Anonymous crowdsourcing-based WLAN indoor localization

Digital Communications and Networks 5 (2019) 226–236

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Anonymous crowdsourcing-based WLAN indoor localization Mu Zhou, Yiyao Liu *, Yong Wang, Zengshan Tian School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

A R T I C L E I N F O

A B S T R A C T

Keywords: WLAN localization Crowdsourcing Mobility map Pixel template matching Robust extended Kalman Filter

In order to solve the problem of location privacy under big data and improve the user positioning experience, a new concept of anonymous crowdsourcing-based WLAN indoor localization is proposed by employing the MicroElectro-Mechanical System (MEMS) motion sensors as well as WLAN module in off-the-shelf smartphones. First of all, the crowdsourced motion traces with similar Received Signal Strength(RSS) sequences are assembled into a motion graph. Second, the mobility map is constructed according to traces segmentation and clustering. Third, the pixel template matching is adopted to physically label the pre-constructed mobility map. Finally, the robust Extended Kalman Filter (EKF) is designed to perform localization by matching the newly-collected RSS measurements against the mobility map. The extensive experimental results show that the proposed approach is capable of constructing a physically-labeled mobility map from the sporadically-collected crowdsourced motion traces as well as achieving satisfactory localization accuracy in a cost-efficient manner.

1. Introduction The rapid development of various wireless devices (e.g., smartphones, tablets, and laptops) has driven an imperious demand for Location-Based Services (LBSs), such as shopping guidance, personnel searching, and emergency rescue [1–3]. In recent years, a large number of indoor positioning media are proposed, such as the Wireless Local Area Network (WLAN) [4], Radio-Frequency IDentification (RFID) [5], ultrasound [6], Bluetooth [7], ultra-wideband [8], MEMS motion sensors [9], vision images [10], and audible sound [11], which well compensates the shortages of the Global Positioning System (GPS) [12]. Since the WLAN has been widely-deployed on campus, shopping malls and various public places, and the WLAN-based localization has become a priority for cost-efficient indoor localization. By considering the complicated indoor multipath effect and the problem of poor time synchronization of many commercial WLAN modules, it is difficult to perform an accurate localization by using the concepts of propagation modeling [13], Time of Flight (ToF) [14], and Time of Arrival (ToA) [15]. Thus, Received Signal Strength (RSS) [16] schemes in WLAN fingerprint localization have been widely studied. In general, the process of location fingerprinting involves two phases, namely, the offline phase and the online phase. In the offline phase, the fingerprint database is constructed from the RSS measurements at each labeled Reference Point (RP), and then in the online phase, the target locations are estimated by matching the newly-collected RSS

measurements against the pre-constructed fingerprint database. However, the process of fingerprint database construction is normally time-consuming and labor-intensive, and meanwhile, with the environmental change, the fingerprint database needs to be updated periodically, which significantly increases the maintenance cost. In response to this compelling problem, we propose to use a new cost-efficient Simultaneous Localization And Mapping (SLAM) approach to construct the indoor mobility map as well as perform the real-time localization by employing both the Micro-Electro-Mechanical System (MEMS) motion sensors and WLAN module in off-the-shelf smartphones. In concrete terms, the crowdsourced motion traces collected in the target environment are assembled into a motion graph by using gene sequencing [17] and Personal Dead Reckoning (PDR) [18], and meanwhile the data from MEMS motion sensors are utilized to identify the pedestrian walking transition between different floors. Then, the Minimum Description Length (MDL) [19]-based Density-Based Spatial Clustering of Applications with Noise (DBSCAN) [20] is performed to convert the motion graph into a mobility map. After that, the pixel template matching is adopted to physically label the mobility map. Finally, the robust Extended Kalman Filter (EKF) [21] is designed to achieve satisfactory localization accuracy in a cost-efficient manner. The rest of this paper is organized as follows. Section 2 surveys some related works on the indoor localization using MEMS motion sensors and WLAN module. The proposed approach is described in detail in Section 3. Then, in Section 4, we discuss the improvement of our system by

