Reference Device-Assisted Adaptive Location

sensors Article

Reference Device-Assisted Adaptive Location Fingerprinting Dongjin Wu and Linyuan Xia * School of Geography and Planning, Sun Yat-Sen University, 135 # Xingangxi Road, Guangzhou 510275, China; [email protected] * Correspondence: [email protected]; Tel./Fax: +86-20-8411-5833 Academic Editor: Vittorio M. N. Passaro Received: 3 March 2016; Accepted: 16 May 2016; Published: 1 June 2016

Abstract: Location fingerprinting suffers in dynamic environments and needs recalibration from time to time to maintain system performance. This paper proposes an adaptive approach for location fingerprinting. Based on real-time received signal strength indicator (RSSI) samples measured by a group of reference devices, the approach applies a modified Universal Kriging (UK) interpolant to estimate adaptive temporal and environmental radio maps. The modified UK can take the spatial distribution characteristics of RSSI into account. In addition, the issue of device heterogeneity caused by multiple reference devices is further addressed. To compensate the measuring differences of heterogeneous reference devices, differential RSSI metric is employed. Extensive experiments were conducted in an indoor field and the results demonstrate that the proposed approach not only adapts to dynamic environments and the situation of changing APs’ positions, but it is also robust toward measuring differences of heterogeneous reference devices. Keywords: adaptive location fingerprinting; interpolation; Universal Kriging; device heterogeneity; differential RSSI

1. Introduction The explosive growing of location-based services (LBS) has brought high demands for location information, and fostered research interest in positioning technology. Besides Global Navigation Satellite Systems (GNSS), indoor positioning technology has gained much attention. Existing wireless infrastructures such as WiFi access points (AP), that are designed for ubiquitous network access and communication, show great potential for providing wireless positioning and augmenting GNSS indoors. Received signal strength indicator (RSSI)-based location fingerprinting approaches are often adopted in indoor wireless positioning systems. Although the construction of radio maps involves great labor costs, location fingerprinting can provide more accurate estimations compared to other techniques, such as Cell-ID and trilateration, especially in dynamic environments. Location fingerprinting involves two steps: radio map construction and location estimation. The radio map is a combination of signal strength profiles of the APs that cover the target area. It is always approximated by discrete location fingerprints collected at predefined calibration points. Based on the constructed radio map, online RSSI measurements are matched to find the most similar location fingerprints which are further used for location estimation [1]. For practical use, constructing a radio map is a burdensome task. Even worse, the radio map needs continuous updating to accommodate the changing environments. Environmental dynamics, such as people moving, and doors opening and closing can cause rapid RSSI fluctuations. Moreover, the movement of APs or furniture will change the RSSI profiles. All the mentioned factors can lead to an outdated radio map which deteriorates the location fingerprinting performance and therefore repeated site surveys or calibrations are needed Sensors 2016, 16, 802; doi:10.3390/s16060802

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from time to time. As a result, approaches that adapt to dynamic and complex environments are more applicable [2–9]. However, heterogeneity [10] of reference devices is an additional issue as for adaptive approaches which always rely on real-time or online RSSI samples measured by a group of reference devices or users’ devices. Unfortunately, the issue of reference device heterogeneity has not been addressed in former adaptive approaches. In this paper, we propose an approach that adapts to dynamic and complex environments and is robust with respect to reference device heterogeneity. Based on real-time RSSI samples measured by a group of reference devices, a modified Universal Kriging (UK) algorithm is applied to estimate radio maps. In addition, a differential RSSI metric is applied to alleviate the impacts of reference device heterogeneity. The contributions of our work can be summarized as follows: ‚

‚ ‚

A modified UK method that builds semivariograms relying on a novel way is proposed for the estimation of RSSI. The modified UK-based adaptive location fingerprinting approach can provide better location performance, compared with the conventional UK-based approach. Compared with other adaptive techniques, our proposed approach can not only adapt to dynamic environments, but also accommodate to changing AP positions. The issue of reference device heterogeneity in adaptive approaches is addressed for the first time. A differential RSSI metric is verified to be appropriate to alleviate the impacts caused by heterogeneous reference devices.

The rest of this paper is organized as follows: Section 2 presents related work on adaptive approaches for radio map construction and methods for handling device heterogeneity, whereas Section 3 introduces the proposed adaptive location fingerprinting method. Experiments and results are shown in Section 4. Section 5 draws the conclusions. 2. Related Work 2.1. Adaptive Approaches for Radio Map Construction Dynamic environments have been widely considered in research on wireless positioning. To obtain robust estimates of RSSI, mean or median sample values are applied. However, these estimates that rely on samples from a short time period cannot represent exactly the long term characteristics of RSSI measurements, not to mention the fact that RSS samples may have complex distributions during different time periods. For example, RSS values at a sampling point sometimes approximate a Gaussian distribution [11]. However, the distributions are always skewed [12], and sometimes with a long tail [13]. Besides, two peak distribution [14] and multimodal distribution [12] are also found. To overcome the limitations of samples over specific time periods, and to reduce the heavy data collection burden, crowd-sourcing-based methods [15,16] or reference device-based methods [2–9] provide alternatives. Our work focuses on the reference device-based manner. On the one hand, RSSI measurements can be mapped to geographical distances [2], and trilateration is then applied to estimate locations. On the other hand, RSSI measurements can be used to estimate the signal strength profiles of APs [3–9], and location fingerprinting is then used for location estimation. In this paper, the discussions follow the latter approach. Although we can place one reference device at each predefined point just as the LANDMARC system does [6], the method relies on too many reference devices. Applying interpolation methods can effectively reduce the number of reference devices. For example, in the LEASE system [7], the Akima Spline interpolation method is used to estimate radio maps. Besides, other interpolation methods, such as the inverse distance weighting (IDW) [17,18], radial basis function (RBF) [19], linear [18,20], and Kriging ones [21–23] can be applied to generate radio maps too. Before applying these interpolation methods, we should learn the characteristics of each one and make them suit the estimation of RSSI. For example [24], the IDW method estimates the values at unsampled points using a linear combination of values at sampled points weighted by an inverse value of the distance from the unsampled point to the sample points. The assumption is that

