Crowdsourcing and Multi-source Fusion Based ...

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Crowdsourcing and Multi-source Fusion Based Fingerprint Sensing in Smartphone Localization Wanlong Zhao, Shuai Han, Senior Member, IEEE, Rose Qingyang Hu, Senior Member, IEEE, Weixiao Meng, Senior Member, IEEE, Ziqing Jia

Abstract—Traditional WiFi fingerprint positioning normally uses a time consuming and labor intensive process called site survey. This paper proposes a crowdsourcing and multi-source fusion based fingerprint sensing (CMFS) to replace the traditional site survey approach. In CMFS, motion sensors are used to construct the radio map by volunteers and Pedestrian Dead Reckoning (PDR) based on motion sensors equipped in smartphones is used for positioning. In positioning phase, an Extended Kalman Filter (EKF) based multi-source fusion algorithm is further developed to tackle the nonlinear fusion so that both positioning accuracy and robustness can be improved. Both experimental and simulation results verify that the performance of proposed schemes is comparable to the traditional fingerprint approaches. Further the EKF based fusion scheme is found to improve smoothness and stability of CMFS greatly. Index Terms—Crowdsourcing, Multi-source Fusion, Fingerprint, Motion Sensors, Extended Kalman Filter, Pedestrian Dead Reckoning.

I. I NTRODUCTION

I

N door Location based Service (ILBS) has attracted extensive research attention recently [1] [2]. Global Navigation Satellite System (GNSS) normally performs well in outdoor environments. Yet it has great challenges in indoor environments due to poor indoor satellite coverage and low positioning accuracy. Moreover, GNSS can quickly deplete smartphone battery due to high power consumption [3]. Therefore a number of low power wireless technologies such as Bluetooth [4], Ultra Wideband [5], Zigbee [6], Wireless Sensor Network (WSN) [7], WiFi [8], etc., have been considered in indoor positioning systems. Nowadays, smartphone has been an integral part to everybody [9]. Almost all the smartphones are equipped with WiFi module, Bluetooth module etc., so that smartphone is a very good choice for applying in indoor localization. Meanwhile wireless LANs are deployed widely in both public and private areas for purpose of communication, which creates a high probability of WiFi signal available for smartphone to adopt WiFi positioning technique. WiFi based indoor positioning techniques have been used in many applications [10] [11], which are paid much attention in both industry and academia [12]. There have been many researches on WiFi indoor positioning technology. Literature [13] proposes an improved Wanlong Zhao, Shuai Han(e-mail: [email protected]), Weixiao Meng are with Communication Research Center, Harbin Institute of Technology, Harbin, China. Rose Qingyang Hu is with Department of Electrical and Computer Engineering, Utah State University, Logan, UT 84321, U.S.A. Ziqing Jia is with the 205 Institute of China North Industries Group Corporation, Xi’an, China.

Kalman Filtering based WiFi indoor positioning algorithm. Literature [14] presents a domain clustering based WiFi indoor positioning algorithm. Smartphone WiFi-based positioning technology is used to identify customer’s pathway behavior in [15]. In general there have been two WiFi positioning systems (WPSs) widely used, namely model based and fingerprint based [16] [17]. Some typical radio propagation models are proposed in model based approaches. The distance of signal transmission is measured by various methods including time of arrival (TOA) [18], time difference of arrival (TDOA) [19], angle of arrival (AOA) [20], etc. In TOA, the signal transmission time from access points (AP) to smartphone is estimated firstly, in which it should be noted that three APs are needed as least. Afterwards the distance between smartphone and each AP is calculated based on wireless signal transmission velocity. TDOA is an improved method in which the estimated time is processed before distance computing. AOA is based on incident angle of WiFi signal to estimate transmission distance. The positioning accuracy of model based approaches is normally low mainly due to the additive noise, time-varying interferences, and multipath effects caused by walls or furnitures in an indoor environment [21]. Fingerprint based approaches usually can achieve a much better accuracy. It locates targets by comparing online fingerprint results with offline fingerprint database constructed in advance [22] [23]. The database is normally referred to as radio map. The process of building the radio map is called site survey. Fingerprint has attracted tremendous attentions. Paper [24] proposes nano-scale unmanned aerial vehicles based automating WiFi fingerprint collection method. A spatial multi-points matching algorithm is adopted in WiFi fingerprint in [25]. An energy-efficient indoor positioning system is presented in which WiFi fingerprint is detected by Zigbee radio in [26]. According to literature [9], a site survey of an area 281 m2 for 150 reference points (RPs) can take two manpowers each with 10 hours. Furthermore, fingerprint is susceptible to changing environments, which leads to the requirement of continuous updating of radio map [27]. Thus it is important yet challenging to reduce labor cost and time consumption in radio map building and updating processes. Smartphone based crowdsourcing is a new paradigm that exploits pervasive smartphones to sense, collect, and analyze data with unconscious cooperation among volunteers [28]. There have been many researches on crowdsourcing based fingerprint lately [29]. Literature [30] [31] proposed a crowdsourcingbased radio map updating algorithm as well as its improved version. However, a complete initial radio map is still needed