* Corresponding author. Chongqing University of Posts and Telecommunications, YF508 Yi Fu Building, No. 2 Chongwen Road, Nan’an District, Chongqing, 400065, China. E-mail addresses: [email protected] (M. Zhou), [email protected] (Y. Liu), [email protected] (Y. Wang), [email protected] (Z. Tian). https://doi.org/10.1016/j.dcan.2019.09.001 Received 28 February 2018; Received in revised form 16 September 2019; Accepted 26 September 2019 Available online 18 October 2019 2352-8648/© 2018 Chongqing University of Posts and Telecommunications. Production and hosting by Elsevier B.V. on behalf of KeAi. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Fig. 1. System structure. (1) Motion traces collection. The crowdsourced calibration-free motion traces are sporadically collected by the users following their daily routine in the target environment. (2) Feature landmarks recognition. The data from MEMS motion sensors is utilized to identify a pedestrian’s walking transition between different floors and the pedestrian’s movement route can be deduced through the PDR algorithm. (3) Mobility map construction. The motion traces with similar RSS sequences are assembled into a motion graph by using gene sequencing, and the MDL-based DBSCAN is performed to convert the motion graph into a mobility map according to traces segmentation and clustering. (4) Mobility map calibrating. By converting both the floor plan and the mobility map into binary images, the pixel template matching is adopted to physically label the pre-constructed mobility map. (5) Robust Kalman filter model. The robust EKF is designed to perform the localization by matching the newly-collected RSS measurements against the labeled mobility map with satisfactory accuracy and low cost.

Different from the approaches above, we propose a new mobility map construction approach for the indoor WLAN localization with satisfactory accuracy and low cost. To sum up, the three contributions of this paper are as follows. First of all, the crowdsourced calibration-free motion traces are used and assembled into a motion graph. Second, the MDLbased DBSCAN is performed to convert the motion graph into a mobility map. Third, the pixel template matching is adopted to physically label the pre-constructed mobility map.

parameters optimization. The experiments and corresponding performance are described in Section 5. Finally, Section 6 concludes this paper and addresses some future directions. 2. Related works With the wide deployment of WLAN infrastructure in the indoor environment, WLAN-based localization is recognized as one of the most representative indoor localization techniques. However, this technique generally requires a tedious process of fingerprint database construction [22–24]. To solve this problem, the authors in Ref. [25] use the cubic spline interpolation approach to reduce the fingerprint calibration efforts. The integrated distance-weighted reciprocal spacing and Kriging interpolation approach is proposed in [26] for the sake of constructing a cost-efficient fingerprint database. At the same time, the low-cost MEMS motion sensors are equipped in various mobile devices, such as smartphones and tablets, which makes it effective and efficient to construct a fingerprint database through PDR. Based on this, authors in Refs. [27,28] rely on the motion sensors to label RSS measurements for fingerprint database updating. There are also many other studies [29–31] focusing on the fusion of WLAN and PDR localization, while the performance is limited since PDR is easily affected by error accumulation issues. In this circumstance, much attention has been paid to the utilization of the indoor map. The authors in Ref. [32] construct a semantic information based indoor map from the known calibrated WLAN fingerprints to achieve the room-level localization. In Ref. [33], the authors rely on the built-in motion sensors in off-the-shelf smartphones to automatically construct the floor plan of an anonymous indoor environment. The authors in Ref. [34] make use of various signal sources, such as Complementary Metal Oxide Semiconductor (CMOS) vision, Bluetooth, and MEMS motion sensors, to construct an indoor map. The authors in Ref. [35] propose an approach to match the motion traces constructed from the PDR into trajectories in the floor plan. Although this approach helps a lot for the fast indoor map construction, it ignores the geometrical size of the environment (e.g., the width of corridor), which will consequently result in the low granularity of fingerprints.