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the closer the distance is, the more similar are the values between the unsampled point and the sample point. The nearest neighbours method predicts the value at an unsampled point based on the value of the nearest sample. Among these methods, the Kriging methods first employ the idea of geostatistics that besides the relative positions between the unsampled point and the sample points, additionally the spatial correlation of the variables is considered. Unlike the above conventional interpolation methods, radio signal propagation model-based interpolation methods take the characteristics of radio signals into account and therefore to some extent can provide more accurate RSSI estimates. For example, Atia et al. [8] proposed a solution that is based on online RSSI samples from the existing WLAN APs which have been modified as a combination of reference devices and conventional APs. In the solution, the Gaussian Process Regression (GPR) method was used to augment the Log distance path loss model to obtain AP signal strength profiles. Similarly, modified APs are also applied by Du et al. [9]. With additional self-made sensor anchors, they use the Geography Weighted Regression (GWR) method to obtain a more accurate signal propagation model to construct radio maps. The so called RSSI Geography Weighted Regression (RGWR) is a variable-coefficient regression method that maintains as a significant feature the fact that signals attenuate with different characteristics in different regions. In order to apply the RGWR method, the coordinates of APs and anchors, as well as the distances between each pair of anchor and AP are necessary, besides signal strength information. For the above two approaches, although the modified APs can be replaced by reference devices and conventional APs, APs’ positions are required, which brings additional information to manage and are unpractical for random APs that are much more numerous than deployed APs. Based on the Log distance path loss propagation model, Lee et al. [25] also proposed to refine the model for each partitioned cell depending on a high order Voronoi diagram which is generated according to the reference points. In their method, APs’ positions are estimated simultaneously when estimating the parameters of the propagation model. More than a radio signal propagation model, the RSSI regression relationship between the sampling points of the radio map and neighboring reference devices can be obtained and utilized too. New radio maps can be estimated based on the regression relationship [3–5]. For example, Yin et al. [3] used a decision tree to model the relationship. According to the deployment of all reference devices, the reference-point value space is partitioned into several regions. An assumption is that the RSSI relationship between reference devices and the mobile client is linear when they are in the same region. With the trained model, radio maps can be updated effectively even with one reference device. Wang et al. [4] proposed to use neural networks to build the relationship. In their work, a three-layer structure is applied, and data from all the reference devices are used as the inputs, whereas data at each sampling point is used as the output. Although these methods perform well in time-varying environments, the assumption of invariable RSSI regression relationships between a sampling point and the neighboring calibration points is not true once some APs’ positions are changed. 2.2. Methods for Handling Device Heterogeneity None of the former adaptive approaches solves the issue of device heterogeneity which prevents those approaches from being practically applied. Since receivers with different hardware and software measure totally differently from each other, it is necessary to compensate the differences because the devices that are used for location estimation are various, such as notebooks, smart phones, etc. The solutions for tackling device heterogeneity can be divided into two categories: creating a robust metric and mapping the original values to a standard value space [26]. Depending on the observations, RSSI samples measured by two different devices at the same place have a consistent relationship [27–29]. Thus RSSIs measured by different devices can be mapped to reasonable values based on the relationship. First a linear relationship [27] is found between the RSSI measurements of two devices. Although manual calibration always produces a large improvement in terms of location accuracy [28], it is tedious since every device needs calibration. As a result, automatic calibration has drawn more attention. For example, based on a linear relationship, Haeberlen et al. [28] investigated three manners—manual,

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automatically obtain a transformation function for mapping WiFi signal patterns from an unknown quasi-automatic and automatic calibration—to approximate the model. Tsui et al. [29] proposed an device to the training device. Experimental results show that position error caused by device unsupervised learning method to automatically obtain a transformation function for mapping WiFi heterogeneity reduced about device 4%. However, these methods cannot results work without learning signal patternsisfrom an unknown to the training device. Experimental show thataposition procedure, and they can only work in pairwise mode. Both of these characteristics limit their error caused by device heterogeneity is reduced about 4%. However, these methods cannot work usability. the contrast, robust the step and break the characteristics pairwise mode. without On a learning procedure, andmetrics they cancan onlysave work in learning pairwise mode. Both of these Differential RSSI [15,30–35] is believed to be effective since it eliminates the antenna gains of limit their usability. On the contrast, robust metrics can save the learning step and break the pairwise receivers from a theoretical view [30], but it uses dimension less than original RSSI vector [31] mode. Differential RSSI [15,30–35] is believed to beone effective since it eliminates the antenna gains of and may create a greater range of locations that satisfy a given sample set of RSSI signals [32]. The receivers from theoretical view [30], but it uses one dimension less than original RSSI vector [31] and may create a greater range of locations that satisfy a given sample set of RSSINsignals [32]. The form of ˜ there ¸ form of the differential RSSI vector is presented in [33], and are 2 elements in the vector N the differential RSSI vector is presented in [33], and there are



elements in the vector (N denotes

(N denotes the number of the elements in the original RSSI2 vector) in which only (N − 1) of the the number of the elements in the original RSSIRSSI, vector) in which only (N ´also 1) of the elements are elements are independent. Besides differential other metrics were applied in previous independent. Besides differential RSSI, other metrics werefingerprinting also applied in previous studies. For example, a method named hyperbolic location (HLP) basedstudies. on RSSIFor ratio example, a method named hyperbolic location fingerprinting (HLP) based on RSSI ratio is proposed is proposed in [36]. Although the proposed RSSI ratio is observed to be more stable than absolute in [36].there Although proposedanalysis RSSI ratio observed to why be more stable than absolute values, there is no of values, is no the theoretical onis the reason it mitigates the measuring differences theoretical analysis on the reason why it mitigates the measuring differences of heterogeneous heterogeneous devices. Cheng et al. [37] proposed a combined metric, the ratio of signaldevices. strength Cheng et al. [37] proposed a combined metric, the ratio caused of signalby strength whichand eliminates differences which eliminates measuring differences devicedifferences heterogeneity dynamic measuring differences by device needs heterogeneity and dynamic However, this environments. However,caused this approach RSSI readings from environments. three closely located antennas approach needs RSSI readings from three closely located antennas which are usually unavailable for which are usually unavailable for common users’ devices. common users’ devices.

