated given by: Ratio(R 2, R 1 ) = Dis2 A(N) Dis 2 A(1) Dis 2 (N) (31) The matchg position between R1 R2 is settled as [(m start, n start ), (m end, n end )]. m start m end is obtaed by Equation (29). n start n end are ascertaed by: n start = (n Dis 2 A(n) = Dis 1 (m start )) n end = (n Dis 2 A (n) = Dis 1 (m end )) (32) Similarity Calculation Result In this section, we show magnetism matchg similarity calculation results for some typical situations, cludg two traces generated on same road segment on different road segments. These results are shown Figures Figure 12 shows magnetism matchg similarity calculation result for two traces generated on a same road segment. Figure 12a shows smood magnetism sequences from road segment trace 1 road segment trace 2, which distances from start pot to each magnetic field samplg pot are estimated by detected step empirical stride length (L step = 0.6 m). We can see that magnetism sequences two traces have highly similar shape different distance scales. Figure 12b shows features matchg result similarity (correlation coefficient) se two magnetism sequences. The distance threshold used features alignment is settled as thalign = 2 m, mimum threshold proportion between matched feature couples AF total number features is settled as thfp = 70%. It shows that through features matchg sequence zoomg, matched features are translated to a same distance pot, two magnetism sequences are overlapped to highest extent. The calculated correlation coefficient (valued [ 1, 1]) is 0.98, which shows a high similarity between this two traces, result agrees with real situation.

19 (correlation alignment coefficient) is settled as thalign se two = 2 magnetism m, sequences. mimum The threshold distance threshold proportion used features between alignment matched feature is settled couples as thalign AF = 2 m, total mimum number threshold features is settled proportion as thfp = between 70%. It matched shows that feature through couples features AF matchg total sequence number zoomg, features matched is settled features as thfp are = translated 70%. It shows to a same that distance through pot, features matchg two magnetism sequence sequences zoomg, are overlapped matched to features highest are extent. translated The to Sensors calculated a same 2018, distance 18, correlation 1462 pot, coefficient two (valued magnetism [ sequences 1,1] ) is 0.98, are which overlapped shows to a high highest similarity extent. between 19 The 36 calculated correlation coefficient (valued [ 1,1] ) is 0.98, which shows a high similarity between this two traces, result agrees with real situation. this two traces, result agrees with real situation Magnetism sequence before matchg Magnetism sequence before matchg Matchg Result Matchg Result Smood resultant magnetism tensity (ut) Smood resultant magnetism tensity (ut) 30 Road segment trace Road segment trace Distance (m) Distance (m) Road segment trace 2 Road segment trace 1 20 Road segment trace Distance (m) Figure 12. Magnetism matchg similarity calculation results for two traces generated on Figure 12. Magnetism matchg similarity calculation results for two traces generated on same Figure same road segment: smood magnetism sequences detected features marked by itial road segment: 12. Magnetism smood matchg magnetism similarity sequences calculation detected results features for marked two traces by generated itial estimated on same estimated distance; magnetism sequences after feature matchg sequence zoomg, distance; road segment: magnetism smood sequences magnetism after feature sequences matchg detected sequence features zoomg, marked by itial ir estimated ir calculated similarity. calculated distance; similarity. magnetism sequences after feature matchg sequence zoomg, ir calculated similarity. Figures show anor two situations usg same parameters as those Figure 12. In Figures Figures 13, 13 13trace is show show partly anor anor generated two two situations situations road usg usg segment same that sametrace parameters parameters 1 was generated as as those those on. Figure Figure Through In Infeature Figure Figure matchg 13, 13, trace trace 2 2 is is partly partly sequence generated generated zoomg, on on trace road road segment 2 is segment matched that trace that closely trace 1 was to 1 generated was right generated on. part Through on. trace Through feature 1, feature matchg correlation matchg sequence coefficient sequence zoomg, (=0.91) zoomg, trace shows 2 is matched a trace high 2 similarity is closely matched tobetween closely right m. part to Furrmore, trace right 1, part it trace correlation also 1, shows coefficient that correlation tensity (=0.91) coefficient shows fset abetween (=0.91) high similarity shows magnetism a between high similarity m. sequences Furrmore, between se m. ittwo also Furrmore, traces showsdidn t that it also impact tensity shows that fset similarity between tensity calculation magnetism fset result, between sequences sce magnetism correlation se two sequences traces is maly didn t dependent impact se two similarity on traces didn t shape calculation impact result, two similarity sce sequences. correlation calculation In Figure is14, result, maly traces sce dependent on different correlation onroad shape segments is maly are two dependent processed sequences. usg on In our Figure shape algorithm, 14, traces some two on sequences. different peaks road In troughs segments Figure are 14, are matched traces processed on toger, different usg our but road algorithm, segments similarity some are is peaks at processed a low level troughs usg our are matched algorithm, toger, some peaks but similarity troughs is are at a matched low level toger, but similarity is at a low level Magnetism sequence before matchg Smood resultant magnetism tensity (ut) Smood resultant magnetism tensity (ut) Distance (m) Matchg Result : Similarity Road segment : Similarity trace 1 Road segment trace 2 Road segment trace Magnetism sequence before matchg Matchg Result Smood resultant magnetism tensity (ut) Smood resultant magnetism tensity (ut) Road segment trace 1 Road segment trace 2 30 Road segment trace 1 20 Road segment trace Distance (m) Distance (m) Smood resultant magnetism tensity (ut) Smood resultant magnetism tensity (ut) 70 : Similarity Road segment : trace 1 Similarity Road segment trace 2 30 Road segment trace Road segment trace Distance (m) Distance (m) Figure 13. Magnetism matchg similarity calculation results when trace 2 is partly generated on same road segment that trace 1 was generated on: smood magnetism sequences detected features marked by itial estimated distance; magnetism sequences after feature matchg sequence zoomg, calculated similarity between m.

