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1252 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 2, FEBRUARY 2016

A Robust Indoor Positioning System Based

on the Procrustes Analysis and Weighted

Extreme Learning Machine

Han Zou, Student Member, IEEE, Baoqi Huang, Member, IEEE, Xiaoxuan Lu,

Hao Jiang, Member, IEEE, and Lihua Xie, Fellow, IEEE

Abstract—Indoor positioning system (IPS) has become one of

the most attractive research ﬁelds due to the increasing demands

on location-based services (LBSs) in indoor environments. Various

IPSs have been developed under different circumstances, and most

of them adopt the ﬁngerprinting technique to mitigate perva-

sive indoor multipath effects. However, the performance of the

ﬁngerprinting technique severely suffers from device heterogene-

ity existing across commercial off-the-shelf mobile devices (e.g.,

smart phones, tablet computers, etc.) and indoor environmental

changes (e.g., the number, distribution and activities of people,

the placement of furniture, etc.). In this paper, we transform the

received signal strength (RSS) to a standardized location ﬁnger-

print based on the Procrustes analysis, and introduce a similarity

metric, termed signal tendency index (STI), for matching stan-

dardized ﬁngerprints. An analysis of the capability of the proposed

STI to handle device heterogeneity and environmental changes is

presented. We further develop a robust and precise IPS by inte-

grating the merits of both the STI and weighted extreme learning

machine (WELM). Finally, extensive experiments are carried out

and a performance comparison with existing solutions veriﬁes the

superiority of the proposed IPS in terms of robustness to device

heterogeneity.

Index Terms—Indoor positioning system (IPS), device hetero-

geneity, Procrustes analysis, weighted extreme learning machine

(WELM).

Manuscript received January 2, 2015; revised June 13, 2015 and September

11, 2015; accepted September 28 2015. Date of publication October 7, 2015;

date of current version February 8, 2016. This work was supported in part by the

Republic of Singapore National Research Foundation (NRF) through a grant

to the Berkeley Education Alliance for Research in Singapore (BEARS) for

the Singapore-Berkeley Building Efﬁciency and Sustainability in the Tropics

(SinBerBEST) Program; in part by the Republic of Singapore NRF under

Grant NRF2013EWT-EIRP04-012and Grant NRF2011NRF-CRP001-090; and

in part by the National Natural Science Foundation of China under Grant

61461037 and Grant 41401519. The work of B. Huang was supported by

the Natural Science Foundation of Inner Mongolia Autonomous Region of

China under Grant 2014MS0604 and the Inner Mongolia Autonomous Region

Science and Technology Innovation Guide Reward Fund Project under Grant

20121317. The associate editor coordinating the review of this paper and

approving it for publication was Katsuyuki Haneda. (Corresponding author:

Baoqi Huang.)

H. Zou, X. Lu, H. Jiang, and L. Xie are with the School of Electrical

and Electronics Engineering, Nanyang Technological University, Singapore

(e-mail: zouhan@ntu.edu.sg; xlu010@ntu.edu.sg; jiangh@ntu.edu.sg; elhxie@

ntu.edu.sg).

B. Huang is with the College of Computer Science, Inner Mongolia

University, Hohhot 010021, China, and also with the School of Electrical and

Electronic Engineering, Nanyang Technological University, Singapore 639798

(e-mail: cshbq@imu.edu.cn).

Color versions of one or more of the ﬁgures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TWC.2015.2487963

I. INTRODUCTION

THE explosive proliferation of mobile devices and the

popularity of social networks have spurred extensive

demands on Location Based Services (LBSs) in recent decades.

The Global Positioning System (GPS) has been widely used

in outdoor positioning, but is incapable of providing posi-

tioning services with sufﬁcient localization accuracy in indoor

environments due to the lack of line of sight (LoS) transmis-

sion channels between satellites and an indoor receiver [1].

Therefore, great efforts have been devoted to developing Indoor

Positioning Systems (IPSs) so as to enable reliable and precise

indoor positioning and navigation in the past two decades [2]–

[5]. Unlike other wireless technologies requiring the deploy-

ment of extra infrastructures, the existing IEEE 802.11 (WiFi)

network infrastructures, such as WiFi routers, have been widely

available in large numbers of commercial and residential build-

ings, and more importantly, nearly every existing commercial

mobile device is WiFi enabled. As such, WiFi based IPS has

become the primary alternative to GPS for indoor positioning.

Though received signal strength (RSS) is related to the dis-

tance of a transmitter-receiver pair, it is hard to characterize the

relationship by using explicit formulas. Hence, the WiFi ﬁn-

gerprinting approach [6]–[9] is proposed by leveraging RSS

as location ﬁngerprints, which involves two phases: an ofﬂine

training phase and an online localization phase. In the ofﬂine

training phase, a site survey is performed to record the ﬁnger-

prints (i.e. WiFi RSS values) from multiple access points (APs)

at some known locations, based on which a ﬁngerprint database

(radio map) is produced. In the online localization phase, when

a device sends a location query containing its current WiFi RSS

values from multiple APs, its location will be estimated using

the ﬁngerprint database.

It is acknowledged that the ﬁngerprinting approach results in

high localization accuracy provided that the testing device is the

same as the reference device and under the same environment,

but can be severely degenerated for heterogeneous devices [10].