3. 3. Reference Device-Assisted Reference Device-AssistedAdaptive AdaptiveLocation Location Fingerprinting Fingerprinting Reference adaptivelocation location fingerprinting approach consists tworadio steps: Referencedevice-assisted device-assisted adaptive fingerprinting approach consists of two of steps: radio construction and location estimation. However, the two are both performed online, mapmap construction and location estimation. However, the two steps are steps both performed online, which is which is different from conventional location fingerprinting. The following subsections present different from conventional location fingerprinting. The following subsections present the approach inthe approach in detail. First, modified UK interpolation proposed for the interpolation of RSSI. detail. First, a modified UKainterpolation is proposed for theisinterpolation of RSSI. Second, a differential Second, a differential RSSI metric is adopted and deduced for multiple reference device-based RSSI metric is adopted and deduced for multiple reference device-based location estimation. The flow location Theapproach flow chart of the proposed is depicted in Figure 1. chart ofestimation. the proposed is depicted in Figureapproach 1.

Figure adaptivelocation locationfingerprinting. fingerprinting. Figure1.1.Flow Flowchart chartofofreference reference device-assisted device-assisted adaptive

3.1. Radio Map Construction 3.1. Radio Map Construction Radio signals large-scaleattenuation attenuationand andsmall-scale small-scale fading [38]. Radio signalshave havetwo twoinherent inherent characteristics: characteristics: large-scale fading [38]. Large-scale the impacts impactsofofthe thetravel travel paths of signals. Small-scale fading Large-scaleattenuation attenuationindicates indicates the paths of signals. Small-scale fading refersrefers to to the theimpacts impactsofoflocal local environmental dynamics. The fluctuations caused by the small-scale fading environmental dynamics. The fluctuations caused by the small-scale fading are arealways always time-varying, are highly correlated with human [5]. For during example, time-varying, andand theythey are highly correlated with human activitiesactivities [5]. For example, during work hours, RSSI values fluctuate more rapidly, and if offline calibration is conducted work hours, RSSI values fluctuate more rapidly, and if offline calibration is conducted during this during time this time period, will be unsuitable for online usenon-work during non-work hours. Thusconstruct we mustsuitable construct period, it will beit unsuitable for online use during hours. Thus we must suitable radioformaps forestimation. location Radio estimation. Radio maps estimated using real-time can RSSI radio maps location maps estimated by using real-timeby RSSI measurements be the candidates for the this.candidates for this. measurements can be 3.1.1. RSSI Estimation by Using the UK [39] Method To construct a radio map which is a combination of location fingerprints, RSSI estimates with respect to each AP at predefined points should be obtained first. In this paper, we choose UK as the primary estimation method, and propose a novel way of obtaining the semivariogram models accommodating the characteristics of RSSI spatial distribution.

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3.1.1. RSSI Estimation by Using the UK [39] Method To construct a radio map which is a combination of location fingerprints, RSSI estimates with respect to each AP at predefined points should be obtained first. In this paper, we choose UK as the primary estimation method, and propose a novel way of obtaining the semivariogram models accommodating the characteristics of RSSI spatial distribution. Kriging interpolants are but variants of the linear estimator [40]: n ÿ

Zˆ px0 q ´ m px0 q “

ωi rZ pxi q ´ m pxi qs

(1)

i “1

where m px0 q and m pxi q are expected values of Z px0 q and Z pxi q. x0 is the unsampled point, and {xi } are the neighboring sampled points. ωi is the weight of sampled point xi . Z px0 q is treated as a random field with a trend component, m px0 q and a residual component, R px0 q “ Z px0 q ´ m px0 q. For RSSI, m px0 q is not just a constant but a linear or higher-order trend in the (x, y) coordinates of the data point. Assume that: p ÿ m pxq “ β k sk pxq (2) k“1

where, sk p¨q is a function of location, β k is an unknown parameter. This kind of Kriging with a trend is known as UK. Substituting Equation (2) into Equation (1), we get: Zˆ px0 q “

n ř

p ř

ωi Z pxi q `

i “1

β k sk px0 q ´

n ř

ωi

i “1

k “1

p ř

β k sk pxi q

(3)

k “1

We require: p ÿ

β k sk px0 q ´

p ÿ

n ÿ

ωi i“1

k “1

β k sk pxi q “ 0

(4)

k “1

leading to an UK estimator: Zˆ UK px0 q “

n ÿ

ωiUK Z pxi q

(5)

i “1

with:

p ÿ

β k sk px0 q “

p ÿ

n ÿ

β k sk pxi q

(6)

ωi sk pxi q “ sk px0 q , k “ 1, ..., p

(7)

ωi i “1

k “1

k“1

For simplification, we require: n ÿ i“1

Note that we can still hold the constraint Equation (7). Thus we have a minimization problem with p constraints that can be solved using Lagrange multipliers, λk : L “ σE2 px0 q ` 2

p ř k “1

„ λk

n ř

 ωi sk pxi q ´ sk px0 q

(8)

i “1

By solving the partial derivatives λk and ω i , we get equations of the Kriging weights: $ n p “ ` ˘‰ ř ř ’ ’ ω j Cov Z pxi q , Z x j ` λk sk pxi q “ Cov rZ pxi q , Z px0 qs, i “ 1, ..., n & j “1

’ ’ %

k “1

n ř i “1

ωi sk pxi q “ sk px0 q , k “ 1, ..., p

(9)