3. System description As shown in Fig. 1, the proposed system consists of five modules: 3.1. Feature landmarks recognition After the crowdsourced calibration-free motion traces have been sporadically collected in the target environment, we first use the collected sensor data to detect the specific landmark(s) (such as staircases, elevators, and corners) in the target environment to enrich the crowdsourcing trajectory information and thus improve the performance of mobility map construction. Specifically, when the pedestrian goes upor down-stairs, the variation of acceleration is more significant than the one when the pedestrian walks on each floor, as shown in Fig. 2. From this figure, we can find that when the pedestrian walks on the floor, the range of acceleration is about 6:07m=s2 ð ¼ 3:04m =s2  ð  3:03m =s2 ÞÞ, which is much smaller than the one when the pedestrian goes up- or down-stairs, 9:16m=s2 ð ¼ 5:28m =s2  ð  3:88m =s2 ÞÞ. Then, we set the threshold1 at 8:5m=s2 such that when the variation of acceleration exceeds this threshold, the floor transition in a staircase occurs. Besides, when the pedestrian takes the elevator, there is overweight or weightlessness corresponding to the ascending or descending of the elevator, as shown in Fig. 3. From this figure, we can find that, during the

1 This threshold is determined by considering different pedestrian height and walking speed in indoor environment.

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into three types: walking up- or down-stairs, taking an elevator, and walking on a floor. The flow chart of the landmarks recognition and floor calculation is shown in Fig. 5. First, according to the sensor data and the landmarks identification method, the user movement pattern can be determined. Then we can get the current floor information through the barometer data and then output it along with the landmark information (whether the user is with stairs, in the elevator or on a floor). Meanwhile, the velocity and heading angle obtained from the sensor data are integrated in the PDR algorithm to construct the relative motion trajectories. As shown in Fig. 6, E and N denote the East and North. Specifically, we denote the user locations at time t0 and t1 as P0 ðN0 ; E0 Þ and P1 ðN1 ; E1 Þ, respectively, and the heading angle is θ0 during t0 to t1 , we have


N1 ¼ N0 þ d1 cosθ0 E1 ¼ E0 þ d1 sinθ0

(1)

Similarly, the user location P2 ðN2 ; E2 Þ at time t2 is


N2 ¼ N1 þ d2 cosθ1 ¼ N0 þ d1 cosθ0 þ d2 cosθ1 E2 ¼ E1 þ d2 sinθ1 ¼ E0 þ d1 sinθ0 þ d2 sinθ1

(2)

So, we can calculate the user location Pk ðNk ; Ek Þ at time tk as ( Nk ¼ N0 þ

Fig. 2. Variation of acceleration when walking on the floor or going up or down the stairs.

Ek ¼ E0 þ

k X i¼1 k X

di cosθi (3) di sinθi

i¼1

¼ fRSS1 ; ⋯; RSSN g to be RSS sequence captured from the We set motion trajectories of r  th user starting from p, where m is the number of starting positions, np is the number of user trails starting from p, and N is the number of RSS samples. According to the timestamp information in RSS trails and the sensing data from MEMS, the relation between the PDR-estimated locations and the RSS samples can be established. In this way, the gene-sequencing method is utilized to identify the RSS similarity among trajectories and thus achieve trajectory assembling. Qpr

3.2. Mobility map construction To construct the mobility map based on crowdsourcing trajectories, motion trajectories with similar RSS signal are first assembled together by gene-sequencing methods. Specifically, for every two RSS sequences RSSm ¼ frssm1 ; ⋯; rssmp g and RSSn ¼ frssn1 ;⋯;rssnq g, where p and q stand for the lengths of RSSm and RSSn respectively, we construct a similarity scoring matrix G, in which the element on the i  th row and j  th column (or called the similarity score with respect to the i  th and j  th RSS measurements in RSSm and RSSn , ai and bj ) is calculated by 9 8 0;   > > > = < Gði  1; j  1Þ þ s ai ; bj ; > Gði; jÞ ¼ max max fGði  k; jÞ þ Wk g; > > 1ki > > ; : maxfGði; j  lÞ þ Wl g;

Fig. 3. Variation of acceleration when taking the elevator up or down.

(4)

1lj

elevator operation, the acceleration remains stable, while there is a sharp variation of acceleration as the elevator starts or ends, due to the occurrence of overweight or weightlessness. This pattern of acceleration variation is utilized to identify the elevator-wise floor transition. In addition, the data from the barometer, namely, the air pressure, can be used to identify the floor, as shown in Fig. 4. As expected, the air pressure generally decreases with the floor getting higher, while the air pressure is much stable when the pedestrian walks on the same floor.2 The movement of pedestrians in the target environment is divided