Due to the proliferation of various types and brands of mobile

devices, it is indispensable and urgent to develop a robust

location ﬁngerprinting technique so as to provide accurate, reli-

able and fast indoor positioning services for heterogeneous

devices. In addition, indoor environments often change over

time, and consequently, the ﬁngerprint database built in the

ofﬂine phase can deviate from the truth during the online

1536-1276 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.

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ZOU et al.: ROBUST IPS BASED ON THE PROCRUSTES ANALYSIS AND WELM 1253

phase, such that the robustness of the ﬁngerprinting-based IPS

is inevitably affected.

In the literature, different methods have been developed for

the treatment of device heterogeneity [10]–[18]. However, these

existing methods require laborious manual adjustment of RSS

values during the ofﬂine stage when the testing device and the

reference device are distinct. Furthermore, only limited existing

work is related to mitigating the inﬂuences of indoor environ-

mental changes; for example, the crowdsourcing based IPS (e.g.

[19]–[23]) is able to partially adapt to indoor environmental

changes for the sake of ﬁngerprints crowdsourced at different

times, but such ﬁngerprints suffer from low accuracy.

In order to address robustness issues with respect to both

the device heterogeneity and environmental dynamics, in this

paper, we propose to standardize WiFi ﬁngerprints based on

a statistical shape analysis method (i.e. Procrustes analysis)

[24], and deﬁne Signal Tendency Index (STI) to measure the

similarity between such standardized location ﬁngerprints. A

theoretical analysis indicates that STI, which is convenient to

be derived in an online fashion, displays outstanding tolerance

of device heterogeneity and indoor environmental changes.

More importantly, STI can be straightforwardly integrated

with existing WiFi localization schemes, such as K Nearest

Neighbors (KNN) based schemes [6], [7], [25], machine learn-

ing based schemes [26], [27] and so on, to improve their robust-

ness. Furthermore, considering the fact that Extreme Learning

Machine (ELM) [26], [27] provides good generalization per-

formance at an extremely fast learning speed, we integrate the

weighted version of ELM, termed WELM [28], and STI to

develop an efﬁcient and robust IPS, termed STI-WELM. To

be speciﬁc, STI-WELM employs STI to standardize RSS val-

ues measured by online testing devices and collected by the

reference device during the ofﬂine site survey. By leveraging

our proposed weighting scheme, which considers the relative

importance of each RSS sample according to its corresponding

STI value, a weight matrix for STI-WELM ofﬂine training is

constructed, which establishes a STI-WELM model with high

robustness. Extensive experiments have been conducted, and

the results show that the proposed STI-WELM scheme pro-

vides more reliable and precise localization accuracy than other

approaches.

To sum up, the main contribution of the paper lies in the

development of a new methodology for handling device het-

erogeneity and environmental dynamics by standardizing RSS

values. A robust indoor localization algorithm: STI-WELM is

developed by integrating the merits of both STI and WELM.

Both theoretical analysis and extensive experiments are carried

out to verify the capability and demonstrate the superiority of

the proposed method.

The rest of the paper is organized as follows. The related

work is brieﬂy reviewed in Section II. Section III introduces

STI and then provides a theoretical and experimental analysis

to demonstrate its capability and usefulness in handling device

heterogeneity and environmental dynamics. Section IV presents

the proposed STI-WELM algorithm. In Section V, our experi-

mental testbed and data collection procedure are elaborated at

ﬁrst, and then experimental results and performance evaluation

of the proposed scheme are reported. We conclude this paper

in Section VI.

II. RELATED WORK

In this section, we shall present a brief overview on

ﬁngerprinting-based IPS and introduce the device heterogeneity

issue in indoor localization.

A. Fingerprinting-based IPS

The basic idea of the ﬁngerprinting technique is to ﬁngerprint

each location of interest and locate a mobile device using near-

est neighbor matching. Miscellaneous techniques have been

incorporated into the ﬁngerprinting approach. For instance, the

Bayesian Inference is exploited in [29] to improve the local-

ization accuracy. Some deterministic inference techniques such

as the KNN inference have also been used to estimate loca-

tions of occupants [6], [7], [25]. Furthermore, other approaches

adopt machine learning methods, including neural networks

[30], Back-propagation (BP) [3], support vector machine for

regression (SVR) [31], compressed sensing [32], factor graphs

[33], kernel estimation [11], [34], [35] and etc. It is note-

worthy that one of the machine learning algorithms, extreme

learning machine (ELM), has attracted signiﬁcant attention in

recent years due to its fast learning and easy implementation

[26], [27]. In [5], [36], an RFID-based IPS adopting the ELM

has been reported to deliver a better performance in terms of

both efﬁciency and localization accuracy. In addition, online

sequential extreme learning machine (OS-ELM), which can

adapt to various environmental dynamics by its online sequen-

tial learning ability, can provide higher localization accuracy

consistently than traditional approaches [37].

B. Device Heterogeneity

The device heterogeneity issue occurs when the clients’

mobile devices (testing devices) are different from the refer-

ence device (device utilized for the ofﬂine site survey). Due to

the heterogeneous factors of mobile devices, including distinct

WiFi chipsets, WiFi antennas, hardware drivers, encapsulation

materials, and even operating systems [17], [38], RSS detected

by heterogeneous devices at the same location usually has dif-

ferent mean values, and will be translated into different physical

locations by the traditional WiFi RSS ﬁngerprinting technique,

with the result that localization accuracy is severely degraded

[10], [11]. To handle the device heterogeneity issue encoun-

tered by the WiFi ﬁngerprinting-based IPS, different schemes

were proposed [10]–[18], [39].