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6 of 17 the solution to these equations, we can obtain the weights. The covariance is generally derived from the semivariogram model γ p¨q which has the following form: where Z(x) and Z(x + h) are values of two points separated by vector h. The semivariogram depends ” ı 1 to only on the vector h. There are several ways estimate the model. The classical formula is: γ phq “ E pZ pxq ´ Z px ` hqq2 (10) 2 2 1 ˆ  h   Z  xi   Z  x j  (11) where Z(x) and Z(x + h) are values of two2 N points separated by vector h. The semivariogram depends  h  xi  x j h only on the vector h. There are several ways to estimate the model. The classical formula is: where xi and xj are a pair of two points separated by vector h, and N(h) denotes the number of pairs. ÿ ` ` ˘˘2 1 γˆ phq “ Z pxi q ´ Z x j (11) 2N phq 3.1.2. A Novel Method for Constructing the Semivariogram Models x ´ x “h



i



j

Conventional semivariogram model-based UK can certainly be used for RSSI estimation. where xi and xj are a pair of two points separated by vector h, and N(h) denotes the number of pairs. However, by considering the characteristics of then spatial RSSI distribution, the performance may be improved. The spatial distribution of RSSI from an AP is similar to light waves spreading out 3.1.2. A Novel Method for Constructing the Semivariogram Models from a point light source. Two pairs of data points that have equal separation distances may Conventional semivariogram model-based UKin canFigure certainly used forof RSSI estimation. produce totally different variances. 2a, be two pairs data points A,However, B and C,  For example,  by considering the characteristics of then spatial RSSI distribution, the performance may be improved. D are separated by vectors AB and CD which have equal norms and the same orientations. The spatialthe distribution of RSSI from anpoint AP isAsimilar light from point light However, RSSI variance between and Btocan bewaves totallyspreading different out from the acounterpart source. Two pairs of data points that have equal separation distances may produce totally different between points C and D, since the resulting factors are different. Besides environmental factors, the variances. For example, in Figure 2a, two pairs of data points A, B and C, D are separated by vectors two á pairsáof data points have their own specific factors. For points A and B, the main factor is the and CDofwhich have equal normsofand same orientations. However, RSSI AB difference attenuation directions thethe radio signals. While for points Cthe and D, variance the mainbetween factor is point A and B can be totally different from the counterpart between points C and D, since the resulting the difference of travel distances between radio signals. As we know, the impacts on RSSI caused by factors are different. environmental factors, directions the two pairs data points have their specific radio signals’ travelBesides distances and attenuation areoftotally different, and own if the RSSI factors. For points A and B, the main factor is the difference of attenuation directions of the radio variances caused by the two factors have not been treated discriminatively, the obtained signals. While for points C not andbe D,exact the main factor is the difference of travel distances between radio semivariogram model will enough. signals. As we know, the impacts on RSSI caused by radiovector signals’ travel distances attenuation In this paper, we propose to decompose the original h between two dataand points into two directions are totally different, and if the RSSI variances caused by the two factors have not vectors h1 and h2 according to the differences of attenuation directions and travel distances ofbeen two treated discriminatively, thetwo obtained semivariogram model will not be exact enough. radio signals. In Figure 2b, data points P1 and P2 are presented.

(a)

(b)





á AB á Figure 2. (a)Two pairs of data points A, B and C, D separated by two equal vectors and CD ; Figure 2. (a)Two pairs of data points A, B and C, D separated by two equal vectors AB and CD ; (b) the (b) the original vector h is decomposed into h1 and h2 according to the positions of the transmitter original vector h is decomposed into h1 and h2 according to the positions of the transmitter and two and two sampled points. sampled points.

 We have the original vector h ( P1 P2 ). Suppose the spatial location of the transmitter is known, In this paper, we propose to decompose the original vector h between two data points into two so we select P1 which is closer to the transmitter. Then a point P2’ that has the same distance to the vectors h1 and h2 according to the differences of attenuation directions and travel distances of two transmitter as the selected point P1 can be found in the travel path of the radio signal passing radio signals. In Figure 2b, two data and P2 are presented.  points P1  ' ' P through P2. Then we can get h1 ( PP ) and h 2 ( 1 2 2 P2 ). Note that: h = h1 + h2

(12)

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á

We have the original vector h ( P1 P2 ). Suppose the spatial location of the transmitter is known, so we select P1 which is closer to the transmitter. Then a point P2 ’ that has the same distance to the transmitter as the selected point P1 can be found in the travel path of the radio signal passing through á

1

á 1

P2 . Then we can get h1 ( P1 P2 ) and h2 ( P2 P2 ). Note that: h “ h1 ` h2

(12)

Following the above method for deriving two sub-vectors, we can obtain two semivariograms γˆ 1 ph1 q and γˆ 2 ph2 q from the original set of data points. Semivariogram γˆ 1 ph1 q is with respect of the information of RSSI structure on the difference of local environments in the travel paths of radio signals, whereas semivariogram γˆ 2 ph2 q represents the RSSI structure information on the difference of travel distances of the radio signals. The two semivariograms are built independently, and then they are combined as a nested structure γˆ phq: γˆ phq “ γˆ 1 ph1 q ` γˆ 2 ph2 q

(13)

By the way, if the spatial location of the transmitter is unknown, we can still rely on the traditional method to obtain γˆ phq. 3.2. Differential RSSI-Based Location Estimation 3.2.1. Eliminating the Impacts of Heterogeneous Reference Devices In the proposed approach, RSSI is estimated by using the data measured by multiple reference devices. Since RSSI values are related to the configurations of the transmitter and receiver, it is reported that the value of the difference caused by device heterogeneity has a level of 10 to 20 dBm [33]. As a result, the estimated RSSI also contains heterogeneous measurement differences. We conducted an experiment to verify the difference between the estimated RSSI and observed RSSI at the same location. We used a mobile device to measure RSSI values from nine WLAN APs at a location. For each AP, we collected 100 samples, and then obtained the mean value of the RSSI values. That is the observed RSSI sample. At the same location, we also use the modified UK method to estimate RSSI values with respect to the nine APs. Figure 3a presents the estimated and observed RSSI values with respect to the nine detected WLAN APs. Obviously, the more similar these two RSSI samples are the better. However, there are differences (8 to 10 dBm) between the estimated and observed values. Thus, the negative impacts of heterogeneous reference devices should be alleviated beforehand. Since it is hard to establish relationships between pair-wise devices for the proposed multiple reference devices-based solution, we apply the differential value metric which does not need a training process. According to [30], differential RSSI eliminates receiver gains, and therefore reduces the impact of device heterogeneity. Since the estimated RSSI is derived from the data from multiple reference devices, it is verified whether differential RSSI is suitable for the elimination of measuring differences in the estimated RSSI. According to Equation (8), estimated RSSI is a weighted sum of measured RSSI values by multiple reference devices. Suppose: ÿ RSSIi,j “ k t RSSIt,j (14) t

where RSSIt,j denotes the RSSI measured by reference device t from APj , and kt denotes the associated weight. Thus, differential RSSI between RSSIi,1 and RSSIi,2 has the form of: ∆RSSI1,2 “ RSSIi,1 ´ RSSIi,2 “