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for both algorithms. Literature [32] proposed an autonomous crowdsourcing of handheld devices for indoor navigation, in which the radio map is built through less time consuming crowdsourcing mechanism. Whereas, the access point (AP) information including location and propagation parameters (PPs) is needed in advance. Some other research attempts to fuse fingerprint with other positioning approaches. For example, literature [33] proposes a particle filter based fusion approach on fingerprint and smart sensors, which achieves a positioning accuracy of 1.2 m. However, the traditional site survey is still needed in such a scheme. Moreover, there is a high complexity in the implementation of particle filter. In this paper, a crowdsourcing and multi-source fusion based fingerprint sensing (CMFS) scheme is proposed, in which radio map is conducted by motion sensors instead of using site survey. All the APs are off-the-shelf and their information is not needed in advance. CMFS scheme consists of two phases, namely sensing phase and positioning phase. Motion sensors play an important role in both phases. During the sensing phase, a crowdsourcing based fingerprint collection approach is proposed, in which motion sensors, received signal strength indicator (RSSI), and floor plan are used synchronously to build up radio map. Smartphones are equipped with various sensors, such as accelerometers, gyroscopes, magnetometers, etc, using which motion states of smartphones can be measured. Based on floor plan, the collected RSSI can be conformed with its corresponding location. During the CMFS positioning phase, a multi-source fusion positioning algorithm is used, in which WiFi fingerprint and Pedestrian Dead Reckoning (PDR) are considered as positioning fusion sources. The current smartphone location can be estimated based on its initial location, step length, step event, and heading direction in PDR. A new step length estimation based on human height, acceleration variance, and step frequency is developed in this paper. Multi-source data fusion localization merges data from different location sources to achieve a better accuracy [34]. The proposed fusion approach in this paper takes the Extended Kalman Filter (EKF) as the fusion algorithm to solve a nonlinear problem with different fusion sources. Benefiting from the new fusion algorithm, CMFS performs well with no need to use the traditional site survey. The major contributions of this paper are summarized in the following. CMFS scheme is proposed to alleviate the labor and time cost issues experienced in the traditional fingerprint schemes. To further improve the positioning accuracy and robustness of CMFS, an EKF based fusion algorithm is used to consolidate the localization information among fingerprint and PDR. In addition, key problems in PDR are analyzed including step event detection, step length estimation and heading direction estimation. The reminder of this paper is organized as follows. In Section II, an overview on CMFS scheme is presented. Section III describes the details of crowdsourcing based sensing phase in CMFS. The multi-source fusion based positioning phase in CMFS is elaborated in Section IV, in which PDR and EKF based fusion algorithm are described in details respectively.

Experiments and simulations are presented in Second V. Finally, conclusions are given in Section VI. II. OVERVIEW A WiFi fingerprint positioning technique usually consists of two phases, off-line phase and online phase, as shown in Fig. 1. In the offline phase, a number of APs are first deployed. Then site survey is taken on to build the radio map, which is the database to store RSSI from APs at each reference point (RP). In the online phase, the RSSI of the positioning target is compared with the radio map using a matching algorithm such as k-nearest neighbors (KNN) [35] [36], weighted k-nearest neighbor (WKNN) [37], etc., to get the location information.

AP1 AP2

1

RP1  (r11 , r12 , r13 ,

, r1m )

2

RP2  (r21 , r22 , r23 ,

, r2m )

3

RP3  (r31 , r32 , r33 ,

, r3m )

…

...

Radio Map n

…

RPn  (rn1 , rn2 , rn3 ,

, rnm )

APm

Offline

TP  ( s1 , s 2 , s 3 ,

, sm )

Online

Fig. 1.

Match Algorithm

Location

WiFi Fingerprint Scheme.