One effective but time-consuming solution is to manually

adjust RSS values for distinct testing devices by a linear trans-

formation method [11], [13], [14]. Various transformation func-

tions, such as Kullback-Leibler divergence [11], time-space

sampling [13], Gaussian ﬁt sensor model [14], have been lever-

aged. The main drawback of this approach is that it requires the

types of the heterogeneous mobile devices be known in advance

such that an ofﬂine regression procedure can be conducted to

1254 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 2, FEBRUARY 2016

derive pairwise linear relationships. This imposes strict limita-

tions on widespread applications involving a mass of new and

unknown mobile devices. Moreover, as pointed out in [11], the

linear transformation could not satisfactorily resolve the device

heterogeneity issue since the simple linear relationship cannot

effectively characterize the difference across mobile devices.

Some calibration-free methods were proposed in [16], [17]

to avert the tedious manual RSS calibration procedure for

each testing device. Collaborative mapping was employed to

estimate a linear mapping function by training online mea-

sured RSS values [16]. Unsupervised learning methods such

as online regression and expectation-maximization have been

leveraged to learn the mapping function [17]. Nevertheless,

these methods rely on time-consuming online processing to

guarantee localization accuracy. Another way to address the

device heterogeneity issue is to deﬁne and use alternative loca-

tion ﬁngerprint instead of absolute RSS values. For instance,

signal strength difference (SSD), which leverages the differ-

ence of RSS values as a location ﬁngerprint, was proposed in

[10], [18]. The main drawback of SSD is the effect of shadow-

ing variation and reduced number of RSS ﬁngerprint vectors.

On the other hand, hyperbolic location ﬁngerprinting (HLF)

employs the RSS ratio between a pair of APs as a location

ﬁngerprint [15], [39]. In [10], [12], the experimental results

demonstrated that SSD is better than HLF for heterogeneous

devices as a location ﬁngerprint.

III. STANDARDIZING WIFIFINGERPRINTS BASED ON THE

PROCRUSTES ANALYSI S METHOD

In this section, we shall introduce a technique to stan-

dardize WiFi ﬁngerprints to improve the robustness of the

ﬁngerprinting-based IPS.

A. Deﬁnitions

During the ofﬂine site survey phase, only one mobile device

(MD) is required as a reference device (RD), and the RSS ﬁn-

gerprints from all the APs at each reference point (RP) are

collected and stored in the ﬁngerprint database. Suppose that

there are mRPs and nAPs in total, and at each RP, pRSS

ﬁngerprints are collected by the RD from nAPs. The mean

RSS vector at the i-th RP (denoted by RP

i) is deﬁned as

RDS

i∈Rn, in which the j-th element is the mean RSS value

collected at RP

ifrom the j-th AP (denoted APj) during a

period of time. In the case when the location of RP

iis out of the

detectable range of APj, we let the corresponding mean RSS be

the minimum detectable RSS value, i.e. −100 dBm.

During the online phase, the RSS values measured by a

testing device (TD) from all the APs are denoted by a vec-

tor TDS =[P1,...Pj,...,Pn], in which Pjis the mean RSS

value collected over a period of time from APj. Likewise, the

minimum detectable RSS value of any TD is −100 dBm.

B. Experimental Analysis

In order to better understand device heterogeneity and grasp

the key features of RSS values from heterogeneous devices,

Fig. 1. WiFi RSS values measured by different mobile devices at the same

location.

we conduct an experiment using ﬁve different mobile devices,

including two mobile phones (iPhone 5S and Nokia E71),

two tablets (iPad Air and Samsung GT-P1000 Galaxy Tab)

and one laptop (Fujitsu LifeBook T4220). In a typical indoor

environment (The Internet of Things Laboratory in School of

Electrical and Electronic Engineering, Nanyang Technological

University), 60 RSS samples are measured within one minute

for each of the ﬁve mobile devices at the same location with

respect to 8 WiFi APs installed at different locations. As can

be seen in Fig. 1, each curve connects the average RSS values

between one device and 8 APs. The RSS values associated with

different mobile devices are signiﬁcantly different, which ver-

iﬁes the effect of device heterogeneity. It is also conceivable

that, if one device (say Nokia E71) is employed as a reference

device in the ofﬂine site survey to create the WiFi ﬁngerprint

database and another device (say iPad Air) is considered to be

positioned in the online phase, then the ﬁngerprint matching

result (say using Euclidean distance) will return the true loca-

tion or any nearby location at an extremely low probability due

to the obvious gap between any pair of the curves. Hence, the

indoor localization accuracy will be remarkably degraded.

It is notable that, although the differences exist between

any pair of curves from different devices, the shapes of the

curves display certain similarities, as shown in Fig. 1; in other

words, one curve can be roughly recovered from another one

via translation and scale operations. This observation motivates

us that, instead of matching RSS ﬁngerprints directly, a bet-

ter performance may be obtainable by comparing the shapes of

the curves associated with different devices. Intuitively, since

shape comparison is immune to rotation, translation and scale,

the negative effect of device heterogeneity can be mitigated.