20 Sensors 2018, 18, x FOR PEER REVIEW Figure 13. Magnetism matchg similarity calculation results when trace 2 is partly generated on same road segment that trace 1 was generated on: smood magnetism sequences Sensors detected 2018, 18, features 1462 marked by itial estimated distance; magnetism sequences after feature matchg sequence zoomg, calculated similarity between m. 70 Magnetism sequence before matchg 70 Matchg Result Road segment trace 1 Road segment trace 2 Smood resultant magnetism tensity (ut) Smood resultant magnetism tensity (ut) Similarity : Road segment trace 1 Road segment trace Distance (m) Distance (m) Figure 14. Magnetism matchg similarity calculation results for two traces generated on Figure 14. Magnetism matchg similarity calculation results for two traces generated on different different road segments: smood magnetism sequences detected features marked by road segments: smood magnetism sequences detected features marked by itial estimated itial distance; estimated magnetism distance; sequences magnetism after feature sequences matchg after feature sequence matchg zoomg, sequence calculated zoomg, similarity calculated between m. similarity between m. As results above show, proposed geomagnetism-based similarity calculation algorithm As results above show, proposed geomagnetism-based similarity calculation algorithm is is proved to have a good performance for judgg similarity between two road segment traces. proved to have a good performance for judgg similarity between two road segment traces Road Segment Clusterg 3.3. Road Segment Clusterg Preprocessg Before Clusterg For For one road segment, re are two possible walkg directions for users, identified as as positive opposite opposite direction. direction. Due Due to to this this fact, fact, a preprocessg a preprocessg step step is implemented is implemented for for users users road segment road segment traces obtaed traces obtaed by traceby segmentation trace segmentation (shown (shown Section 3.1) Section before 3.1) clusterg before clusterg to make to make magnetism magnetism sequence sequence be generated be generated on a generally on a similar generally direction. similar Consequently direction. Consequently correlation correlation coefficient between coefficient two between magnetism two magnetism sequences can sequences be calculated can be correctly. calculated correctly. We We use use Rori Rori user s user s road road segment segment trace trace R for for walkg walkg direction direction judgment judgment two two road road segment segment traces traces ( ( same same direction direction or or opposite opposite direction). direction). Rori Rori is is mean mean value value all all Ori data Ori data R ( R details ( details can be can found be found Section Section 3.1). 3.1). For For two two user s user s road road segment segment traces traces R1 R1 R2, R2, road road orientations orientations are are denoted denoted as as Rori Rori 1 1 Rori 2. The difference between Rori 1 Rori Rori 2 2is is denoted denoted as as Rori. Rori Considerg. uniqueness uniqueness Rori, Rori we, use we value use value between between to dicate 180 to it, dicate value it, Rori value can be calculated Rori can by: be calculated by: { Rori Rori = 1 Rori 2, Rori 1 Rori 2 [0, 180 ] Rori1 Rori 2, Rori Rori2 [0,180 ] Rori3 = Rori 1 Rori 2, Rori 1 Rori 2 (180, 3 (33) ) (33) 3 Rori1 Rori2, Rori1 Rori2 (180,3 ) Considerg orientation fset between Rori real orientation, we set ±45 as Considerg orientation fset between Rori real orientation, we set ± 45 as uncertaty road orientation Rori, as shown Figure 15, so true orientation road segment uncertaty road orientation Rori, as shown Figure 15, so true orientation road can be dicated by: segment can be dicated by: Rori true = Rori ± 45 (34) true Rori = Rori ± 45 (34) Here Rori true is true orientation Rori is measured value. Thus, difference between true measured Here orientations Rori is (Rori true 1 orientation Rori 2 ) can also Rori be dicated is measured by: value. Thus, difference between measured orientations ( Rori 1 Rori 2 ) can also be dicated by: Rori = Rori 1 Rori 2 = (Rori1 true ± 45 ) (Rori2 true ± 45 ) (35)

21 Sensors 2018, 18, x FOR PEER REVIEW Sensors 2018, 18, 1462 true true Rori = Rori Rori2 = ( Rori1 ± 45 ) ( Rori2 ± 45 ) (35) true true If R1 R2 are generated on same walkg direction ( Rori If R1 R2 are generated on same walkg direction (Rori1 true 1 = Rori2 = Rori2 true ), orientation ), orientation difference Rori would fall [0 difference Rori would fall [0,90, 90 ]. If R1 R2 are generated on opposite walkg ]. If R1 R2 are generated on opposite walkg direction (Rori1 true true = Rori2 true true direction ( Rori1 = Rori ), 180 ), orientation orientation difference difference Rori would Rori would be [90 be, 180[90 ].,180 ]. 0 Rori Figure Figure 15. Coordate 15. Coordate system system for road for road orientation orientation uncertaty uncertaty ( ± 45 (±45 ) ) Rori Rori shown it. it. As As discussed discussed above, above, we we calculate calculate orientation orientation difference difference Rori Rori between between R1 R1 R2, R2, implement implement data processg data processg shown shown as followg: as followg: When When Rori [0,90 [0 ],, 90it ], is it estimated is estimated that R1 that R1R2 are R2generated are generated same direction, same direction, 1 2 similarity similarity calculation calculation will be will implemented be implemented directly directly between between Mag Mag 1 Mag Mag usg 2 usg algorithm shown Section 3.2. Here Mag 1 1 Mag 2 are 2 resultant magnetism sequences algorithm shown Section 3.2. Here Mag Mag are resultant magnetism from R1 R2, respectively. sequences When Rori from R1 [90, 180 R2, ], respectively. it is estimated that R1 R2 are generated opposite direction, When so before Rori similarity [90,180 calculation, ], it is estimated sequence that R1 Mag 2 would R2 are be generated reversed firstly, opposite denoted direction, as Mag 2, 2 so before n similarity similarity calculation, with Mag sequence 1 calculated. Mag would be reversed firstly, denoted as Mag 2, 1 If n Rori = similarity 90, as shown with Mag above calculated. two bullets, similarity would be calculated twice usg If both Rori Mag = 90 2, as Mag shown 2, higher above one two isbullets, settled as similarity fal similarity would between calculated R1 twice R2. 2 usg In actual both cases, Mag probability Mag 2, that R1higher is perpendicular one is settled to as R2 exists fal when similarity Roribetween [45, 135 R1 ], but this R2. step, only wher R1 R2 are same direction or opposite direction is it generally detected to decide wher Mag 2 or Mag 2 would be used for similarity calculation. Wher R1 In actual cases, probability that R1 is perpendicular to R2 exists when Rori [45,135 ], R2 are generated on a same road segment or not will be judged maly by magnetism similarity but followg this step, procedures. only wher R1 R2 are same direction or opposite direction is it 2 generally detected to decide wher Mag or Mag 2 would be used for similarity calculation. Wher Road R1 TraceR2 Clusterg are generated on a same road segment or not will be judged maly by magnetism In this similarity step, preprocessed followg road procedures. segment traces are clustered to some separate road segment clusters based on DBSCAN algorithm. A road segment cluster is defed as a collection users road Road segment Trace traces Clusterg whose magnetism sequences are similar to or ones same cluster are dissimilar In this to step, those preprocessed or clusters. road DBSCAN segment is atraces kd are density-based clustered to spatial some clusterg separate method road segment which is clusters commonly based used on DBSCAN many fields algorithm. [32]. In A road DBSCAN segment algorithm, cluster is adefed centre-based a collection density is defed users road usgsegment a distance traces metric, whose magnetism numbersequences pots are with similar settled to or distance ones metric same is cluster density are central dissimilar pot. to If those density or clusters. central DBSCAN pot reaches is a kd a settled density-based threshold, n spatial it will clusterg be defedmethod as a core which pot. is commonly used many fields [32]. In DBSCAN algorithm, a centre-based (1) C-neighborhood density is defed DBSCAN usg Clusterg a distance metric, number pots with settled distance metric is density central pot. If density central pot reaches a settled threshold, For n database it will be defed user road as a segment core pot. traces, denoted as D; elements it are road segment traces to be clustered, denoted as R i ; road segment cluster is a collection road segment traces (1) which C-neighborhood are generated DBSCAN a same Clusterg road segment, denoted as C k. To implement DBSCAN algorithm to get road segment cluster C k from database D, notion Eps-neighborhood values Eps MPts are defed firstly.