One of the major challenges in the traditional fingerprint is its time-consuming and labor-intensive site survey process. Furthermore, radio map can be difficult to be updated when the environment changes or when APs join or leave. To tackle these issues, a crowdsourcing and multi-source fusion based fingerprint sensing scheme (CMFS) is developed. The diagram of the CMFS scheme is shown in Fig. 2. Similar to the traditional fingerprint schemes, there are also two phases in CMFS, namely sensing phase and positioning phase.

Motion Sensors

RSSI

Radio map

Floor Plan

Crowdsourcing based Sensing Phase Multi-source Fusion based Positioning Phase

Fingerprint PDR

EKF

Location

Fig. 2. Crowdsourcing and Multi-source Fusion Based Fingerprint Sensing Scheme.

Smartphones are equipped with motion sensors such as accelerometers, gyroscopes and magnetometers. In the crowdsourcing based sensing phase, these sensors can acquire information to estimate step length, step direction and step

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Volunteer RSSI2

RSSI1

RSSI4

RSSI3

RSSIm Radio map

... 1

2

3

4

5

6

...

Step Direction n Step Numbers

Step Length Fig. 3.

Illustration of CMFS Sensing Phase.

numbers, all of which help to build the radio map. RSSI is collected by WiFi scanners. The floor plan is used to map RSSI with its corresponding location. As a result, radio map can be constructed by using motion sensors, WiFi scanner and floor plan altogether. In the multi-source fusion based positioning phase, an EKF based fusion algorithm is used to merge positioning results from PDR and fingerprint. In the PDR positioning, the location information is acquired by accumulating step number and step heading direction of smartphones. In the fingerprint positioning, KNN is employed as the matching algorithm, in which K nearest RPs are obtained by computing the RSSI distance between the positioning target and all RPs in the radio map. The location coordinates of the positioning target are calculated based on the average value of K RPs. The positioning results of PDR and fingerprint are then fused in the EKF fusion algorithm.

cluster. When a volunteer walks around a corner, the current cluster ends and the last location in the current cluster is the initial location in the next new cluster. An Android system based software is developed to scan and store RSSIs from APs. As shown in Fig. 4, a pixel map of floor plan is downloaded to the smartphone firstly. A volunteer finds his initial location in the pixel map and clicks the relevant position in the smartphone screen. Based on the detected heading direction, WiFi signal, and step events, RSSI, step number, and step length can be achieved. Assume there are in total n steps, the initial location is (x0 , y0 ), the average estimation step length is l, heading direction is χ, and RSSI is scanned m times in one cluster. For every RSSI, the location coordinate is calculated accordingly. Then the fingerprint information can be obtained, as shown in Table I. The radio map constructed by this fingerprint information is called sensing radio map.

III. CMFS S ENSING P HASE

TABLE I S ENSING R ADIO M AP OF O NE C LUSTER

The sensing phase in CMFS is a process to build radio map based on crowdsourcing that is different from the traditional site survey. CMFS sensing phase jointly uses information from RSSI, motion sensors, and floor plan. By using motion sensors and floor plan, RSSI is no longer gathered at every RP, but collected through volunteers walking in an indoor environment. The illustration of CMFS sensing phase is shown in Fig. 3. In sensing phase, on the basis of floor plan, RSSI is collected uniformly by WiFi scanner at fixed time intervals. Simultaneously, step length, step number, and heading direction of volunteers are estimated based on motion sensors, which will be discussed in details in Section IV. A. Pedestrian Dead Reckoning. However, from Fig. 3, it can be seen that RSSI measurements are not synchronous with the step events, due to the fact that WiFi scanning interval at smartphones is fixed while the volunteers’ step length tends to be less regular. In order to reduce the matching error, the fingerprint building process is divided into several clusters. One straight walking route is considered to be one elementary sensing cluster. In each cluster, step length is calculated by dividing the total length into a number of portions evenly. The total portion number is determined by the number of WiFi scanning times in this

Location Coordinate (x0 , y0 ) (x0 + l·n cos χ, y0 + l·n sin χ) m m (x0 + 2·l·n cos χ, y0 + 2·l·n sin χ) m m .. . (m−1)·l·n (m−1)·l·n (x0 + cos χ, y0 + sin χ) m m (x0 + l · n cos χ, y0 + l · n sin χ)

Received Signal Strength Indicator RSSI0 RSSI1 RSSI2 .. . RSSIm−1 RSSIm

IV. CMFS P OSITIONING P HASE From the CMFS sensing phase, a crowdsourcing based sensing radio map is built up. In the CMFS positioning phase, an EKF based fusion algorithm is used to merge positioning results from multiple sources including PDR and fingerprint to improve positioning accuracy and robustness. A. Pedestrian Dead Reckoning Motion sensors in smartphones can provide motion states of a positioning target. There have been two models, namely Inertial Navigation model and Pedestrian Dead Reckoning

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Initial Location

( x0 , y0 )

Heading Direction Detection

Wifi Signal Detection

Step Detection

RSSI

Step Number Step Length

Store Sensing Fingerprint

Radio Map

Fig. 5.