C. Standardizing RSS Fingerprints

Based on the analysis in the previous subsection, we adopt

the most well-known and popular ordinary Procrustes analysis

(PA) method [24] in the ﬁeld of statistical shape analysis for the

purpose of shape comparison. To compare the shapes of two

ZOU et al.: ROBUST IPS BASED ON THE PROCRUSTES ANALYSIS AND WELM 1255

or more objects, the PA method ”superimposes” all the given

objects by optimally translating, uniformly scaling and rotating

them. In our case, a ﬁngerprint (which is represented by a RSS

vector, e.g. TDS) denotes an object, but due to the fact that such

a ﬁngerprint can be regarded as a one-dimensional object, only

the translation and uniformly scaling operations of the ordinary

PA method are involved.

Given a RSS vector of a TD, namely TDS, the translation

step of the ordinary PA method will produce

P1−TDS,P2−TDS,...,Pn−TDS (1)

where

TDS =1

n

n

j=1

Pj.

Then, in the uniformly scaling step, we have

TDS =[P1−TDS,P2−TDS,..., Pn−TDS]/ˆσ, (2)

where

ˆσ=

1

n

n

j=1

(Pj−TDS)2.

The vector

TDS is thus the transformed object for superimpo-

sition, namely the standardized RSS ﬁngerprint. Similarly, the

transformed objects of all the RSS vectors collected by the ref-

erence device are derived and stored in the database. Suppose

that one of the standardized RSS vector stored in the database,

namely

RDS, is chosen for matching with the RSS vector

TDS

from the TD. To evaluate the similarity between the two original

curves in terms of their shapes, the Procrustes distance between

the two vectors

TDS and

RDS, termed signal tendency index

(STI), is computed as follows

s=

TDS−

RDS(3)

where ·denotes the Euclidean norm.

After elementary mathematical operations (see Appendix A),

we can obtain

s=2n(1−ρ), (4)

where ρdenotes the sample Pearson product-moment correla-

tion coefﬁcient (PPMCC) [40] between the vectors TDS and

RDS. Although (4) establishes an equivalence relation between

the STI and sample PPMCC, it does not imply that the pro-

posed STI method can be replaced by the sample PPMCC.

To be speciﬁc, due to the ability of standardizing RSS ﬁnger-

prints from heterogeneous and anonymous devices in an online

fashion, the STI method can be applied to preprocess RSS ﬁn-

gerprints, so as to alleviate the effect of device heterogeneity on

any RSS ﬁngerprints based treatment that follows, whereas the

sample PPMCC cannot be used in this way. For example, the

STI method can be integrated with existing WiFi ﬁngerprinting

localization schemes, such as KNN based schemes, machine

learning based schemes, and so on, to improve their robustness

to heterogeneous devices; moreover, in any practical crowd-

sourcing based IPS (e.g. [19]–[23]), RSS ﬁngerprints, which are

normally collected at different times and from heterogeneous

devices, can be ﬁrstly standardized by the STI method and then

used for building the ﬁngerprint database, which is helpful in

mitigating the negative impact of device heterogeneity.

D. Theoretical Analysis

In the ﬁrst place, we investigate why the STI method is robust

to heterogeneous MDs from a theoretical perspective.

Without loss of generality, let the APs be transmitters and

MDs be receivers. Suppose P(dj)denotes the RSS by a MD

at an arbitrary distance djfrom the transmitter of the j-th AP.

According to the LDPL model [41], we have

P(dj)(dBm)=10 log τ2

jGjGMDTj

16π2−10αlog dj+Zj

(5)

where τjis the wavelength of the propagating signal in meter,

Gjand GMD are the transmitter and receiver antenna gains

at the AP and MD, respectively, Tjis the signal transmission

power, αis the path loss exponent, and Zjis a random variable

representing the shadowing effect in dBm which is assumed to

be normally distributed with mean zero and variance σ2

j.Itis

acknowledged that (5) holds only if djis beyond a closed-in

reference distance. Accordingly, the mean RSS value can be

expressed as follows:

P(dj)(dBm)=10 log τ2

jGjGMDTj

16π2−10αlog dj(6)

Since the values of parameters Gj,Tjand GMD depend on

the hardware of the AP and MD, if the same pair of AP and

MD is considered, the relationship between the mean RSS value

and the distance from the AP to the MD is one-to-one. But,

if APs or MDs with different hardware are adopted, the cor-

responding relationship becomes many-to-one; that is to say,

given one mean RSS value, there are multiple possible dis-

tances. Hence, with the WiFi ﬁngerprinting technique, there

exist certain discrepancies between a location and its ﬁnger-

print (i.e. the corresponding RSS values) if heterogeneous APs

or MDs are used, which will degrade the IPS performance. This

explains why device heterogeneity degrades the performance of

the ﬁngerprinting-based IPS.

Signal strength difference (SSD) is a location signature

which leverages the differences of signals perceived at APs

from a MD [10]. With the SSD method, if the ﬁrst AP is used

as reference AP, then the SSD associated with the j-thAPis

produced as new ﬁngerprints as follows

P(dj)(dBm)−P(d1)(dBm)

=10 log τ2

jGjTj

τ2

1G1T1

−10αlog dj

d1

+Zj−Z1(7)

1256 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 2, FEBRUARY 2016

with j=2,...,n. As suggested in [10], since the parameter

GMD depending on the MD hardware does not exist in (7), the

SSD is entirely free from the inﬂuence of the device hetero-

geneity caused by using different MDs. But, it is noticeable that

the SSD variance is σ2

j+σ2

1.