ÿ t

k t pRSSIt,1 ´ RSSIt,2 q

(15)

By the way, if the spatial location of the transmitter is unknown, we can still rely on the traditional method to obtain ˆ  h  . 3.2. Differential RSSI-Based Location Estimation Sensors 2016, 802 3.2.1.16, Eliminating the Impacts of Heterogeneous Reference Devices

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In the proposed approach, RSSI is estimated by using the data measured by multiple reference devices. Since RSSI values are related to the configurations of the transmitter and receiver, it is We can observe from the above expression that, although the estimated RSSI is derived from the reported that the value of the difference caused by device heterogeneity has a level of 10 to 20 dBm [33]. data measured by several reference devices, measuring differences are still reduced since the receiver As a result, the estimated RSSI also contains heterogeneous measurement differences. We gains conducted are eliminated likewise in ∆RSSI . As Figure 3b presents, differential values respectively an experiment to verify the1,2difference between the estimated RSSI and observed RSSI at derived from observed andaestimated RSSIstoare plotted. Since ninefrom APs nine are observed, 36 at pairs the same location. RSSIs We used mobile device measure RSSI values WLAN APs a of APs are used to calculate differential values. Compared with Figure 3a, observed differential RSSIs location. For each AP, we collected 100 samples, and then obtained the mean value of the RSSI and the estimated ones the same point appear similar in Figure 3b. Thus in differential values. That is the atobserved RSSI sample. Atmore the same location, we also use the modified UKRSSI method to estimate RSSI values respect to themore nine APs. metrics, the degree of similarity canwith be represented accurately. -30 Estimated -40

Observed

RSS (dBm)

-50 -60 -70 -80 -90 -100 -110 1

2

3

4

5

6

7

8

9

AP index

(a) 40 Estimated

30

Observed

RSS (dBm)

20 10 0 -10 -20 -30 -40 1

3

5

7

9

11 13 15 17 19 21 23 25 27 29 31 33 35

AP pair index

(b) Figure 3. Observed values and estimated values by the modified UK from different APs (or AP pairs)

Figure 3. Observed values and estimated values by the modified UK from different APs (or AP pairs) at the same location. (a) Raw RSSI; (b) Differential RSSI. at the same location. (a) Raw RSSI; (b) Differential RSSI.

3.2.2. Location Estimation Based on the estimated radio map, K Weighted Nearest Neighbors (KWNN) is used for location estimation: O K K ÿ ÿ ˆ X“ Xi w i wi (16) i“1

i “1

where Xi denotes the location of selected location fingerprint, K denotes the number of selected location fingerprints, and wi denotes the weight which is always derived from the inverse distance between two RSSI vectors (one is the online measurement, and the other is the related location fingerprint). For example, the inverse Euclidean distance: Og fÿ fN ` ˘2 wi “ 1 e RSSIi,j ´ RSSI0,j

(17)

j “1

where N denotes the number of APs, RSSI0,j denotes the online measurement from the jth AP, and RSSIi,j denotes the measurement in the location fingerprint from the jth AP. This kind of calculation of weight doesn’t consider measuring differences which may degrade localization accuracy of a system. In our adaptive location fingerprinting, radio maps are generated by multiple reference devices.

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And measuring difference becomes a crucial problem for˜location ¸ estimation. We apply the form of N differential RSSI vector presented in [33]. Although it has elements (N denotes the number of 2 the elements in original RSSI vector) which seems redundant since only (N ´ 1) of the elements are independent, it is free from the process of selecting a key element which is essential for generating a vector to contain independent elements only. Given the form of differential RSSI vector, the weight wi of the selected location fingerprint is still derived from the inverse Euclidean distance between two differential RSSI vectors: Sensors 2016, 16, 802 9 of 17 Og f N ´1,N vector, the weight w i of theÿ selected`` location fingerprint is still from the inverse ˘˘ Euclidean f ˘ derived ` 2 e w “ 1 (18) distance ibetween two differential RSSI RSSI vectors: i,j ´ RSSIi,k ´ RSSI0,j ´ RSSI0,k j“1,k“2,jăk wi  1

N 1, N

   RSSI

j 1, k  2, j  k

i, j

 RSSI i , k    RSSI 0, j  RSSI 0, k 



2

(18)

4. Experimental Evaluation 4. Experimental Evaluation

4.1. Setup 4.1. Setup

The proposed approach was evaluated on the fifth floor in a research building. The floor plan is The proposed approach was evaluated on the fifth floor in a research building. The floor plan is shown in Figure shown4.in Figure 4.

(a)

(b) Figure 4. Layout of the test bed. (a) Spatial distributions of offline survey points; (b) Spatial

Figure 4. Layout of the test bed. Spatial distributions distributions of multiple reference(a) devices and online test points. of offline survey points; (b) Spatial distributions of multiple reference devices and online test points. The area measures 48 × 21 m2, and the test bed covers the whole corridor and three rooms. Sixteen PCs marked as RD1 to RD16 in Figure 4b are uniformly placed to play the roles of reference devices. There are whichtest is embedded with one three types of IEEE 802.11 area measures 4810ˆdesktops, 21 m2 ,each andof the bed covers theofwhole corridor and three wireless network interface cards (WNICs): Netcore NW335, D-link DWA-123, and D-link

The rooms. Sixteen PCs marked as RD1 to RD16 in Figure 4b are uniformly placed to play the roles of reference devices. There are 10 desktops, each of which is embedded with one of three types of IEEE 802.11 wireless network interface cards (WNICs): Netcore NW335, D-link DWA-123, and D-link DWL-G122.