No

Cluster End Detection Yes Next Cluster

End

Fig. 4.

Flowchart of CMFS Sensing Phase.

model (PDR), to calculate the location information based on motion states. Inertial Navigation is a double integration method. However, there is a limitation on the smartphone sensor accuracy, which can lead to a significant accumulative error in Inertial Navigation. Furthermore, human motion mechanics does not allow the use of Inertial Navigation for pedestrian navigation purposes. For these reasons PDR receives more and more applications in smartphone localization. PDR is a model based on human behavior as well as motion sensors. Walk steps can be detected from the variation of acceleration, which will be discussed in detail in Section IV-A1 Step Event Detection. If the initial location is known, smartphone’s current location and its moving trajectory can be acquired based on step by step accumulative sensing. The relationship between nth step location and (n + 1)th step location can be expressed as ( xn+1 = xn + l · cos α, (1) yn+1 = yn + l · sin α, where (xn , yn ) and (xn+1 , yn+1 ) represent the smartphone locations at step n and n + 1 respectively. l stands for the step length of smartphone movement and α is the level course angle. As shown in Fig. 5, acceleration is defined in three directions ax , ay , az . Azimuth, pitch, and roll indicate rotation angle velocity of z-axis, x-axis and y-axis respectively and their values can be estimated by gyroscopes. In PDR, three major problems that need to be tackled are step event detection, step length estimation, and heading estimation. 1) Step Event Detection: There can be many different modes for users to hold smartphones and examples include

Illustration of Acceleration Sensor in a Smartphone.

hand swinging, phoning, texting, in the pocket, etc. In the proposed sensing phase of CMFS, volunteers should pay attention to their smartphones, so that the motion mode of smartphone in pocket is not considered and phoning, texting, swinging modes are considered in this scheme. From literature [38], it is known that acceleration can be used to estimate step length in all of texting mode, phoning mode and swinging mode. Therefore acceleration force is used to detect step event in this paper. Let ax , ay , az stand for components of acceleration in three direction (x, y, z), as shown in Fig. 5. Then the Root Mean Square (RMS) of three components of acceleration is defined as asd in Equation (2). q asd = a2x + a2y + a2z . (2) In order to avoid the interference of local gravitational acceleration, asd is redefined in Equation (3) as q asd = a2x + a2y + a2z − glocal , (3) where glocal stands for local gravitational acceleration. In an experiment to test acceleration, a pedestrian walks 15 seconds carrying a smartphone. As shown in Fig. 6, the acceleration force goes up and down as pedestrian walks. The sampling frequency of the collected data in Fig. 6 is 50Hz, however, which is a much higher frequency than practical human walking. So that a sliding-window mean filtering [39] with length of 10 is adopted to process original data. After the filtering, the frequency becomes 5Hz, which means that asd is presented every 200ms. Afterwards, a peak detection algorithm [40] is adopted to detect step event. As for highlighting the wave peak, the cube of RMS of acceleration after filtering is employed, as shown in Fig. 7. Once step event is detected, acceleration shows a peak followed by a sharp falling-off in the curve. A threshold is then set to detect step event. Once the acceleration force is larger than the threshold, step number increases by one, as shown in Equation (4). apeak > a , sd

StepN um + +,

(4)

where a is the threshold and is normally set to 0.65m/s2 .

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Acceleration (m/s2)

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Time (ms)

Illustration of changing curve of acceleration in step event detection.

Acceleration (m/s2)

Fig. 6.

Time (ms)

Fig. 7.

Illustration of changing curve of acceleration after filtering in step event detection.