Using the STI method, the average RSS from all the APs,

denoted by TDS, can be formulated as follows

TDS(dBm)=10

n

n

p=1

log(τ 2

pGpTp)+10 log GMD

16π2

−10α

n

n

p=1

log dp+1

n

n

p=1

Zp(8)

and the translating RSS associated with the j-th AP is

P(dj)(dBm)−TDS(dBm)

=10 log(τ 2

jGjTj)−10

n

n

p=1

log(τ 2

pGpTp)−10αlog dj

+10α

n

n

p=1

log dp+Zj−1

n

n

p=1

Zp.(9)

It follows from (9) that the translating RSS in the STI method

is uncorrelated with GMD (i.e., the parameter depending on

the MD hardware). In addition, according to (3) the scaling

parameter sis uncorrelated with GMD as well. Hence, it can

be concluded that location ﬁngerprints standardized by the STI

method is immune to the device heterogeneity induced by MDs

like the SSD method.

Furthermore, the variance of the translating RSS is equal to

σ2

j−2σj/n+pσ2

p/n2, which is generally small in compar-

ison with the SSD method; e.g., if σ1=... =σnand n1,

the variance in the STI method is much smaller than that in

the SSD method. Since a small variance indicates a narrow

range of ﬁngerprints (e.g., translating RSS and SSD) associated

with each physical location, it is accordingly easy to discrim-

inate these locations through ﬁngerprints. Therefore, it reveals

that STI is superior to SSD, which is further veriﬁed by the

experimental study in Section V.

Next, we analyze how the STI method improves the robust-

ness to indoor environmental changes under certain conditions.

As pointed out in [41], in some environments, such as build-

ings, stadiums and other indoor environments, the path loss

exponent (PLE) can take values in the range of 4 to 6. In a given

indoor environment, if the number and distribution of objects,

such as people, furniture, and so on, change over time, one con-

stant PLE cannot accurately characterize the path attenuation

at all times; that is to say, the ﬁngerprint collected at one loca-

tion during the site survey procedure will most likely deviate

from its counterparts in the online phase due to indoor environ-

mental changes, which inevitably impairs the robustness of the

ﬁngerprinting-based IPS.

On these grounds, deﬁne α+α to be the real PLE in the

online phase, where α reﬂects indoor environmental changes.

Provided that the nAPs are homogeneous or have similar

hardware parameters (i.e. G1,...,Gnand T1,...,Tn), (9) can

be simpliﬁed as

P(dj)(dBm)−TDS(dBm)=Zj−1

n

n

p=1

Zp

+(α +α) ⎛

⎝−10 log dj+10

n

n

p=1

log dp⎞

⎠.(10)

Equation (10) indicates that, given G1=... =Gnand

T1=...=Tn, the translating RSS P(dj)(dBm)−

TDS(dBm)is just scaled by α+α if ignoring the noise

terms, and as a result, the shape of the ﬁngerprint at this

location is scaled in the same way as well. Considering the

fact that the PA method is able to compare the shapes of

objects under different scales, the scaling issue caused by the

indoor environmental changes is thus mitigated when using

the standardized ﬁngerprint. However, when using the original

ﬁngerprinting technique and SSD, the scaling issue cannot be

addressed, and the IPS performance will be degraded.

To sum up, the theoretical analysis reveals that the translat-

ing and scaling operations adopted in the STI method are able

to alleviate the effect of device heterogeneity and indoor envi-

ronmental changes. Moreover, it is also convenient to deduce

similar conclusions as above if we let the MD be the transmitter

and APs be receivers.

IV. PROPOSED STI-WELM ALGORITHM

In this section, we ﬁrst introduce preliminaries on WELM,

and then describe the structure of the proposed algorithm

combining STI and WELM.

A. Preliminaries on WELM for Indoor Localization

Data in real applications such as RSS from different APs

usually have imbalanced class distribution, which means some

of the data are important than others in the database. WELM

is proposed in [28] to tackle the regression or classiﬁcation

tasks with imbalanced class distribution. It inherits the advan-

tages from original ELM, which is simple in theory that the

hidden nodes are randomly generated and the output weight is

analytically determined. It has therefore been adopted for easy

and fast implementation [26], [27]. Furthermore, it is able to

deal with data of imbalanced distributions by incorporating the

information of imbalance dataset [28].

WELM is a machine learning algorithm based on a general-

ized Single-hidden Layer Feedforward neural Network (SLFN)

architecture. As a machine learning algorithm, it requires a

training process to establish the trained WELM model for

online use. For the scenario of IPS, assume there are MWiFi

RSS ﬁngerprints in total collected at RPs. These WiFi RSS ﬁn-

gerprints and their physical coordinates are adopted as training

inputs and training targets respectively to build up the WELM

model. As demonstrated in Table. I, each training sample can

ZOU et al.: ROBUST IPS BASED ON THE PROCRUSTES ANALYSIS AND WELM 1257

TAB L E I

TRAINING INPUT xAND TRAINING TARGET tFOR WIFIRSS FINGERPRINT DATABASE

be represented as (xi,ti)∈Rn×R2, where the training input

xi=[RSS1

i,RSS2

i,...,RSSn

i] is a vector of RSS received

from nAPs in the environment, and training target ti=(t1

i,t2

i)

is the 2-D physical coordinates of the RP.