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The others are laptops, two HP Mini 110s with Broadcom 802.11 b/g WNIC, two Lenovo E40s with Intel(R) dual band wireless-AC 3160 WNIC, one Acer Aspire 5100 with Atheros AR5005G WNIC, and one LenovoThinkpadSL400with Atheros AR5008 WNIC. In the experiments, the reference devices were activated to collect real-time RSSI data. A Dell Inspiron 14-7447 PC with Intel(R) Dual Band Wireless-AC 3160 was used as the mobile device. Using the mobile device, we collected test data during four time periods in two days for location calculation at 43 points marked by circles in Figure 4b. Details of the four time periods are as follows, one time period, 7 p.m. to 8 p.m. on the first day, and three time periods 10 a.m. to 11 a.m., 3 p.m. to 4 p.m., and 4 p.m. to 5 p.m. on the next day. At each point 100 samples were collected. To form an offline radio map, the mobile device was used to collect 88 location fingerprints at the survey points marked by crosses in Figure 4a. At each point we also collected 100 samples. All the devices have the same sample frequency (1 Hz). Tens of wild WLAN APs with unknown positions can be scanned in the area, and three more marked by AP1, AP2, AP3 are added. The wild APs may be on the same floor outside this test bed or on different floors, or even in different buildings. All the wild and added APs were used for positioning. However none of the APs covers the entire area, and at each sampling point 10 to 20 APs can be scanned on average. To evaluate the proposed approach, two interpolants, IDW and Universal Krigingas well as the neural network (NN)-based approach proposed in previous work [4] are used as the baseline.Since location results based on the offline radio map are not so good which prevent those offline radio map-based adaptive approaches [3,4] from providing ideal location performances, we use the RSSIs estimated by our modified UK method to train the NN-based regression functions between each survey point and its neighboring reference devices. Default settings for all the experiments are as follows, the threshold forneural network training are 2000 times, the smoothing window size for the data used for RSSI estimation and location estimation is 20K in KWNN for location estimation equals 8. 4.2. Results and Analysis For Kriging interpolants, the semivariogram model should be determined first. In the following tests, we applied the models approximated depending on the collected offline radio map. Although the semivariograms are derived from the offline radio map, the two UK interpolants, conventional UK and the modified UK still produce accurate location results as presented in the following tests. This fact implies that the two UK interpolants both adapt to dynamic environments. As for each of the added APs, the semi-variances of RSSI values in the test area with respect to different manners were calculated and presented in Figure 5, respectively. Each curve for an AP was obtained by using a different manner, and it represents quantitative structural characteristics of RSSIs’ spatial distribution in the test area. We find that the obtained statistical results based on the difference of travel distances of radio signals are similar with the results based on the conventional manner. But the results based on the difference of attenuation directions of radio signals are somewhat different. It implies that a combination of semivariograms based on the difference of attenuation directions and the difference of travel distances of radio signals contains more information about the environments than conventional semivariogram, since the difference of attenuation directions of radio signals represents the difference of local environments in the travel paths of radio signals. And therefore, the combination can enhance the prediction of RSSI. To fit the experimental semivariogram, we choose the spherical model [40]: $ 0, h“0 ’ ’ ˆ & ´ ¯3 ˙ γ phq “ C0 ` C 32 ha ´ 12 ha , 0ăhďa ’ ’ % C0 ` C, hąa

(19)

where a denotes range, C0 denotes nugget, and C0 + C denotes sill. γ p0q = 0 means a discontinuity at the origin, which is called the “nugget effect”. For each AP, the parameters C0 and C were obtained according to the approximated model, but the parameter a was assumed as a fixed value, 8 m.

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(c) AP3 Figure 5. Semivariograms of different APs, (a) AP1; (b) AP2; and (c) AP3 obtained by using three Figure 5. Semivariograms of different APs, (a) AP1; (b) AP2; and (c) AP3 obtained by using three different manners. different manners.

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With the given parameters of UK interpolants, experiments were first conducted to With the parametersofofthe UKradio interpolants, experiments werereal-time first conducted to evaluate the evaluate thegiven performances maps estimated by using data against the offline performances of the radio mapsperiods, estimated by using datafirst against radio map during radio map during two time 7 p.m. to 8 real-time p.m. on the day the andoffline 10 a.m. to 11 a.m. on the two time periods, 7 p.m. to 8 p.m. the first day and 10 a.m. 11 a.m. deviations on the second Figure 6 second day. Figure 6 shows the on average location errors and to standard (SD)day. of the location shows theAll average location estimated errors andradio standard deviations (SD) ofresults the location All the real-time errors. the real-time maps provide better in twoerrors. time periods, compared estimated radio maps results two time periods, compared to theradio offline radio It to the offline radioprovide map. It better implies that in it is possible to replace the offline map by map. real-time implies is possible replace the offline map byaverage real-time radio errors maps for use. radio that mapsit for practicaltouse. Estimated radioradio maps-based location are practical all around 2 m. Estimated maps-based errors all around 2 m. Andwith we can that And weradio can also observeaverage that thelocation modified UKare performs comparable thealso NNobserve method, and theperforms modifiedbetter UK performs with methods. the NN method, and performs better thansemivariogram the UK and than thecomparable UK and IDW As mentioned above, all the IDW methods. As mentioned above, all the semivariogram models are the offlineadapt radio to models are derived from the offline radio map, and therefore thederived two UKfrom interpolants map, and therefore the two UK interpolants adapt to dynamic environments. dynamic environments. 10

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(b) Figure 6. Average location errors (SDs of the location errors are used as the error bars) with respect Figure 6. Average location errors (SDs of the location errors are used as the error bars) with respect to to the offline radio map and the radio maps estimated by using the NN, IDW, UK, and the modified the offline radio map and the radio maps estimated by using the NN, IDW, UK, and the modified UK UK methods respectively in two time periods, (a) 7 p.m. to 8 p.m. in the first day and (b) 10 a.m. to methods respectively in two time periods, (a) 7 p.m. to 8 p.m. in the first day and (b) 10 a.m. to 11 a.m. 11 the next day. in thea.m. nextin day.