22 Sensors 2018, 18, As discussed above sections, we use magnetism similarity between two road segment traces to dicate distance between two pots. Sce correlation coefficient was utilized for similarity calculation between two road segments, we defe a kd correlation coefficient neighborhood (CC-neighborhood) for clusterg. CC-neighborhood a road segment trace R i is defed as road segment traces R j whose magnetism similarity (correlation coefficient magnetism sequence) is with settled range (ccrange) is termed as CC-neighborhood road segment R i represented as N CC (R i ). It is defed as followg equation: N CC (R i ) = { R j D cc(ri, R j ) ccrange } (36) cc(r i, R j ) means magnetism sequence correlation coefficient between R i R j usg method Section 3.2. The ccrange is settled as [0.9, 1] this paper. Then core road segment R i is defed as one whose CC-neighborhoods are not littler than MPts, R j is directly density-reachable from R i respect to Eps MPts when R j N CC (R i ), defed as: R j N CC (R i ) N CC (R i ) MPts (37) In DBSCAN algorithm, if R j is directly density-reachable from R i, R k is directly density-reachable from R j, n accordgly R k is density-reachable from R i, consequently R i, R j R k will be collected to same cluster. Considerg case that R j R k are both generated road segment RS1 R i is from road segment RS2; assumg that magnetism from R j are terfered with by noise which lead to a high similarity (respect to ccrange) between R i R j ; n, when we carry out CC-neighborhood DBSCAN clusterg, all traces from road segment RS1 RS2 would be judged to belong to same cluster. However, if we assume that magnetism terference happens occasionally, N CC (R i ) N CC (R j ) would tersect a few elements. On contrary, when N CC (R i ) N CC (R j ) tersect a large amount elements, it is probable that R i R j are generated on same road segment. As discussed above, we defe notion C-neighborhood based on CC-neighborhood via addg requirement cocidence between N CC (R i ) N CC (R j ). C-neighborhood a road segment trace R i is defed as: road segment traces R j, which is a CC-neighborhood R i whose CC-neighborhood (denoted as N CC (R j )) cocide with N CC (R i ) respect to a settled proportion, is termed as C-neighborhood road segment R i represented as N C (R i ). It is defed as followg equation: N C (R i ) = { R j N CC (R i ) P(Ri, R j ) thc } P(R i, R j ) = N CC(R i ) N CC (R j ) N CC (R j ) P(R i, R j ) is cocidence proportion between N CC (R i ) N CC (R j ). thc is accepted mimum P(R i, R j ). We set thc = 80% this paper. Consequently, for database user road segment traces D = {R i }, road segment clusters {C i } are obtaed usg C-neighborhood DBSCAN Clusterg by followg steps: All core traces {R c } are found usg C-neighborhood with respect to ccrange, thc MPts, represented by: R c D (39) N C (R c ) MPts (38)

23 Sensors 2018, 18, Road segment traces directly density-reachable density-reachable from one core trace R k { } c (denoted as R k r ) are found from database D, a cluster C k is settled by: C k = {R } k c, R k r C k D Or clusters are found by repeatg second step, collection road segment clusters are obtaed fally, represented by: () C = {C k }, k = 1, 2,..., K C k D k 1, k 2 (k 1 = k 2, k 1 = 1, 2,..., K, k 2 = 1, 2,..., K), C k1 C k2 = (41) where K is total number clusters. Traces that couldn t be collected to any clusters will be treated as noise don t participate followg process. Fally, number road segments a floor ( number clusters) clusters user traces from each road segments are obtaed from crowdsourcg database, represented by: C k = { C = {C 1, C 2,. }.., C K } R1 k, Rk 2,..., Rk Ck, k = 1, 2,..., K (42) Ri k is i-th road segment trace k-th cluster, Ck is total number traces k-th cluster. (2) Clusterg Result We collect one hundred test traces from five different corridors (road segments) usg different type smartphones to test performance proposed clusterg algorithm. Table 2 shows cluster result after applyg C-neighborhood DBSCAN. The correct clusterg trace is one which is collected cluster which most traces are generated same corridors with it. The correct clusterg trace is one which is collected a cluster which most traces are not generated same corridors with it. Table 2. Road segment clusterg result usg C-neighborhood DBSCAN. Number Test Traces Number Corridors Number Obtaed Clusters Number Correct Clusterg Traces Number Incorrect Clusterg Traces Correct Ratio Incorrect Ratio % 0 As shown Table 2, correct clusterg ratio is 100%, but number obtaed clusters is more than that corridors. Through data analysis, we found that data overdetected four clusters are all acquired from one same smartphone. This result proves good classification performance proposed C-neighborhood DBSCAN algorism, overdetected clusters will be merged followg procedure by connection estimation between different road segment clusters Topology Construction In this section, traces each cluster are merged, while connections between clusters are estimated usg turns detected from origal user traces Section 3.1, fally, topology map all road segments obtaed from user traces is constructed. Moreover, topology modification is implemented to deal with errors resultg from angle road length estimation.