1  i  p; 1  j  q

where 8 < Gði; 0Þ ¼ 0; 1  i  p Gð0; jÞ ¼ 0; 1  j  q : Gð0; 0Þ ¼ 0   s ai ; bj ¼


2

In our experiment, the variation of air pressure on the floor is less than 0.45 hPa. 228






(5) 

α; if ai  bj 2  ε β; otherwise

Wk ¼ kðα  βÞ Wl ¼ lðα  βÞ

(6)

(7)

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Fig. 6. Displacement recursive schematic. Fig. 4. Variation of air pressure when taking the elevator or walking on the floor.

noise line segments. The first category refers to the line segments with the number of neighboring line segments not less than the threshold MinPts in their Eps-domain. The second category refers to the line segments with the number of neighboring line segments less than MinPts in their Eps-domain, and meanwhile these line segments are neighboring to core line segments. And the third category refers to the rest line segments. The three main steps of the motion traces clustering by the DBSCAN are as follows: Step 1: Traverse each line segment and find the corresponding neighboring line segments in its Eps-domain. If a line segment whose neighboring is not less than MinPts, this line segment and its neighboring are merged into a cluster, and this line segment is set as the core line segment of this cluster. Step 2: Merge the line segments which are directly density-reachable [36] to the same core line segment, and merge the clusters which are corresponding to the same core line segment. Step 3: Eliminate the rest line segments which have not been merged into any cluster (referred as noise line segments). After clustering, the trajectories of each motion region are processed separately, and the main path of each region is extracted to construct a local motion map. For example, the cluster T, including t line segments, is represented as VT . We first construct a series of sweep lines which are perpendicular to their direction vectors V ⇀ T .Then select the locations as the feature points where the line segments intersect the sweep line. Finally, all the feature points are connected to obtain the feature trajectory Ttrace representing the movement trend of the T-th cluster. In Fig. 8(a), the sweep lines with distance d are constructed, and the green-dot line indicates the direction vector of this kind of tracks. In Fig. 8(b), all the positions of sweep lines intersecting with the line segment are determined, and the final feature trace (see the red polyline) is obtained in Fig. 8(c). Based on the constructed feature trace for each cluster, the corresponding upper and lower boundaries are determined as follows: As shown in Fig. 9, by taking the k  th cluster as an example, the interval between the feature trace and the boundary (either upper or lower one), lk , is determined by setting numinclude ==numtotal  ε, where ε ¼ 0:95 is a k k

Fig. 5. Flow chart of the landmarks recognition and floor number calculation.

ε is the similarity threshold, the notation “k  k2 ” represents the 2-norm operation, and α and β stand for the similarity gain and loss respectively. Then, based on the similarity scoring matrix for each pair of RSS sequences, we continue to construct the corresponding correlation set. Fig. 7 shows an example of constructing the correlation set with respect to two time-stamped RSS sequences. From this figure, we can find that the largest value in the similarity scoring matrix is located at ð9; 7Þ , which is marked with a red star. Meanwhile, the correlation set is constructed from the yellow-marked elements along the blue-arrowed direction, notated as fð9; 7Þ; ð8; 6Þ; ð7; 5Þ; ð6; 4Þ; ð5; 3Þ; ð4; 2Þ; ð3; 1Þg. After all crowdsourcing trajectories are assembled by using gene sequencing, the relative motion trajectories are clustered by DBSCAN algorithm to distinguish each movable region in the target environment. To achieve this goal, we define three categories of line segments, namely, the core line segments, the boundary line segments, and the

and numinclude stand for the number of line segthreshold, and numtotal k k ments contained in this cluster and in the corresponding region bounded by the upper and lower boundaries respectively. 3.3. Mobility map calibrating In order to determine the absolute position of the mobility map in the target environment, we proposed a pixel template matching algorithm with special landmark information. First, we convert the floor plan and the constructed mobility maps into binary images, in which the pixel 229

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Fig. 7. An example of correlation set construction.

values of the accessible and inaccessible locations are set as 0 and 1 respectively, as shown in Fig. 10. Fig. 10 (a) is a local mobility map constructed by crowdsourcing trajectories, and Fig. 10 (b) shows its image representation after the binary conversion. Then, based on section 3.1, the key landmarks information in the mobility map is identified, and the pixel coordinate of landmarks is recorded. This greatly reduces the time cost in location matching. Next, the mobility map is slid within the limited stride, and the similarity between the mobility map and the extracted template map is calculated at each move. Finally, the location of the extracted template map is determined as the absolute location of the overlapped mobility map with the greatest similarity. The steps of pixel template matching are shown in Algorithm 1. By selecting the binary images of the floor plan and the mobility map as template and target images, the steps of pixel template matching are as follows: Algorithm 1.