2) Step Length Estimation: In PDR, the distance traveled by a smartphone is measured from step number and step length. Adopting step event detection, step number can be achieved. Step length estimation methods are discussed in this section. There are many methods used for estimating step length, which adopt linear or nonlinear models to relate different variables like human height, step frequency, acceleration variance, gender, etc. A series of researches on step length estimation have been conducted. Literature [41] adopted principal fourth root and logarithm of acceleration variance to estimate step length, as shown in Equations (5) and (6).

or la = βlog(apeak − avalley ) + γ, t t

where la stands for the step length estimation value, β is a constant, apeak and avalley indicate peak and valley values of t t the acceleration in certain time t, respectively. γ represents the offset. Literature [41] employs β = 1.479, γ = −1.259 in Equation (5) and β = 1.131, γ = 0.159 in Equation (6). Another typical way to estimate step length is to consider pedestrian height and step frequency simultaneously. For instance, the estimation model adopted in literature [38] is shown in Equation (7). lhf = h(afstep + b) + c,

q 4 la = β apeak − avalley + γ, t t

(5)

(6)

(7)

where a, b, c are parameters related to pedestrian height and

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step frequency. In a general way, pedestrian height is a constant, however the step frequency is inconstant caused by different pedestrian movements. A experiment is conducted to observe the relationship between step length and step frequency, in which the selected pedestrian height is 173cm. The experiment result is presented in Table II and Fig. 8. From Fig. 8, it is clear that step length increases as step frequency goes up.

the magnetic strength in global coordinate system is MGCS = (mx , my , mz ). Then we can get Equation (9).

TABLE II E XPERIMENT ON RELATIONSHIP BETWEEN STEP LENGTH AND STEP

where Θ is the transfer matrix, as shown in Equation (11), and can be calculated by azimuth, pitch and roll.

FREQUENCY

Walking Time (s)

Step Number

Step Length (m)

87.101 66.004 50.052 42.264 30.112 26.021

94 84 76 71 61 56

0.500 0.560 0.619 0.663 0.771 0.840

Step Frequency (Hz) 1.092 1.280 1.536 1.715 2.037 2.155

χ = tan(−1)

my . mx

(9)

The transformational relation between the local coordinate system and the global coordinate system is MGCS = Θ · MLCS ,

(10)

B. EKF Based Fusion Positioning Approach When the smartphone is static, only fingerprint technique is adopted. Otherwise, an EKF based fusion positioning algorithm is used to combine results from both fingerprint and PDR. Thus a motion state detection algorithm is described first. 1) Motion State Detection: In order to detect the motion state of a smartphone, the motion state detection algorithm in [42] is used. The weighting Euclidean distance between two adjacent acceleration vectors is considered as the variable of judgment. Assume that the accelerations are (atx , aty , atz ) t+1 t+1 at time t and (at+1 x , ay , az ) at time t + 1, respectively. The weighting Euclidean distance between (atx , aty , atz ) and t+1 t+1 (at+1 x , ay , az ) is defined as Da in Equation (12).

0.85

0.8

Step Length (m)

0.75

Da =

0.7

0.65

0.6

0.55

0.5 1

1.2

1.4

1.6

1.8

2

2.2

Step Frequency (Hz)

Fig. 8.

Relationship between Step Length and Step Frequency.

Taking above two step length estimation schemes into consideration, a weighting based fusion method can be used to estimate the step length. l = ω1 la + ω2 lhf (8) q 4 = ω1 (β apeak − avalley + γ) + ω2 (h(afstep + b) + c), t t where ω1 + ω2 = 1 and the values of two weights can be adapted in real-time. For example, ω1 is set to be zero when the pedestrian height is unknown; ω2 is set to be zero at the beginning of movement when step frequency cannot be acquired yet; any outlier can be removed from this fusion process by setting the corresponding weight to zero. 3) Heading Direction Estimation: Heading direction can be estimated by using gyroscopes and magnetometers. Azimuth θA , pitch θP , and roll θR are provided by gyroscopes. And the magnetometer puts forward the magnetic strength MLCS in local coordinate system. Assuming the heading direction is χ,

q

− atz )2 , − aty )2 + Ω3 (at+1 − atx )2 + Ω2 (at+1 Ω1 (at+1 z y x (12)

where Ω1 , Ω2 , Ω3 are weighting factors and Ω1 +Ω2 +Ω3 = 1. Let StageF lag represent the motion state. StageF lag = 0 if the smartphone is static and StageF lag = 1 if the smartphone is mobile. D is the motion state detection threshold. ( StageF lag = 0, Da < D , (13) StageF lag = 1, Da ≥ D . In reality the acceleration change of motion state is different between “static” to “dynamic” and “dynamic” to ”static”. yaxis acceleration shows a big fluctuation when motion state changes from static to dynamic. On the contrary, z-axis, y-axis, and x-axis fluctuations decrease progressively from dynamic to static. The empirical parameter setting of motion state detection based on experiments is shown in Table III. TABLE III PARAMETER S ETTING OF M OTION S TATE D ETECTION A LGORITHM

Variable D Ω1 Ω2 Ω3

Static to Dynamic 0.7 0.0 1.0 0.0

Dynamic to Static 0.3 0.1 0.3 0.6

Fingerprint positioning result is adopted to position the smartphone in CMFS when smartphone is static. Otherwise, an EKF based fusion algorithm will be employed. The positioning result from fingerprint in static motion is set to be the initial input of the fusion algorithm.