Next, we tested the approaches in the situations of changing APs’ positions. The experiments Next, we tested the approaches in the situations of changing APs’ positions. The experiments were conducted during another two time periods, 3 p.m. to 4 p.m. and 4 p.m. to 5 p.m. The were conducted during another two time periods, 3 p.m. to 4 p.m. and 4 p.m. to 5 p.m. The involved involved APs are the added ones. First, the positions of two APs were changed (we interchanged APs are the added ones. First, the positions of two APs were changed (we interchanged the positions the positions of AP1 and AP2), and then three APs changed their positions (AP1 moves to the of AP1 and AP2), and then three APs changed their positions (AP1 moves to the position of AP3, AP2 position of AP3, AP2 moves to the position of AP1, and AP3 moves to the position of AP2). Figure 7 moves to the position of AP1, and AP3 moves to the position of AP2). Figure 7 presents the average presents the average location errors and SDs of the location errors. Since the test depicted in location errors and SDs of the location errors. Since the test depicted in Figure 6b is conducted on Figure 6b is conducted on the same day as the two tests here, and is without the impact of changing

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the same day as the two tests here, and is without the impact of changing APs’ positions,13itofis used Sensors 2016, 16, 802 17 as the baseline for comparison. For the offline radio map and the NN-based method, compared with the location resultsitpresented in Figure average location errors increase about and 100%, APs’ positions, is used as the baseline6b, forthe comparison. For the offline radio map and the 25% NN-based method, when compared location results presented in Figurein6b, the average respectively, two with APs’ the positions are changed (as presented Figure 7a), andlocation increaseerrors over 60% increase about 25% when and 100%, when two APs’ positions are changed (as presented in and 300%, respectively, threerespectively, APs’ positions are changed (as presented in Figure 7b). This implies Figure 7a), and increase over 60% and 300%, respectively, when three APs’ positions are changed that the NN-based method cannot accommodate the change of APs’ positions. However, IDW and (as presented in Figure 7b). This implies that the NN-based method cannot accommodate the UK interpolants are flexible with the changing of APs’ positions and the average location errors with change of APs’ positions. However, IDW and UK interpolants are flexible with the changing of APs’ respect to the estimated radio maps by using the interpolants does not increase compared with the positions and the average location errors with respect to the estimated radio maps by using the results presenteddoes in Figure 6b, which meanswith thatthe theresults conventional model of an AP can interpolants not increase compared presentedsemivariogram in Figure 6b, which means that still be used when the AP’s position has been changed. For the proposed method, the semivariogram the conventional semivariogram model of an AP can still be used when the AP’s position has been models are associated with themethod, positions APs, but the changing APs’ positions brings about changed. For the proposed theofsemivariogram models areofassociated with the positions of little APs, but compared the changing of the APs’ positions brings about little impact. points, Since compared with between the impact. Since with distance from an AP to the sampling the distances distance from anare APmuch to theshorter. sampling points, the sampling points are much the sampling points And thusthe thedistances impacts between on the difference of attenuation directions shorter. And thus the impacts on the difference of attenuation directions and the difference of and the difference of travel distances of two radio signals caused by the changing of APs’ positions travel distances of two radio signals caused by the changing of APs’ positions are trivial. are trivial. 12

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Figure 7. Average location errors with respect to the offline radio map and the radio maps estimated by using different approaches in two scenarios, (a) two APs’ positions are changed; (b) three APs’ by using different approaches in two scenarios, (a) two APs’ positions are changed; (b) three APs’ positions are changed. In addition, SDs of the location errors are used as error bars. positions are changed. In addition, SDs of the location errors are used as error bars.

In the following, we used the data collected during the time period from10 a.m. to 11 a.m. to testthe thefollowing, approacheswe in used cases the of removing different numbers of APs. The from10 involveda.m. APsto are11also theto test In data collected during the time period a.m. added ones. Figure 8 presents the average location errors. If the added APs are all removed (three the approaches in cases of removing different numbers of APs. The involved APs are also the added are removed), location error based If onthe theadded offline radio mapallincreases significantly, ones.APs Figure 8 presentsthe theaverage average location errors. APs are removed (three APs are but the estimated radio maps-based location accuracy still maintains high levels. And UK and the removed), the average location error based on the offline radio map increases significantly, but the estimated radio maps-based location accuracy still maintains high levels. And UK and the modified UK

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modified UK methods perform better than IDW method and the NN-based method in all cases. methods perform better IDW and the NN-based method in all thecases. positions When the UK positions ofthan more thanmethod two APs areIDW known (one AP isthe removed orcases. none isWhen removed), the modified methods perform better than method and NN-based method in all improvements of the proposed method in location accuracy are observable, compared with of more than two APs are known (one AP is removed or none is removed), the improvements of the When the positions of more than two APs are known (one AP is removed or none is removed), the the conventional UK method. improvements the proposed method in location accuracy arewith observable, compared UK withmethod. the proposed method inoflocation accuracy are observable, compared the conventional conventional UK method. 9 Offline

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Last but one, we tested the impact of the number of reference devices on the approaches based Last but one, we tested theperiod, impact the number devices the approaches approaches based on on the data during thetested time 10ofa.m. to 11 a.m.of To ensure that the lefton reference devices based cover Last but one, we the impact of the number ofreference reference devices on the the entire weperiod, divided 16 eight groups, RD1 and RD2, RD3cover and the the data during thebed, time 10alla.m. to 11toa.m. To ensure that the left devices cover on the datatest during the time period, 10reference a.m. 11devices a.m. Tointo ensure that the leftreference reference devices RD4, RD5 and RD6, RD7 and RD8, RD9 and RD10, RD11 and RD12, RD13 and RD14, as well as RD5 test divided bed, we all divided all 16 reference intogroups, eight groups, RD1 andRD3 RD2,and RD3RD4, and entirethe testentire bed, we 16 reference devices devices into eight RD1 and RD2, RD15 and RD 16, and make sure at least one reference device in each group is in operation during RD4,RD7 RD5and and RD8, RD6, RD9 RD7 and and RD10, RD8, RD9 and RD10, RD11 andand RD12, RD13 as well and RD6, RD11 and RD12, RD13 RD14, as and wellRD14, as RD15 and as RD 16, each at leastsure eight reference devices are required. Figure 9 ispresents the average RD15test. and Therefore, RD 16, and least one reference device each group in operation and make sure at least onemake referenceatdevice in each group is in in operation during each test.during Therefore, location errors with respect to eight different numbers of reference devices.Figure 9 presents the average each test. Therefore, at least reference devices are required.

at least eight reference devices are required. Figure 9 presents the average location errors with respect location errors with respect to different numbers of reference devices. to different numbers of reference devices. 5

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Figure 9. Average location errors of different approaches versus the number of reference devices.