Fig. 8. Motion trend depiction of the line segments in a cluster.

As shown in Fig. 10(c), the mobility map is mapped on the floor plan. We first identify the key landmarks in the mobility map based on the sensor data, and then use the pixel template matching method in Algorithm 1 to determine the absolute position of the local mobility map.

Fig. 9. Upper and lower boundaries setting.

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Fig. 10. Result of line segments clustering.

8 >  > > > X t ¼ f ðXt1 ; Wt1 Þ > >  > > Pt ¼ Ft1 Pt1 F Tt1 þ Qt1 > <  1 T 1 T K ¼ P t H t Ht Pt H t þ R t > t   > 1 > > Xt ¼ X  > t þ Kt Zt  Ht X t > > >  > ¼ ðI  K H ÞP P t t : t t

3.4. Kalman filter model In order to make full use of the crowdsourcing trajectories containing RSS sequences and sensor data, we design a robust Kalman filter to combine the two kinds of measurements to achieve a high-precision positioning. As such, the state vector Xt and measurement vector Zt are constructed [37] as


Xt ¼ Φt;t1 Xt1 þ Wt1 b t þ Vt Zt ¼ Ht X

where X  t and Xt , the function f ðÞ, describe the nonlinear variation of variable, and P t and Pt stand for the state estimation and state estimation covariance matrices before and after updating at time t respectively, Kt is the Kalman gain matrix at time t, Ht is the observation matrix at time t, I is the unit matrix, Ft , Rt , and Zt respectively stand for the Jacobian, measurement noise covariance, and observation matrices at time t, and Wt is the state noise matrix at time t under the normal distribution Nð0;Qt Þ, in which Qt is the covariance matrix of state noise at time t.

(8)

where Xt ¼ ½xt ; yt ; vt ; ϕt T , in which ðxt ; yt Þ is the target location at time t; vt and ϕt are the target velocity and heading at time t respectively; Vt is the observed noise matrix at time t under the normal distribution Nð0; Rt Þ, in which Rt is the covariance matrix of the observed noise at time t; and Φt;t1 is the transfer matrix from time t  1 to t, which is 2

1 60 6 Φt;t1 ¼ 4 0 0

0 1 0 0

sinϕt1 cosϕt1 1 0

3 0 07 7 05 1

4. Performance optimization (9) 4.1. Clustering optimization Since the parameters Eps and MinPts have significant impact on the performance of the DBSCAN, we rely on the concept of Jaccard similarity to optimize these two parameters based on a small number of known motion traces collected in the target environment. Specifically, by assuming M subareas in the target environment and am RSS measureP ments collected in the m  thðm ¼ 1; ⋯; MÞ subarea, where M m¼1 am ¼ L and L is the total number of RSS measurements, the transformation matrix Cphy in the physical space is constructed in (12). In this equation,

T

M W M W W Zt ¼ ½xW t ; y t ; vt ; ϕt  , in which ðxt ; y t Þ is the estimated target locaM tion by WLAN fingerprinting-based localization at time t, vM t and ϕt stand for the estimated target velocity and heading by the PDR at time t respectively, and Ht is

2

1 60 Ht ¼ 6 40 0

0 1 0 0

0 0 1 0

3 0 07 7 05 1

(10)

¼ 1 indicates that the i  th and j  th line segments are collected in Cphy ij ¼ 0. the same subarea, and otherwise Cphy ij

The robust EKF is constructed as

0 C phy 11 B B B⋯ B phy BC B a1 1 B B⋯ phy C ¼B B C phy B ða þ a þ ⋯Þ 1 1 2 B |fflfflfflfflfflfflfflfflfflffl ffl{zfflfflfflfflfflfflfflfflfflffl ffl} B i B B⋯ B @ C phy ða1 þ ⋯ þ aM Þ 1 |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl}

(11)