24 Sensors 2018, 18, Road Length Estimatg { } For road segment cluster C k = Ri k, i = 1, 2,..., Ck, Ck is total number traces cluster C k. The trace with most magnetism features is chosen as basic trace (denoted as R k base ), or traces it are matched with R k base usg method proposed Section 3.2. Then we can get zoomg radio Ratio(Ri k, Rk base ) distance sequence Disi A after features alignment. Fally, all elements Ri k (except R k base ) are zoomed to same distance scale translated to same start pot (Dis = 0) with R k base. In Section 3.1, origal user trace is segmented to some straight sub-traces correspondg with different road segments, turns connectg each sub-trace are detected denoted as: I = { R i, R j, Type, Angle } (43) In above procedures, R i R j will be clustered to different road segment clusters, denoted as Ri k1 R k2 j. Assumg that, for one origal trace, user s walkg state would be basically stable, n distance scales would be same m, represented as: Then it can be reckoned that: Scale(Ri k1 ) = Scale(R k2 j ) (44) Scale(R k1 base ) Ratio(Rk1 i, Rbase k1 ) = Scale(Rk2 base ) Ratio(Rk2 j, R k2 base ) (45) Scale(R k2 base ) = Ratio(Rk1 i, Rbase k1 ) Ratio(R k2 j, Rbase k2 ) Scale(Rk1 base ) (46) where Scale( ) represents distance scale a road segment trace. Then based on Equation (46), distance scale or R k base from different road segment clusters can be set identically to Rk1 base cluster C k1 (called base road segment) by connected sub-traces. Furrmore, distance sequence each C k (except base road segment) would be updated to new distance scale, denoted as Dis i B for Sensors Ri k 2018, C k 18,. The x FOR process PEER REVIEW is represented as Figure Figure 16. The process to make distance scale j be identical with i usg connections Figure 16. The process to make distance scale C j be identical with C i usg connections between m. After that, length each road segment is estimated based on same distance scale, usg followg equation: L = Dis n Dis n i i = Ck (47) i1 i2 C max( ( )) m( ( )), 1, 2 1, 2,..., k B B where Ck is total number traces cluster C k. L C k is length road segment

25 Figure 18. A kd topology error caused by accurate angles: a rectangle four calculated ner angles; topology result rectangle usg accurate ner angles. C C don t overlap. Sensors 2018, 18, After that, length each road segment is estimated based on same distance scale, usg followg equation: L Ck = max(dis i 1 B (n)) m(dis i 2 B (n)), i 1, i 2 = 1, 2,..., Ck (47) where Ck is total number traces cluster C k. L Ck is length road segment cluster C k Connection Estimatg Between Clusters Utilizg turng connections I between R i R j clusterg different clusters, connections between different road segment clusters are found by: T = { C i, C j, P i, P j, Angle i,j } Angle i,j = angle(r x, R y ), R x C i, R y C j (48) T is connection between C i C j. P i P j are respectively distance identification this connection C i C j. Angle i,j is connection angle defed as same with connection between two different road segments trace, valued by mean all detected turng angles between C i C j. This is shown Figure 17. Sensors 2018, 18, x FOR PEER REVIEW Figure 17. The process for estimatg connection angle between clusters C i C j. Figure 17. The process for estimatg connection angle between clusters C i C j Topology Modification Map Construction Topology Modification Map Construction After estimation road segment length connection angle all clusters, topology After estimation road segment length connection angle all clusters, topology road segments can be constructed. Settg start pot base road segment (mimum road segments can be constructed. Settg start pot base road segment (mimum distance sequence from base road segment cluster) as (0,0) a 2D plan, n all road distance sequence from base road segment cluster) as (0, 0) a 2D plan, n all road segments segments can can be be displayed displayed plan plan by by geometry geometry calculation. calculation. Sce Sce re re should should be be measurement measurement calculation calculation errors errors for for lengths lengths angles, angles, topology topology modification modification will will be be implemented implemented to to revise revise topology topology errors. errors. The The topology topology error error is is typically typically shown shown Figure Figure