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

cos θA cos θR − sin θA sin θP sin θR  Θ =  − sin θA cos θR − cos θA sin θP sin θR − cos θP sin θR

− sin θA cos θP − cos θA cos θP sin θP

2) EKF Based Fusion Algorithm: Kalman Filter (KF) is an optimal recursive data processing algorithm based on linear minimum variance estimation. The state of a dynamic system can be estimated from a series of noise measurements in KF. The state equation and observation equation in KF are respectively shown in Equation (14). ( xk = A · xk−1 + wk , (14) zk = H · xk + vk . xk and xk−1 represent the state vectors at time k and k − 1, respectively. zk is the measurement vector. A stands for the state-transition matrix. H indicates measurement matrix. wk and vk indicate the noise vector of state vector and measurement vector respectively. wk and vk are both assumed to be white Gaussian noise and their covariance matrixes are Q and R. The classical Kalman Filter consists of the following five steps. • Step 1: State vector estimation xk|k−1 = A · xk−1|k−1 .

(15)

• Step 2: Estimation on error covariance of state vector Pk|k−1 = A · Pk−1|k−1 · AT + Q,

(16)

where Pk|k−1 and Pk−1|k−1 indicate the error covariance matrixes of state vector at time k and at time k−1 respectively. • Step 3: Kalman Gain estimation T

Kk =

Pk|k−1 · H . H · Pk|k−1 · HT + R

(17)

Kk stands for the Kalman Gain matrix at time k. • Step 4: Update state vector estimation with measurement xk|k = xk|k−1 + Kk · (zk − H · xk|k−1 ).

(18)

• Step 5: Update error covariance of state vector Pk|k = (I − Kk · H) · Pk|k−1 .

(19)

I is a unit matrix. Finally, state vector xk|k is acquired by fusing the former state vector xk−1|k−1 and the measurement vector zk . Kalman Filer is normally applied in linear systems, in other words, the state-transition matrix A and measurement matrix H are both time invariant. In reality, WiFi scanning results may not be synchronous with PDR location outputs. When fusing fingerprint and PDR, the measurement matrix H may not be constant, which can be seen in Equation (20).  xk = xk−1 + l · sk−1 · cos χk−1 + wxk ,    y = y k k−1 + l · sk−1 · sin χk−1 + wyk , (20)  sk = sk−1 + wsk ,    χk = χk−1 + wχk .

 cos θA sin θR + sin θA sin θP cos θR  − sin θA cos θR − cos θA sin θP sin θR  . cos θP cos θR

(11)

(xk , yk ) and (xk−1 , yk−1 ) indicate the location coordinates of PDR at time k and at time k −1, respectively. sk stands for the step number at time k. χk represents the heading direction at time k. l indicates estimated step length. w is noise. Based on Equation (20), the state vector is expressed in Equation (21). ( xk = [xk , yk , sk , χk ]T , (21) xk−1 = [xk−1 , yk−1 , sk−1 , χk−1 ]T . It is clear that xk cannot be transformed from xk−1 in a linear way. Different from KF, Extended Kalman filter (EKF) finds a linear approximation for a nonlinear function, making it more suitable to tackle nonlinear problems. As such EKF is adopted in the fusion algorithm. Similarly to KF, the state vector and measurement vector in EKF are defined in Equation (22). ( xk = fk (xk−1 ) + wk , (22) zk = hk (xk ) + vk . fk and hk indicate the nonlinear transform relationship function between time k and k − 1 for the state vector and for the measurement vector respectively. Different from KF, the transform matrix is expressed by the partial derivative k of fk and hk , i.e., state-transition matrix Φ = fk0 = ∂f ∂x k and measurement matrix Ψ = h0k = ∂h in EKF. The ∂x corresponding five steps of EKF are shown in the following. • Step 1: State vector estimation xk|k−1 = fk (xk−1|k−1 ).

(23)

• Step 2: Error covariance of state vector Pk|k−1 = Φ · Pk−1|k−1 · ΦT + Q,

(24)

where Pk|k−1 and Pk−1|k−1 indicate the error covariance matrixes of the state vector at time k and at time k − 1 respectively. • Step 3: Kalman Gain estimation Kk =

Pk|k−1 · ΨT , Ψ · Pk|k−1 · ΨT + R

(25)

where Kk stands for the Kalman Gain matrix at time k. • Step 4: Update state vector estimation with measurement xk|k = xk|k−1 + Kk · (zk − hk (xk|k−1 )).