⋯ Cphy 1a1

⋯ C phy 1ða1 þ a2 þ ⋯Þ |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl}

⋯ ⋯ ⋯ Cphy a1 a1

⋯ ⋯ ⋯ C phy a1 j

⋯ ⋯

⋯ ⋯

⋯ Cphy ia1

⋯ C phy ij

⋯ ⋯

⋯ ⋯

⋯ Cphy La1

⋯ C phy Lj

j

1 ⋯ C phy 1ða1 þ ⋯ þ aM Þ |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} C L C C ⋯ ⋯ C phy C ⋯ C a1 L C C C ⋯ ⋯ C phy C ⋯ C iL C C C C C ⋯ ⋯ C A ⋯ C phy LL

L

231

(12)

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4.2. Robust EKF model

At the same time, the DBSCAN is performed to merge the line segments into N clusters. By assuming that the n  thðn ¼ 1; ⋯; NÞ cluster P contains bn line segments, where Nn¼1 bn ¼ L, we similarly construct the seg transformation matrix C in the signal space in (13). In this equation, Cseg ij ¼ 1 indicates that the i  th and j  th line segments belongs to the

To mitigate the gross error of observation values, the IGG  III equivalent weight function [38] is used to constrain the weight of anomalous observation values. To achieve this goal, we divide the observation values into three categories, namely, the normal observation values in the weight maintained region, the available observation values in the drop weight region, and the error observation values in the reject

same cluster, and otherwise Cseg ¼ 0. ij

0 Cseg 11 B B B⋯ B seg BC B b1 1 B B⋯ C seg ¼ B B Cseg B ðb1 þ b2 þ ⋯Þ 1 B |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} B i B B⋯ B seg @C ðb1 þ ⋯ þ bN Þ 1 |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl}

⋯ C seg 1b1

⋯ C seg 1ðb1 þ b2 þ ⋯Þ |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl}

⋯ ⋯ ⋯ C seg b1 b1

⋯ ⋯ ⋯ C seg b1 j

⋯ ⋯

⋯ ⋯

⋯ C seg ib1

⋯ C seg ij

⋯ ⋯

⋯ ⋯

⋯ C seg Lb1

⋯ C seg Lj

j

1 ⋯ C seg 1ðb1 þ ⋯ þ bN Þ |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} C L C ⋯ ⋯ C C seg C ⋯ C b1 L C C C ⋯ ⋯ C seg C ⋯ C iL C C C C C ⋯ ⋯ C seg A ⋯ C LL

(13)

L

Then, the Jaccard similarity of the transformation matrices in the physical and signal spaces is calculated by   J C phy ; C seg ¼

〈Cphy ; C seg 〉 〈C phy ; C phy 〉 þ 〈C seg ; C seg 〉  〈C phy ; Cseg 〉

(14)

where the notation “〈 ;  〉” represents the inner product operation between two matrices. Finally, we use the parameters Eps and MinPts, which are corresponding to the highest Jaccard similarity (or called optimal parameters) for the DBSCAN. Fig. 11 shows the variation of Jaccard similarity as the values of Eps and MinPts increase from 0.2 to 1.1 and from 1 to 10. From this figure, we can find that when the value Eps is too large or small, the Jaccard similarity will decrease significantly or even tend to approximate 0, while the increase of value MinPts has slight impact on the Jaccard similarity. Therefore, considering both the DBSCAN performance and computation efficiency, we set the parameters as shown in the results that follow.

Fig. 12. Environmental layout.

Fig. 11. Jaccard similarity under different values of Eps and MinPts. 232

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Fig. 13. Photos of APs and the interface of data collection.