26 After estimation road segment length connection angle all clusters, topology road segments can be constructed. Settg start pot base road segment (mimum distance sequence from base road segment cluster) as (0,0) a 2D plan, n all road segments can be displayed plan by geometry calculation. Sce re should be measurement calculation errors for lengths angles, topology modification will be implemented to revise topology errors. The topology error is typically shown Figure 18. Sensors 2018, 18, Figure 18. kd topology error caused by accurate angles: rectangle four calculated Figure 18. A kd topology error caused by accurate angles: a rectangle four calculated ner angles; topology result rectangle usg accurate ner angles. C C don t ner angles; topology result rectangle usg accurate ner angles. C C overlap. don t overlap. The sum all ner angles a loop road is a fixed value, represented by: The sum all ner angles a loop road is a fixed value, represented by: sum( angle) = 180 ( n 2), n 3 (49) sum(angle) = 180 (n 2), n 3 (49) Here n is number road segments formg loop. In most cases, road loop is shaped Here as n a is quadrilateral, number road segments sum formg ner loop. angles In most is 3 cases,. Therefore road loop we is modify shaped as topology a quadrilateral, map usg loop sum angle correction. ner angles As is 3 shown. Therefore Figure we 19, modify startg topology with pot map C, usg position loop angle correction. pots D, As A, shown B, C are Figure calculated 19, startg usg with geometry pot C, by position road segment pots D, lengths A, B, C are connection calculated usg angles geometry (respectively by denoted road segment as l i lengths α i, i = connection 1,2,..., n, angles n is (respectively total number denoted road as segments l i α i, i = this 1, 2, loop)...., n, In n isfact, for total a loop, number pot road C should segments be overlapped this loop). with In fact, C, so for a loop, angles pot { α i } C, should i = 1,2,..., benoverlapped will revised with to C, so { α i }, angles i = 1, 2,..., {α i n},, i until = 1, y 2,... can, n will satisfy: be revised to {α i }, i = 1, 2,..., n, until y can satisfy: C = f( l, α, C), i = 1, 2,..., n i i () new 2 C = f (l αi i, α = i, αc), i { C i = C1,, m[ 2,..., n( αi αi) ], α i = 180 ( n 2)}, i = 1,2,..., n i i αi new = α i {C = C, m[ (α i α i ) 2 ], α i = 180 (n 2)}, i = 1, 2,..., n () i i f ( ) dicates geometry calculation for lengths angles. { αi new }, i = 1, 2,..., n are modified angles that satisfied requirement shown Equation (). To keep ma shape loop, angle modification will be carried out range ±10 for each angle. Fally, topology map will be modified usg new angles, represented by: Map = {V, E} V = {(x m, y m ), m = 1, 2,..., M} E = {(d m1,m 2 ), m 1 = 1, 2,..., M, m 2 = 1, 2,..., M} (51) V is a vector coordates all vertexes graph, E is a matrix to represent length each edge. M is total number vertexes. In addition, map can be adjusted furr, if we get real length orientation one road segment constructed map. What needs to be explaed here is that we have adopted a simpler method for topological modification map. It can reduce complexity algorithm is suitable for layout most door corridors. However, this method is only applicable to straight road segments (corridors). For curved corridors non-channel open areas, desired results may not be obtaed. Of course, for more complex door scenes, we can use more door map formation implement detection for curved corridors to achieve better result Radio Map Construction After fal topology Map is constructed by user traces, 2D position coordates magnetism sample pots will be estimated usg vertexes coordates V distance sequence

27 Sensors 2018, 18, { } Dis i B for each road segment R k i cluster C k, denoted as Pos i Mag. Because Wi-Fi fgerprt F user s road segment trace Ri k has a different sample frequency form magnetism tensity Mag, 2D position coordates will be terpolated learly on each fgerprt sample time, denoted as Pos i F. So far, Wi-Fi fgerprt collected by crowdsourcg users have been labeled by position coordates. Sce re is more than one user trace road segment cluster C k, this step, we will merge RSSs collected from different crowdsourcg traces same road segment to generate Wi-Fi RPs which form radio map RP Generation Considerg one edges constructed map Map = {V, E}, vertexes connected by this edge are V m1 = (x m1, y m1 ) V m2 = (x m2, y m2 ). The Wi-Fi RPs will be generated along this edge to make a grid with even distance d. The coordates RPs are calculated by: x p = x m1 + p d xm 2 x m1 d m1,m 2 y p = y m1 + p d ym 2 y m1 p = 1, 2,..., dm1,m 2 d means gettg a round number downward. Then all vertexes calculated grid pots (x p, y p ) for each road segment cluster constitute RP location pots our map RSS Mergg on RP For each RP generated above, we use Gaussian terpolation weights to merge Wi-Fi RSS from different user traces to RPs locations. On RP location (x p, y p ), RSS for one detected Wi-Fi APs is calculated by: d m1,m 2 (52) RSS AP m p = n ϖ p (n) RSS AP m(n) ϖ p (n) = 1 2πσ exp( 1 2σ 2 [(x n x p ) 2 + (y n y p ) 2 ]) (53) (x n, y n ) are coordates labeled fgerprt one road segment cluster, RSS AP m(n) is correspondg RSS value for m-th Wi-Fi { AP. } Then for road segment cluster C k = Ri k, i = 1, 2,..., Ck, fgerprt database is acquired represented by: FD k = { } (Pos k, F k ), i = 1, 2,..., Ck Pos k = { (x p, y p ) }, F k = { } f p p, p = 1, 2,..., P f p p = (RSS AP 1 p, RSS AP 2 p,..., RSS AP M p ) FD k is fgerprt database for road segment cluster C k. (x p, y p ) are RP coordates for fgerprt f p p. P is number RPs. RSS AP m p is Wi-Fi RSS received from AP m. M is total number APs which can be scanned C k. Fally, fgerprt database for whole topology Map is constructed by: FD = {FD k }, k = 1, 2,..., K (55) where FD is whole fgerprt database for Map. K is number road segment clusters. 4. Results Discussion In this section we show radio map construction result validate its localization performance. The experiment took place an underground parkg garage Beijg New Technology Park Chese Academy Sciences, which is covered with Wi-Fi signals (2.4 GHz). Figure 19 shows floor plan underground parkg some test traces (imitatg crowdsourcg user traces) (54)