Assume that a SLFN with Lhidden nodes can approximate

these Msamples with zero error, then there exist βu,auand bu

such that

ti=

L

u=1

βuG(au,bu,xi), i=1,2,...,M,(11)

where auand buare the learning parameters of the hidden

nodes, βuis the output weight, and G(au,bu,xi)is the acti-

vation function which gives the output of the uth hidden node

with respect to the input xi.

Given Marbitrary distinct training samples (xi,ti), i=

1,2,...,M, by substituting xwith xiin (11) we obtain

Hβ=T(12)

where

H=⎡

⎢

⎣

G(a1,b1,x1) ... G(aL,bL,x1)

.

.

. ... .

.

.

G(a1,b1,xM) ... G(aL,bL,xM)

⎤

⎥

⎦M×L

=h(x1)T,h(x2)T,...,h(xM)TT

M×L,

β=β1,...,β

LT

L×2and T=t1,...,tMT

M×2.

In the above, His the hidden layer output matrix, βis the out-

put weight matrix and Tis the training target matrix of WELM;

the uth column of His the uth hidden node’s output vector

with respect to inputs x1,x2,...,xM, and the ith row of His

the output vector of the hidden layer with respect to the input

vector of xi. Unlike the traditional training algorithms for neu-

ral networks which adjust the input weights and hidden layer

biases, [26] proved that the parameters of Hcan be randomly

assigned if the activation function is inﬁnitely differentiable.

Therefore, the hidden layer output matrix Hremains unchanged

once these parameters are randomly initialized. After that, an

M×Mdiagonal matrix Wis deﬁned which is associated with

every training sample xi.

Regarding the IPS, we apply WELM to solve the localiza-

tion problem by regression, namely minimizing the weighted

cumulative localization error with respect to each training

sample (xi,ti), which can be mathematically written as

min

ξ,β∈RL×2LP=1

2β2+WC

2

M

i=1

ξi

s.t.h(xi)β=tT

i−ξT

ii=1,2,...,M(13)

where ξiis the training error of xi, which is caused by the

difference of the output h(xi)βand desired output ti, and

Cis a hyper-parameter for better generalization performance

[42]. The solution of the output weight vector βis analyti-

cally determined using the Moore-Penrose generalized inverse

ˆ

H. Dependent on the size of training samples, there are two

versions of solutions of β:

β=⎧

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎩

HTI

C+WHHT−1

WT,M<L

I

C+HTWH−1

HTWT,M>L

(14)

It can be seen from the above two formulas that a positive deﬁ-

nite matrix I/Cis added to the diagonal of WHHTor HTWH.

Since the weight matrix W=diag(Wii), i=1,...,Mis sig-

niﬁcant in WELM, two weighting schemes are proposed in

[28]. One weighting scheme assigns a uniﬁed Wii to each sam-

ple, the other adopts the value of golden standard that represents

the perfection in nature. However, both of these weighting

schemes are static and have not considered the importance of

each training sample. We shall propose a new weight scheme

in Section IV.B. which assigns different weight to each sample

according to its signiﬁcance.

In summary, the training process of WELM is conducted in

the following three main steps:

Step 1: Randomly assign the input parameters: input weights

auand biases bu,u=1,...,L.

Step 2: Calculate the hidden layer output matrix Hand the

weight matrix W.

Step 3: Calculate the output weight β.

B. STI-WELM

The proposed STI-WELM algorithm inherits the merits of

both STI and WELM, and consists of two main phases: online

construction phase and online localization phase.

1) Online Construction Phase: The skeleton of the online

construction procedure is depicted in Algorithm 1.

1258 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 2, FEBRUARY 2016

Algorithm 1. STIWELM

1. Construct TDS

newbased on STI measurements

2. Build up the WiFi RSS ﬁngerprint database for STI-WELM

training

3. Construct the weight matrix Wof STI-WELM

4. Establish the trained STI-WELM model for online localiza-

tion

First of all, we calculate the STI value sibetween TDS and

each RDS

i. Since a smaller siindicates that RDS

iis more sim-

ilar with TDS, we further deﬁne a weight value wifor each

RDS

i, which is calculated as follows:

wi=

1

si

m

i=1

1

si

(15)

Then, the mRPs are sorted according to their wiin a descend-

ing order. For the next step, we reconstruct the TDSaccording

to the RSS values RDS

icollected by the RD at the QRPs, with

their corresponding wiweight values being larger than a thresh-

old wth (setting wth =0.01 in general), to alleviate the negative

effect of device heterogeneity between TD and RD. For those

RPs whose corresponding wiweight values are smaller than

wth, their RSS values are discarded since they are not critical

for localization anymore.

The TDS

newis calculated based on the following formula,

TDS

new=1

Q

q=1

1

sq

Q

q=1

RDS

q·1

sq

(16)

It can be seen from the above equation that TDS

newis con-

structed from RDS

q,q=1,...,Qat the QRPs, which means

that it is more relevant to the RSS vectors in the database than

the raw TDS.

The next step is to build up a WiFi RSS ﬁngerprint

database for STI-WELM training process. Unlike conventional

ﬁngerprinting-based IPS which requires to put the RSS ﬁn-

gerprints collected at all mRPs into a database for training,

STI-WELM only requires to leverage the RSS ﬁngerprints from

the QRPs whose corresponding wweight values are larger

than wth to build up the database. It largely reduces the com-

putational burden for the training process. Suppose fRSS

ﬁngerprints are collected at each RP. Therefore, the training set

of STI-WELM becomes a fQ×nmatrix, where the order of

the fRSS ﬁngerprints collected at each RP is based on its wi

weight values from the largest to the smallest.