(26)

• Step 5: Update error covariance of state vector Pk|k = (I − Kk · Ψ) · Pk|k−1 .

(27)

Based on the five steps in EKF, when fusing fingerprint and PDR, the state vector is set to be x = [x, y, s, χ]T , in which (x, y) indicates the location coordinate, s stands for the step number, χ represents the heading direction. The measurement vector is set to be z = [xwif i , ywif i , spdr , χpdr ]T , in which (xwif i , ywif i ) is the location result of fingerprint. The

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state equation and measurement equation can be respectively expressed in Equations (20) and (28).   xkwif i = xk + wxwif i ,     yk = y + w k ywif i , wif i (28) k   spdr = sk + wspdr ,    χpdr = χk + wχpdr .

TABLE IV PARAMETERS OF A DOPTED S MARTPHONE

Parameter Type Operating System RAM ROM Sensors WiFi Modes

Parameter Value Android OS 4.1 2GB 4GB Acceleration, Compass, Gyroscope. etc 802.11a/b/g/n

The state-transition matrix Φ is shown in Equation (29).    Φ=  

1 0 0 0

0 l · cos χk−1 1 l · sin χk−1 0 1 0 0

−l · sk−1 · sin χk−1 l · sk−1 · cos χk−1 0 1

    . (29)  

The measurement matrix Ψ is shown in Equation (30).    Ψ=  

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

   .  

(30)

TABLE V M EAN L OCATION E RROR OF DIFFERENT A LGORITHMS

The noise covariance matrices Q and R of state vector and measurement vector are shown in Equations (31) and (32), respectively.    Q=  

   R=  

the CMFS sensing phase, experiments and simulations can be carried out. An experiment is then taken on to verify the performance of CMFS, in which a fixed point is chosen to test the positioning error. As shown in Fig. 10, the probability that the positioning error is less than 2 meters is about 63%. Furthermore, the mean location error (MLE) of CMFS is measured, which is contrasted with FS-knn [2] and Radar shown in Table V. From this experiment it can be seen that CMFS can provide a comparable result relative to the traditional fingerprint approaches.

2 0 0 0

0 2 0 0

0 0 0 0 1 0 0 90



8 0 0 0

0 8 0 0

0 0 0 0 1 0 0 90



  .  

  .  

(31)

(32)

Once the initial values of x and P are provided, the optimal fusion estimation can be achieved by following the five steps in EKF. V. E XPERIMENTS AND S IMULATIONS In this section we present both experimental and simulation results for the proposed scheme. The experiments are conducted in the 12th floor, 2A Building in Harbin Institute of Technology. As shown in Fig. 9, the experiment environment is a typical office environment with size of 1100 m2 . A number of off-the-shelf APs are deployed randomly in the experimental area. Galaxy Note II N7100 smartphones are used in the experiments and their parameters are displayed in Table IV. The floor plan shown in Fig. 9 is first transferred to a pixel picture from the original CAD drawing and is then uploaded into N7100. In the CMFS sensing phase, volunteers holding smartphones walk along the blue solid line in Fig. 9. After

Algorithms MLE (m)

CMFS 2.68

FS-knn 1.70

Radar 3.13

Furthermore, a simulation is conducted to evaluate the influence of different AP placements. All the APs used in CMFS can be off-the-shelf and the accurate placements of APs are not necessary. However it does not mean that there is no impact of AP placements on CMFS. RSSI distribution differs with different AP placements and it can impact fingperint positioning accuracy. Furthermore, the variation of fingerprint positioning accuracy will lead to variation of initial value of step estimation in PDR, which will impact the positioning error caused by the estimation of step length and heading direction. This simulation is conducted to see how the AP numbers and placements impact positioning accuracy. For a testing, four different AP placements are considered in this simulation. As shown in Fig. 11, 13 APs are adopted in placements 1 and 2, and 7 APs are used in placements 3 and 4. From Fig. 11, it can be seen that there is a big difference on cumulative positioning error between 7-AP placement and 13-AP placement. The probabilities of having positioning error less than 2 meters are 63% and 33% in placement 1 with 13 APs and placement 3 with 7 APs, respectively. Even though in the placements with the same number of APs, a low error difference appears caused by the different random arrangement of APs’ locations. From this simulation, it can be seen that though AP placement information is not needed in CMFS, it remains an important factor in the performance of CMFS. One more experiment is carried out that focuses on the performance of crowdsourcing based fingerprint sensing phase. Eight volunteers are participated in this experiment. Their heights are between 170cm to 175cm. Every volunteer carries one smartphone in texting mode. Volunteers walks with their