28 Sensors 2018, 18, used our experiment. The crowdsourcg data are only collected parkg area except for entry exit paths car. The size parkg area is about m 100 m. In Figure 19b, we show floor plan parkg area high light pathway (road) this area usg blue. In order to imitate crowdsourcg data, y are collected by four different persons, whose height weight are shown Table 3. Pedestrians walk along road optionally experimental area meanwhile record orientation, acceleration, angular velocity, magnetic field Wi-Fi RSS smartphone. The sensors data are collected usg AndroSensor APP, Wi-Fi RSSs are collected usg self-developed RSSCollection APP. Table 3. Different pedestrians who collected crowdsourcg data our experiment. Height/cm Weight/kg Pedestrian Pedestrian Pedestrian Pedestrian Usg test crowdsourcg data, road segments are picked out topology map pathway experimental area is constructed through proposed method mentioned Section 3. Sensors 2018, 18, x FOR PEER REVIEW Furrmore Wi-Fi fgerprt map is constructed along each pathway. In followg content, followg we give content, topology we give map construction topology map result construction Wi-Fi fgerprt result Wi-Fi localization fgerprt result localization usg constructed Wi-Fi radio map. In addition, discussion test result are given about road width result usg constructed Wi-Fi radio map. In addition, discussion test result are given about fluence durg geomagnetism based similarity calculation road segment. road width fluence durg geomagnetism based similarity calculation road segment. Figure 19. Experimental area plan examples for crowdsourcg traces: floor plan Figure 19. Experimental area plan examples for crowdsourcg traces: floor plan underground underground parkg; parkg; parts parts test test traces traces collected collected by by crowdsourcg crowdsourcg users users our our experiment. experiment Topology Map Construction Result 4.1. Topology Map Construction Result Figure Figure shows shows pathway pathway map map constructed constructed by by crowdsourcg crowdsourcg traces. traces. Figure Figure 20a 20a is is rough result topology map after road length estimation connection estimation between rough result topology map after road length estimation connection estimation between road road segment segment clusters. clusters. The The blue blue les les represent represent road road segments segments red red pots pots represent represent connections connections between m. Some obvious topology mistakes are shown this result because measurement calculation errors for lengths angles. Figure 20b is pathway map after topology modification. We can get that ner angle revisg makes each road segments displayed on right connection pots which is alike to real pathway experimental area. Figure 20c is result after orientation length correction left road segment usg 0 real road

29 Figure 19. Experimental area plan examples for crowdsourcg traces: floor plan underground parkg; parts test traces collected by crowdsourcg users our experiment Topology Map Construction Result Figure 20 shows pathway map constructed by crowdsourcg traces. Figure 20a is Sensors 2018, 18, rough result topology map after road length estimation connection estimation between road segment clusters. The blue les represent road segments red pots represent connections between between m. m. Some Some obvious obvious topology topology mistakes mistakes are are shown shown this this result result because because measurement measurement calculation errors for lengths angles. Figure 20b is pathway map after topology calculation errors for lengths angles. Figure 20b is pathway map after topology modification. modification. We can get that ner angle revisg makes each road segments displayed on right We can get that ner angle revisg makes each road segments displayed on right connection pots connection pots which is alike to real pathway experimental area. Figure 20c is which is alike to real pathway experimental area. Figure 20c is result after orientation result after orientation length correction length correction left road segment usg 0 left road segment usg 0 real road real road length. length. 0 C C Y (m) - C1 C5 C6 C3 Y (m) - Y (m) C X (m) X (m) X (m) (c) Figure 20. Topology map construction results: rough result after road length connection Figure 20. Topology map construction results: rough result after road length connection estimations; estimations; pathway map after topology modification; (c) fal pathway map after orientation pathway map after topology modification; (c) fal pathway map after orientation correction. correction. In experiment, we collected a total 35 sets data, 85 sets road segment traces are segmented from m. After calculatg magnetic field similarity implementg clusterg algorithm, we obtaed seven road clusters, which are labeled as C1~C7 Figure 20a. It can be seen that re are topology errors Figure 20a path cannot form a loop like a real road. Therefore, we n used loop angle correction algorithm proposed this paper to correct topology. Because re are maly quadrilateral roads this testg area, we only modified angle usg quadrilateral loop order to improve computational efficiency. There are eight loops that used this process, y are [C1,C2,C3,C4], [C1,C2,C5,C4], [C1,C2,C6,C4], [C2,C3,C4,C5], [C2,C3,C4,C6], [C2,C3,C7,C5], [C2,C5,C4,C6] [C3,C4,C5,C7]. We measure accurate 2D coordates each connection pots experiment area, calculate distance error connection pots constructed map. Table 4 shows distance error each connection pots ( vertex ID is shown Figure 20c). The average distance error map vertex is 1.52 m. The mimum error is about 0.05 m maximum one is 4.69 m. And stard uncertaty is 1.4 m. Table 4. Distance errors vertex pots constructed pathway map. Vertex ID Error/m Vertex ID Error/m Based on calculation result corner position error, we fd that position error Vertex10 is largest, reachg 4.68 m. In addition, Vertex5 Vertex9 errors also exceed 2 m. Ors are below 2 m. Compared with real door map, it can be seen that error Vertex10 is maly from length estimation error C2. Because re is no floor plan formation, road segment length is difficult to correct. Therefore, when topology correction is performed, we only correct connection angle so that error length estimation is not elimated.

30 Sensors 2018, 18, At same time, loop correction, order to obta fal connection path, road segment length optimization is performed at same time as angle correction. However, simulation stware algorithm, we extract loop accordg to list number detected road segment cluster. Therefore, C1 C2 are always located at begng loop. And loop optimization, ir length is not adjusted. Then after calibration usg true length direction C1, length error C2 becomes more obvious. In addition, test area is an underground parkg, with a wide road width (more than 6 m) a large area at each corners, which may also cause deviations length estimations. Our algorithm does not rely on accurate door floor plan, but if more accurate map formation can be troduced, this error can be furr elimated Radio Map Construction Positiong Result The Wi-Fi radio map are fally acquired usg constructed pathway map that is shown Figure 21. Each pot figure dicates RP pots fgerprt. The distance d RP grid is settled as 2 m. The parameter σ for RSS mergg is 2 m. In order to validate localization performance constructed Wi-Fi radio map, we pick 25 position pots as test locations experiment area at each test location we measure Wi-Fi RSS twice calculate fgerprt positiong result usg KNN algorithm (K = 3). The localization error is statistically 1.8 m (%) 5 m (70%), which is competitive compared with or systems based on crowdsourcg data. Sensors 2018, 18, x FOR PEER REVIEW Y (m) X (m) Figure Figure Wi-Fi Wi-Fi RPs RPs generated constructed map. map. Table Table 5. Results 5. comparison with with method proposed by by or or researchers. Method Floor Plan Assistant Sensors Reported Accuracy Method Floor Plan Assistant Sensors Reported Accuracy Zee [24] with Acc., gyro., comp. 1.2 m (%), 2.3 m (80%) Zee [24] with Acc., gyro., comp. 1.2 m (%), 2.3 m (80%) RACC [25] with Acc., gyro., comp. 2.9 (%), 4.3 (80%) RACC [25] with Acc., gyro., comp. 2.9 m (%), 4.3 m (80%) PiLoc PiLoc [15] [15] without without Acc., Acc., gyro., gyro., comp. comp. Average Average m This This paper paper without without Acc., gyro., comp., mag. 1.8 m (%) 5 m (70%) Table 5 shows comparison our algorithm with or similar methods. These algorithms Table 5 shows comparison our algorithm with or similar methods. These algorithms all all use passive crowdsourcg user data can provide contuous corridor localization. Zee s use passive crowdsourcg user data can provide contuous corridor localization. Zee s reported reported positiong accuracy is superior to ours, but it uses a floor plan. The positiong result positiong accuracy is superior to ours, but it uses a floor plan. The positiong result RACC is RACC is similar to ours, a floor plan is also used this method. Our algorithm does not similar to ours, a floor plan is also used this method. Our algorithm does not depend on an depend on an accurate floor plan, which makes it perform better an unknown door area. PiLoc accurate floor plan, which makes it perform better an unknown door area. PiLoc does not require a does not require a floor plan, authors report higher positiong accuracy than our algorithm, floor plan, authors report higher positiong accuracy than our algorithm, however, authors however, authors experimental scenario is an fice floor, which isolation Wi-Fi experimental scenario is an fice floor, which isolation Wi-Fi signal is better compared with signal is better compared with underground parkg garage we used for our test. This helps underground parkg garage we used for our test. This helps PiLoc system to form a Wi-Fi tensity PiLoc system to form a Wi-Fi tensity distribution map with obvious features obta better positiong results. In addition, PiLoc also used an optimized positiong algorithm stead basic KNN algorithm. Figure 22 shows anor set test results. The test site is a floor an fice buildg. There is one major corridor this area some smaller corridors leadg to stairs, elevators toilets. The fice rooms are on two sides corridor. Figure 22a shows a floor plan experimental