Fig. 15. Result of the line segments clustering. Fig. 14. Result of motion graph assembling.

residual, σ vi is the mean square deviation of the observation residuals, and k0 and k1 are the thresholds for determining the drop weight and reject regions. In our model, the values of k0 and k1 are set as 1.5 and 2.5, indicating that the drop weight and reject regions are corresponding to the confidence probabilities of errors outside 1:5σ vi and 2:5σ vi , which are smaller than 0.13 and 0.01, respectively. In addition, by considering

region. Based on this, by assuming the weight of the i th observation value as ϖ i , the corresponding equivalent weight is ϖ i ¼ ϖ i ωi , where ωi is the resistance weight factor. Then, we set ωi to be 1 and 0 for the normal and error observation values, while the ωi for available observation values is calculated by

ωi ¼

1þb 1 þ b k0jvσi vj

that ∂ωi ==∂b ¼ ð1 jvi j =k0 σ vi Þ==ð1 þ bjvi j=k0 σ vi Þ2 < 0 , which indicates that the value ωi decreases with the increased b, and meanwhile ωi → k0 σ vi ==jvi j when b → ∞, (12) can be simplified into

(15) i

where b is the weight factor coefficient, vi is the i  th observation

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8 < 1; jui j  k0 ωi ¼ k0 =jui j; k0 < jui j  k1 : 0; jui j > k1

experiments in an office environment. As shown in Fig. 12, the experimental environment consists of two floors, with a 57m  52m floor plan. During the experiments, we placed 9 APs as Wi-Fi signal transmitters on both floors, and the Galaxy SIII was utilized to collect RSS and the sensor data. Fig. 13 shows the AP devices as well as the interface of our data collection API. Volunteers used smartphones to collect crowdsourcing trajectories following their daily behavior. In order to increase the feasibility of the collected trajectory data, volunteers started from different and unmarked locations, and a total of 350 motion trajectories were collected.

(16)

where ui ¼ vi ==σ vi . Finally, ϖ i is obtained as

ϖi ¼

8 > > < > > :

k0 ϖ i d 2i

ϖ i ; jui j  k0 jui j; k0 < jui j  k1 0; jui j > k1

(17)

where di ¼ ðk1 jui jÞ==ðk1 k0 Þð 2 ½0; 1Þ is the smoothing factor. Based on the previous discussion, the proposed robust EKF model can adaptively update the Kalman gain according to the difference between the observed and the estimated values. In concrete terms, when jui j  k0 , the observation values are equal to the state estimation values, which is in accordance with the conventional Kalman filter. However, when k0 < jui j  k1 , the covariance matrix of the observation noise is adapted into Rt ¼ ϖ 1 i , while the observation values are recognized to be deviated from the state estimation values when jui j > k1 . In this case, we set ϖ i ¼ 0, which indicates Rt → ∞.

5.2. Result of mobility map construction Fig. 14 (a) is crowdsourcing trajectories with unknown starting points. We let the starting position of each track at the same origin and use PDR algorithm to determine the relative position of each track. At the same time, we rely on the sensor data to determine the feature landmarks in the trajectories. In Fig. 14 (b), the line segments with similar RSS signals are assembled together by gene-sequencing algorithm. Fig. 15 (a) is the physical area division in the actual environment, Fig. 15 (b) is the clustering result by DBSCAN algorithm, and Fig. 15 (c) shows the clustering result after removing the noise line segments. After clustering for the line segments, the mobility map is constructed in Fig. 16 (a), and Fig. 16 (b) shows the result of the binary image conversion of the mobility map. In addition, Fig. 16 (c) illustrates the locations of all identified landmarks (involving the staircases and elevators) in the target environment. The constructed mobility map of the two

5. Experimental results 5.1. Experimental setup To evaluate the performance of the proposed system, we conduct the

Fig. 16. Mobility map construction.

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Table 1 Localization performance by different localization approaches.

The proposed CIMLoc The approach in Ref. [26] GrassMA

Time cost for data collection (minute)

Number of locations to be calibrated

67% error (m)

Mean error (m)

90 90 600

0 35 220

2.9 4.4 4.6

2.3 3.0 4.1

300

100

3.6

2.5

sizes. 6. Conclusion In this paper, a new pixel template matching approach for the indoor WLAN localization is proposed. The crowdsourced motion traces are sequenced, segmented, and clustered to construct a mobility map, which is then physically labeled by pixel template matching. Furthermore, the robust EKF is designed to perform localization with higher accuracy and lower cost compared with other two state-of-the-art approaches. Meanwhile, using the geographical skeleton of the target environment to perform fast searching of pixel templates in a complicated indoor environment forms an interesting work in future.

Fig. 17. CDF of errors with respect to locations on the testing path.