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1210

1211

1208

1212 1213

AP2 1206 1207

AP12

1224

1226 AP13 1227

AP1

1225

1209

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1223

1214 1215

AP6

AP11 1221 1222

AP7

AP10 AP8 1201

1220

positioning error less than 4 meters are 20%, 30%, 61%, 62%, 78%, with 1, 2, 5, 6, 8 volunteers, respectively. It can be seen that when the number of volunteers increases, the positioning performs better, due to the reason that the density of the radio map conducted by crowdsourcing based fingerprint sensing becomes higher when there are more volunteers participated in CMFS.

0.9 0.8 0.7 0.6

CDF

AP9

Experiments Floor Plan.

1

0.5 0.4

1

0.3

0.9

0.2

0.8

0.1

0.7

0 2

4

6

8

Positioning Error (m) Fig. 10.

0.6

10

CDF

0

Performance of Single Fixed Point Test in CMFS.

0.5 0.4

0.2

0.9

0.1

0.8

0

0.7

0

1

2

3

4

5

6

7

8

Positioning Error (m)

0.6

Fig. 12.

0.5 0.4 Placement 1 with 13 APs Placement 2 with 13 APs Placement 3 with 7 APs Placement 4 with 7 APs

0.3 0.2 0.1 0 0

2

4

6

8

10

Positioning Error (m) Fig. 11.

1 Volunteer 2 Volunteers 5 Volunteers 6 Volunteers 8 Volunteers

0.3

1

CDF

1219

1m

1218

AP5

1217

Fig. 9.

1203 AP4 1204

1216

1205

1202

AP3

Performance of Different AP Placements.

normal walking speeds in the experiment. Five groups of experiments are conducted with 1, 2, 5, 6, 8 volunteers, respectively. The performance of crowdsourcing sensing with five tests is shown in Fig. 12, the probabilities of having

Performance of Crowdsourcing Sensing.

Finally, a simulation is conducted to show the performance of EKF based fusion algorithm. A volunteer, whose height is 173cm, walks along the corridor in the experiment environment with his normal walking speed. The smartphone is carried in hand swinging mode. The motion route of this volunteer is shown as green solid line in Fig. 13. In Fig. 13, the blue chain line represents the estimated route of CMFS without PDR, which is called fingerprint sensing route. The red dotted line stands for the estimated route of CMFS with the fusion process of fingerprint and PDR, which is named EKF based fusion route. It is clearly seen that the fusion route is much smoother and closer to the real route than the fingerprint sensing route. Fig. 14 presents positioning error CDFs of using fingerprint sensing and EKF based fusion approaches, which further verify the effectiveness of the proposed EKF based

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Actual Route Fingerprint Sensing Route EKF based Fusion Route

Fig. 13.

Illustration of Estimated Routes of Fusion Approach.

1

ACKNOWLEDGEMENT

0.9

This work is supported by the Provincial Natural Science Foundation of Heilongjiang (No. ZD2017013), the National Natural Science Foundation of China (No. 61401119), National Science Foundation NeTS project (1423348), the National Science and Technology Major Project (No. 2015ZX03004002-004) and Natural Science Foundation of Jiangsu Province (BK20171023).

0.8 0.7

CDF

0.6 0.5 0.4 0.3

EKF based Fusion Fingerprint Sensing

0.2

R EFERENCES

0.1 0 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Positioning Error(m)

Fig. 14. Performance Comparison of Fingerprint Sensing and EKF based Fusion Approach.

fusion algorithm.

VI. C ONCLUSIONS A crowdsourcing and multi-source fusion based fingerprint sensing in smartphone localization is proposed in this paper. Motion sensors are adopted both in sensing phase and positioning phase in CMFS. An EKF based multi-source fusion algorithm is proposed. Different from the traditional fingerprint, labor and time consuming site survey process is removed in CMFS. Radio map is constructed by volunteer ordinary walks. The new acquisition method saves more time and labor compared to the traditional mechanism. Although the radio map of CMFS can be sparse and unstable, it still presents a good performance owing to the fact that the fusion algorithm takes full advantages of PDR and floor plan. The experiments and simulations verify the efficiency of proposed approaches. Future research work can address other practical issues such as device diversity and how to improve robust of proposed scheme in more other practical positioning environments, etc.

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