31 Sensors 2018, 18, distribution map with obvious features obta better positiong results. In addition, PiLoc also used an optimized positiong algorithm stead basic KNN algorithm. Figure 22 shows anor set test results. The test site is a floor an fice buildg. There is one major corridor this area some smaller corridors leadg to stairs, elevators toilets. The fice rooms are on two sides corridor. Figure 22a shows a floor plan experimental area, red les show a part typical user traces our test. Through our clusterg algorithm, major corridor map is identified. Because traces small hallways or fice rooms are ten shorter distance have few magnetic features, y are not clustered to corridors our algorithm, but y are still accurately drawn out constructed pathway map through ir connections with major corridor. Figure 22b shows fal pathway map after orientation Sensors 2018, 18, x FOR PEER REVIEW correction major corridor. Figure 22c shows labeled Wi-Fi sample pots usg coordates constructed map. The average positiong error this test area is 1.7 m. (c) Figure 22. Experiment results an fice floor: floor plan examples for test traces; (c) fal Figure 22. Experiment results an fice floor: floor plan examples for test traces; fal pathway map constructed by proposed method; (c) labeled Wi-Fi sample pots usg pathway map constructed by proposed method; (c) labeled Wi-Fi sample pots usg constructed constructed pathway map. pathway map Road Width Influence 4.3. Road Width Influence When we use magnetism sequences to calculate road segment similarity, road (or corridor) When we use magnetism sequences to calculate road segment similarity, road (or corridor) is is abstracted as a le. However road has a certa width space, when users walk along abstracted as a le. However road has a certa width space, when users walk along road road (corridor), se exact positions on transverse road may be different from each (corridor), se exact positions on transverse road may be different from each or. To check or. To check out fluence different transverse positions users traces on road out fluence different transverse positions users traces on road segment similarity segment similarity calculation, we collected sensor data five times on one road segment usg calculation, we collected sensor data five times on one road segment usg different transverse different transverse positions likely traces on or road segments beside it two times, positions likely traces on or road segments beside it two times, calculated magnetism calculated magnetism similarity between m. Figure 23a shows test traces (red les, similarity between m. Figure 23a shows test traces (red les, numbered from 1 to 7), numbered from 1 to 7), magnetism sequence collected by seven test traces are compared magnetism sequence collected by seven test traces are compared toger Figure 23b. The road toger Figure 23b. The road width is 6 m, transverse terval between each trace from 1 width is 6 m, transverse terval between each trace from 1 to 5 is 1 m. It is seen Figure 23b to 5 is 1 m. It is seen Figure 23b that magnetism sequences have similar shape on same that magnetism sequences have similar shape on same road but different shapes on or roads. road but different shapes on or roads. Table 6 shows similarity calculation results between each test trace. Trace 1, 2, 3, 4 5 show Table 6 shows similarity calculation results between each test trace. Trace 1, 2, 3, 4 5 higher similarities with each or, especially with adjacent ones. On contrary, trace 6 7 show show higher similarities with each or, especially with adjacent ones. On contrary, trace 6 lower similarity with all or ones. We apply C-neighborhood DBSCAN clusterg proposed 7 show lower similarity with all or ones. We apply C-neighborhood DBSCAN clusterg proposed this paper usg parameters as ccrange [0.9,1], MPts 3 thc %. The algorithm obtas one cluster {1,2,3,4,5}, two noise traces 6 7, which matches real situation. Consequently, when we have collected abundant user data on one road segment, road width would not impact road segment clusterg. Even if traces on one road segment are

32 Sensors 2018, 18, this paper usg parameters as ccrange = [0.9, 1], MPts = 3 thc = %. The algorithm obtas one cluster {1,2,3,4,5}, two noise traces 6 7, which matches real situation. Consequently, when we have collected abundant user data on one road segment, road width would not impact road segment clusterg. Even if traces on one road segment are divided to more than one cluster, se traces still have chance to be merged toger graph construction phase by same connections. Sensors 2018, 18, x FOR PEER REVIEW Trace Trace 2 Smood resultant magnetism tensity (ut) Trace Trace Trace Time (sample count) Trace 3 Smood resultant magnetism tensity (ut) Trace Trace Time (sample count) Figure 23. Data comparison for road width fluence. seven test traces (red les); Figure 23. Data comparison for road width fluence. seven test traces (red les); measured measured magnetism sequence m. magnetism sequence m. Table 6. Calculated similarities between seven test traces. Table 6. Calculated similarities between seven test traces. Trace 1 Trace 2 Trace 3 Trace 4 Trace 5 Trace 6 Trace 7 Trace 1 1 Trace Trace 2 Trace Trace Trace.7445 Trace Trace Trace 2 Trace Trace 3 Trace Trace Trace Trace Trace 5 Trace Trace 6 Trace Trace 7 Trace Unconstraed Smartphone Influence In real scenario, it would happen that a pedestrian uses his/her smartphone different postures while walkg, like messagg, callg or just holdg it hs. The unconstraed smartphone attitude maly affects on two factors proposed algorithm: one is user s headg or is magnitude magnetic field, so when we usg crowdsourcg user data for radio map construction our method, se two factors would be considered: User headg In order to obta more accurate user headgs, especially situation unconstraed