Figure Average location the number of reference devices.the For 9. each number, we errors chose of40different randomapproaches subsets ofversus reference devices and compared approaches. Since the offline radio map does not require any data from the reference devices, For each number, we chose 40 random subsets of reference devices and compared the the average does not change the of reference devices. And thedevices, NN-based approaches. Sinceerror the offline radio mapwith does notnumber require any data from thecompared reference the For eachlocation number, we chose 40 random subsets of reference devices and the approaches.

location with number devices. And NN-based Since average the offline radioerror mapdoes doesnot notchange require anythe data from of thereference reference devices, thethe average location error does not change with the number of reference devices. And the NN-based method is more robust than the three interpolants, IDW, UK and the modified UK with respect to the number of reference devices. Among the three interpolants, our proposed method performs better than conventional UK

the number of reference devices. Among the three interpolants, our proposed method performs better than conventional UK method as the number of reference devices decreases from 16 to 8. However, IDW method performs even better when the number of reference devices is less than 12. It implies that with lower density of reference devices, the interpolants should be combined with the NN-based method to provide reasonable estimation. Sensors 2016, 16, 802 15 of 17 As for all the above tests, the estimated radio maps were derived from heterogeneous measurements, and therefore only differential RSSI was applied to location estimation. To reveal the superiority of differential RSSIdevices metricsdecreases over rawfrom RSSI16metrics, comparative tests were finally method as the number of reference to 8. However, IDW method performs conducted. The test is again during time period from 10 12. a.m.Itto 11 a.m.Figure presents the even better when thedata number of reference devices is less than implies that with10 lower density average location errors. We can observe that differential RSSI improves the location accuracy of reference devices, the interpolants should be combined with the NN-based method to provide significantly. This implies that device heterogeneity causes severe negative impacts on multiple reasonable estimation. reference device-based adaptive location fingerprinting, andmaps differential is efficient this situation. As for all the above tests, the estimated radio were RSSI derived from in heterogeneous From the above experiments, we can conclude that the proposed approach not only adapts measurements, and therefore only differential RSSI was applied to location estimation. To reveal the to dynamicofenvironments andmetrics the situations changing positions,tests butwere it is finally also robust with superiority differential RSSI over rawof RSSI metrics,APs’ comparative conducted. respect reference device heterogeneity. it is to less than regression function-based The testto data is again during time period However, from 10 a.m. 11robust a.m. Figure 10 presents the average methods [3,4] with respect to the number of reference devices. Thus, a combination of the proposed location errors. We can observe that differential RSSI improves the location accuracy significantly. This approach and regression function-based methods would be theongood future choice device-based for adaptive implies that device heterogeneity causes severe negative impacts multiple reference location fingerprinting. adaptive location fingerprinting, and differential RSSI is efficient in this situation. 3

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5. Conclusions From the above experiments, we can conclude that the proposed approach not only adapts In this environments paper, we propose an adaptive fingerprinting approach assisted reference to dynamic and the situationslocation of changing APs’ positions, but it is also by robust with devices. The approach is not only robust for dynamic environments and the situation of changing respect to reference device heterogeneity. However, it is less robust than regression function-based APs’ positions, butrespect it alsotoaccommodates measurement differences caused by reference device methods [3,4] with the number of reference devices. Thus, a combination of the proposed heterogeneity. Two issues are studied in the proposed adaptive location fingerprinting approach, approach and regression function-based methods would be the good future choice for adaptive RSSI interpolation in indoor areas, and measurement differences between heterogeneous reference location fingerprinting. devices. For the interpolation of RSSI, the modified UK is proposed and provides better results than 5. Conclusions conventional UK because it takes the characteristics of RSSIs’ spatial distribution into account. Differential RSSI effective alleviation of the negative impacts caused by heterogeneous In this paper,iswe proposeforanthe adaptive location fingerprinting approach assisted by reference referenceThe devices. Since the proposed approach less robustand than devices. approach is not only robust for dynamic is environments theregression situation offunction-based changing APs’ methods [3,4] to the number of reference devices, in the it will be combined with positions, but itwith also respect accommodates measurement differences caused byfuture reference device heterogeneity. thoseissues methods to achieve better location performance. Two are studied in the proposed adaptive location fingerprinting approach, RSSI interpolation in indoor areas, and measurement differences between devices. of For the Acknowledgments: This work is supported by the fund from heterogeneous National Naturalreference Science Foundation China (No. 41071284) of andRSSI, Science Technology Projects Guangdong Province (No.than 2015B010104003). interpolation theand modified UK Planning is proposed andofprovides better results conventional UK because it takes the characteristics of RSSIs’ spatial distribution into account. Differential RSSI is effective for the alleviation of the negative impacts caused by heterogeneous reference devices. Since the proposed approach is less robust than regression function-based methods [3,4] with respect to the number of reference devices, in the future it will be combined with those methods to achieve better location performance.

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Acknowledgments: This work is supported by the fund from National Natural Science Foundation of China (No. 41071284) and Science and Technology Planning Projects of Guangdong Province (No. 2015B010104003). Author Contributions: Dongjin Wu and Linyuan Xia conceived and designed the experiments; Dongjin Wu performed the experiments and wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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