Acknowledgements The authors wish to thank the reviewers for the careful review and valuable suggestions. This work was supported in part by the National Natural Science Foundation of China (61771083,61704015), Program for Changjiang Scholars and Innovative Research Team in University (IRT1299), Special Fund of Chongqing Key Laboratory (CSTC), Fundamental and Frontier Research Project of Chongqing (cstc2017jcyjAX0380, cstc2015jcyjBX0065), University Outstanding Achievement Transformation Project of Chongqing (KJZH17117), and Postgraduate Scientific Research and Innovation Project of Chongqing (CYS17221). References [1] Y. Li, S. Xia, M. Zheng, et al., Lyapunov optimization based trade-off policy for mobile cloud offloading in heterogeneous wireless networks, IEEE Transactions on Cloud Computing (2019) 1–14. [2] Y. Li, J. Liu, B. Cao, et al., Joint optimization of radio and virtual machine resources with uncertain user demands in mobile cloud computing, IEEE Trans. Multimed. 20 (9) (2018) 2427–2438. [3] Y. Li, Y. Liang, Q. Liu, et al., Resources allocation in multi-cell D2D communications for internet of things, IEEE Internet of Things Journal 5 (5) (2018) 4100–4108. [4] H. Guo, Fast authentication method for wireless local area network, Int. J. Secur. Appl. 9 (6) (2015) 53–60. [5] C. Wu, S. Cheng, R. Chang, A data filtering strategy using cluster architecture in radio frequency identification system, Int. J. Radio Freq. Identif. Technol. Appl. 2 (4) (2013) 149–161. [6] L. Zhang, et al., Simultaneous registration of location and orientation in intravascular ultrasound pullbacks pairs via 3D graph-based optimization, IEEE Trans. Med. Imaging 12 (34) (2015) 2550–2561. [7] R. Saiket, S. Soumalya, T. Avranil, A bluetooth-based autonomous mining system, Adv. Intell. Syst. Comput. 243 (2013) 57–65. [8] B. Eleni, V. Demosthenes, N. Nikalaos, Localization error modeling of hybrid fingerprint-based techniques for indoor ultra-wideband systems, Telecommun. Syst. 2 (63) (2016) 223–241. [9] C. Zhu, W. Sheng, Realtime recognition of complex human daily activities using human motion and location data, IEEE Trans. Biomed. Eng. 9 (59) (2012) 2422–2430. [10] Y. Geng, K. Pahlavan, Design, implementation, and fundamental limits of image and RF based wireless capsule endoscopy hybrid localization, IEEE Trans. Mob. Comput. 8 (15) (2016) 1951–1964. [11] A. Mandai, C.V. Lopes, T. Givargis, A. Haghighat, R. Jurdak, P. Baldi, Beep: 3D indoor positioning using audible sound, in: Proc. 2nd IEEE Consum. Commun. Netw. Conf., Jan., 2005, 384-353. [12] C. Cummins, R. Orr, H. Oconnor, et al., Global Positioning Systems (GPS) and micro-technology sensors in team sports: a systematic review, Sport. Med. 43 (10) (2013) 1025–1042. [13] B. Paolo, L. Stefano, C. Stefano, et al., A novel approach to indoor RSSI localization by automatic calibration of the wireless propagation model, IEEE VTC (2009) 1–5.

Fig. 18. CDF of errors by different localization approaches.

target floors is shown in Fig. 16(d). 5.3. Result of target localization To evaluate the localization performance of the proposed method, a test path with an approximated length of 507 m was selected (see Fig. 12), in which totally 35 positions were marked (from #1 to #35). Fig. 17 shows the CDF of errors under different numbers of motion traces, from which we can find that 67% of the errors are within 2.9 m, 4.5 m, 28.0 m, and 28.3 m when the number of motion traces are 15, 30, 110, and 150, respectively. We compare the CDF of errors with CIMLoc [39], WLAN location fingerprint-based localization [29] and the semi-supervised manifold method [40] in Fig. 18. The time cost, calibration cost, and localization errors of different localization approaches are compared in Table 1. From this table, we can find that the time cost for data collection by using the proposed approach and CIMLoc is the same, while our approach requires no location calibration. In contrast, the approach in Ref. [29] involves huge overhead for fingerprint database construction, especially for environments of large 235

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