33 Sensors 2018, 18, Unconstraed Smartphone Influence In real scenario, it would happen that a pedestrian uses his/her smartphone different postures while walkg, like messagg, callg or just holdg it hs. The unconstraed smartphone attitude maly affects on two factors proposed algorithm: one is user s headg or is magnitude magnetic field, so when we usg crowdsourcg user data for radio map construction our method, se two factors would be considered: User headg In order to obta more accurate user headgs, especially situation unconstraed smartphone poses, it is better to use some complex algorithms to calculate user headg, rar than use readgs directly from electronic compass. Some researchers have published relevant research results on this issue, like [30,33,34], but it is maybe still hard to estimate exact user headg for crowdsourcg data, so durg algorithm design, we made great efforts to mimize reliance on headg, maly cludg: (1) The proposed method uses angular velocity changes for turng detection road segmentation, which makes it free from magnetic terference. (2) We use mean value detected user headgs to dicate road segment orientation, which can partly elimate headg errors due to local magnetic field anomalies or short duration errors. (3) When constructg spatial magnetic sequence a trace, magnetic samplg distances are estimated only by step count stride length. Durg this period, headg terference will not affect it, refore headgs will not affect magnetic sequence similarity calculation result. In addition, magnetic field disturbance door buildg would enrich magnetic features corridors, which is conducive to good matchg separation for door corridors. (4) When constructg a pathway map, startg from base road segment, we use estimated lengths road segments connection angles between road segments to calculate plane coordates each vertex map. The whole map can be furr corrected if actual orientation length base road segment are known Magnitude magnetic field In our method, location differentiation ability geomagnetic field is utilized for corridor differentiation. This means that magnitude magnetic field is correspondgly different at different locations an door area, but similar for adjacent locations. We use magnitude magnetic field ( resultant magnetism tensity) our method to evaluate similarity user s trajectory. The magnitude magnetic field is only related to position smartphone rar than any rotation smartphone axis. When user uses or carries smartphone different postures, smartphones are close proximity around user body. Therefore, we speculate that under different smartphone postures, magnitudes magnetic field that users get are similar, we can still use it for magnetic sequence similarity calculation. Below, we collected data smartphone sensors same corridor usg three typical smartphone poses, cludg messagg, callg swg -h. We compared magnitude magnetic field, calculated magnetic sequence similarity between each two three sets data usg our algorithm. Figure 24 shows magnetism sequences comparison for three test traces. The calculated similarities between m are listed Table 7.

34 smartphone different postures, smartphones are close proximity around user body. Therefore, we speculate that under different smartphone postures, magnitudes magnetic field that users get are similar, we can still use it for magnetic sequence similarity calculation. Below, we collected data smartphone sensors same corridor usg three typical smartphone poses, cludg messagg, callg swg -h. We compared magnitude Sensors 2018, 18, 1462 magnetic field, calculated magnetic sequence similarity between each two three sets data usg our algorithm. Figure 24 shows magnetism sequences comparison for three test traces. The calculated similarities between m are listed Table 7. Messagg Origal data Smood data Messagg Resultant magnetism Intensity (ut) Callg Swg -h Callg Swg -h Time (samplg count) Figure 24. Data comparison for different smartphone attitudes. three type postures when a Figure 24. pedestrian Data comparison uses smartphone; for different measured smartphone magnetism attitudes. sequence m. three type postures when a pedestrian uses smartphone; measured magnetism sequence m. Table 7. Calculated similarities between three test traces collected usg different poses. Trace 1 Trace 2 Trace 3 Trace Trace Trace Through comparison result, we fd that magnetic sequences three test traces show similar shape, especially when y are smood usg a movg average filter. Most similarities show high values (>0.9) between m. Among m, similarity between trace 2 (callg) trace 3 (swg -h) is a bit lower (0.8632). The result proves that under different smartphone postures, we can still use proposed algorithm for magnetic sequence similarity calculation. If a user trace can t be clustered to any road segment clusters with or traces, owg to user pose complexity, it will be hled as noise not be used for map construction. 5. Conclusions In this paper, we focus on problem automatic Wi-Fi radio map construction usg crowdsourcg data door fgerprt localization systems. Based on comparison current systems our analysis opportunities challenges smartphone-based door localization methods, we propose a geomagnetism-aided door radio-map construction method via passive smartphone crowdsourcg. The proposed method utilizes magnetism sequence similarity a novel C-neighborhood DBSCAN clusterg algorithm to form pathway graph a floor plan from crowdsourcg traces without needg an exact floor layout, generates RPs by mergg crowdsourcg Wi-Fi signal strengths to construct radio map. The ma contribution our method clude: (1) it recognizes corridors from user traces usg magnetic field similarity which is relatively stable scenario unconstraed smartphone use for crowdsourcg data, also solves problem calculatg exact similarity between magnetism sequences when y are sampled usg different walkg speeds; (2) it forms pathway graph door environments usg clustered road segments, merges crowdsourcg Wi-Fi signal strengths on reference pots generated along pathway to construct radio-map. In designed experiments, proposed method is proved to show good ability to construct door pathway graph Wi-Fi radio map usg passive crowdsourcg data. The constructed Wi-Fi radio map can provide competitive door localization accuracy. Our method is only applicable door environments with obvious corridors (or roads), a hyposis straight corridors (road segments) is needed topology modification phases.

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