After that, construct the weight matrix Wfor the STI-WELM

training process. Note that the two weighting schemes proposed

in [28] are generated regardless of the special property of train-

ing samples. On the contrary, in our scheme, the weight vector

for each RSS ﬁngerprint is designed elaborately based on its

corresponding STI value sq, namely

W=1

Q

q=1

1

sq

diag 1

s1

,..., 1

sQ⊗If,(17)

where Ifis the identity matrix of order fand ⊗denotes the

Kronecker product. Then, these fQRSS ﬁngerprints and their

corresponding physical locations are adopted as the training

inputs xand the training targets trespectively for STI-WELM

ofﬂine training. Similarly to WELM, the STI-WELM model

will be trained as mentioned in Section IV. A. The detailed steps

are illustrated below:

Step 1: Randomly assign the input parameters: input weights

auand biases bu,u=1,...,L.

Step 2: Calculate the hidden layer output matrix Hand the

weight matrix W.

Step 3: Calculate the output weight β.

Additionally, the activation function G and the number of

hidden nodes Lwill be selected carefully in order to guarantee

the performance of STI-WELM. A guideline for these parame-

ter selections is presented in Section V. B. 3.). The STI-WELM

model can be obtained quickly due to the fast training speed of

WELM.

2) Online Localization Phase: When a user sends a loca-

tion query with the real-time TDS measurement, by feeding

the TDS to the trained STI-WELM model, the output of the

model is the estimated location of the user.

V. EXPERIMENTAL STUDY

Extensive experiments were conducted to evaluate the per-

formance of the proposed STI-WELM localization scheme.

We ﬁrst describe the setup of our testbed, and then detail the

experimental results and performance evaluation.

A. System Setup and Data Collection Procedure

The testbed for our experiments was installed at the Internet

of Things Laboratory of the School of Electrical and Electronic

Engineering, Nanyang Technological University. The total area

of the lab is around 580m2(35.1m×16.6m). 36 graduate stu-

dents and 15 undergraduate students work and study regularly

in this lab. Fig. 2 illustrates the layout of the lab, in which 8

Linksys WRT54GS WiFi routers were installed as APs for our

experiments. All the APs were ﬁxed on 1.9-meter-high tripods

to keep them on the same height level.

To examine the inﬂuence of device heterogeneity, we

employed 5 different mobile devices in our experiments, includ-

ing iPhone 5S (Phone), iPad Air (Tablet), Nokia E71 (Phone),

Samsung Galaxy Tab (Tablet) and Fujitsu LifeBook T4220

(Laptop). Table II summarizes the detail information of these

devices. A script program was developed and ran on all the APs

in order to collect RSS ﬁngerprints associated with each mobile

device from multiple APs. By leveraging this program, the

APs were able to scan the 802.11 packets transmitted between

mobile devices and APs so as to retrieve the RSS information of

each packet, and then send the RSS value and the MAC address

of the corresponding mobile device to a master AP which is

connected to a central server. The server will store the RSS ﬁn-

gerprints and further apply our proposed STI-WELM algorithm

to estimate the location of each device.

Speciﬁcally, we collected RSS ﬁngerprints of the ﬁve mobile

devices at 54 different points, including 40 ofﬂine calibration

ZOU et al.: ROBUST IPS BASED ON THE PROCRUSTES ANALYSIS AND WELM 1259

Fig. 2. Layout of the testbed.

TAB L E I I

MOBILE DEVICES USED FOR DATA COLLECTION

points and 14 online testing points, as shown in Fig. 2. For

each mobile device, 500 RSS ﬁngerprints were collected at each

point. The grid spacing between two adjacent locations of the

calibration points was chosen to be larger than 1.25m based

on the analysis in [43]. At each point, the mobile device was

put on a 1.65-meter-high plastic cart for collecting WiFi RSS

ﬁngerprints.

B. Comparison between RSS, SSD and STI as Location

Fingerprints

First of all, we evaluate the performance of the location ﬁn-

gerprints coming from the RSS, SSD and STI. Take the RSS for

example, we ﬁrst include all the RSS ﬁngerprints of ﬁve mobile

devices at each point into a ﬁngerprint set of size 2500, cal-

culate the sample standard deviation associated with each AP,

and evaluate the average standard deviation from the 8 APs to

measure the stability of the location ﬁngerprints at this point.

Likewise, we can calculate the average standard deviations for

the location ﬁngerprints used in SSD and STI. Note that, to

make a fair comparison, the location ﬁngerprints in the STI

method only involves the translating operation.

Fig. 3 demonstrates the distribution histograms of the aver-

age standard deviations at the given 54 points with respect to the

RSS, SSD and STI. As can be seen, the average standard devi-

ation of STI is basically within 6 dBm, while those of the RSS

and SSD are large and much widely scattered, which means that

Fig. 3. Distribution histogram of the average standard deviations of different

location ﬁngerprints.

STI results in more stable and reliable location ﬁngerprints than

the others.

C. Experimental Results and Evaluation

Two well-known localization algorithms, namely K Nearest

Neighbor (KNN) [6] and extreme learning machine (ELM)

[26], are chosen in order to further compare their performance

when RSS, SSD and STI are applied as the location ﬁngerprint.

We include KNN into the comparison because of its wide usage

as one of the classical localization algorithms. Furthermore,

it has been shown in [18] that KNN-based approaches are

superior to Bayesian Inference (BI) based approaches [14]

when the reference device and the testing devices are different.

Therefore, we include KNN instead of BI into our performance

1260 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 2, FEBRUARY 2016

TABLE III

DETAILED AVERAGE LOCALIZATION ERRORS (IN METER)

OF STI-KNN WITHOUT SCALING AND STI-KNN

comparison and evaluation. For KNN, the value of Kis deter-

mined empirically case-by-case according to the related WiFi

RSS ﬁngerprints database of the reference device. During the

online phase, by matching the measured WiFi RSS ﬁngerprints

with the Kclosest WiFi RSS ﬁngerprints in the database, the

location of the target will be calculated. The algorithm is the

same as in [6].

It has been shown in [36] that the performance of ELM

in terms of the ofﬂine training time, the online testing time

and the average localization accuracy are better than classical

machine learning algorithms such as Back-propagation (BP)

algorithm and support vector machine for regression (SVR)

algorithm. Therefore we also choose ELM as the localiza-

tion algorithm when RSS, SSD and STI are applied as the

localization ﬁngerprint respectively. The methodology of it is

introduced in [36].

In practice, it is more likely for the users to carry different

devices from the reference device. Therefore, we only analyze

the situations that the testing device and reference device are

distinct in our experiments.

By leveraging the 500 ×40 WiFi RSS ﬁngerprints at the

40 ofﬂine calibration points of each device, the ofﬂine RSS,

SSD and STI location ﬁngerprint databases are established. The

500 ×14 WiFi RSS ﬁngerprints at the online testing points

of each device are utilized for the performance evaluation of

TAB L E I V

DETAILED AVERAGE LOCALIZATION ERRORS (IN METER)UNDER

VARIOUS SITUATIONS (KNN)

each localization algorithm. The distance error is used to mea-

sure the localization accuracy of each approach. We deﬁne the

location estimation error eto be the distance between the real

location coordinates (x0,y0)and the system estimated location

coordinates (x,y), i.e.:

e=(x−x0)2+(y−y0)2(18)

Since we utilize 5 mobile devices in our experiments, there

are 20 different combinations of reference device and testing

device.

1) Comparison between STI-KNN without scaling and STI-

KNN: In order to evaluate the inﬂuence of the uniform scaling

step of STI on the localization accuracy, we compare the per-

formance of STI-KNN with and without scaling step in the ﬁrst

place. The value of Kis chosen to be 13 for this experiment.

The speciﬁc average localization errors given different com-

binations of reference devices and testing devices are demon-

strated in Table III. As can be seen, STI-KNN can provide

higher localization accuracy in every situation when the uni-

form scaling step is involved in the procedure. In general, the

uniform scaling step enhances the precision of indoor position-

ing of STI-KNN by 3.09%. Therefore, we can conclude that, the

uniform scaling step could facilitate STI to mitigate the effect

of indoor environmental dynamics.

ZOU et al.: ROBUST IPS BASED ON THE PROCRUSTES ANALYSIS AND WELM 1261

Fig. 4. Comparison of distance error distributions for different methods (KNN).

TAB L E V

SUMMARY OF AVERAGE LOCALIZATION ERRORS (IN METER) (KNN)

2) Comparison among RSS-KNN, SSD-KNN and STI-KNN:

Two location ﬁngerprints: RSS and SSD are leveraged and inte-

grated with the KNN localization algorithm to compare with

STI-KNN. Since the value of Kis critical for the performance

of KNN approaches when the reference device is altered, we

analyze the performance of RSS-KNN, SSD-KNN and STI-

KNN with all the possible values of K, and compare their best

performance in each scenario (20 different combinations of ref-

erence device and testing device). Table IV demonstrates the

speciﬁc average localization errors of each combination of ref-

erence device and testing device of these three approaches with

their best performances given the optimal Kvalue.

It is evident from Table IV that STI-KNN provides higher

localization accuracy than RSS-KNN and SSD-KNN in every

situation. Fig. 4 depicts the distance error distribution of the

three approaches when each mobile device is leveraged as the

reference device. Similar to the results shown in Table IV, STI-

KNN has the best performance among the three approaches in

terms of localization accuracy.

To summarize, as shown in Table V, STI-KNN can enhance

the precision of indoor positioning by 26.71% over RSS-KNN

and 22.46% over SSD-KNN respectively. Thus, when KNN

is employed as the localization algorithm, the proposed STI

method can largely alleviate the effect of device heterogeneity

and provide robust and high indoor positioning service consis-

tently even the testing devices are different from the reference

device.

3) Comparison between RSS-ELM, SSD-ELM, STI-ELM

and STI-WELM: As a ﬁngerprinting-based IPS, the relevant

ELM models for online localization are required to be built up

during the online construction phase. For RSS-ELM, the RSS-

ELM model is built up by adopting the 500 ×40 WiFi RSS

ﬁngerprints collected at the 40 ofﬂine calibration points. These

WiFi RSS ﬁngerprints and their physical locations are adopted

as training inputs and training targets respectively to build up

the model. For the construction of SSD-ELM model, the 500 ×

40 WiFi RSS ﬁngerprints collected at the ofﬂine calibration

points are transferred into SSD format ﬁrst. Then the model is

built up in the similar process as RSS-ELM. During the online

testing phase, the raw RSS vectors measured by TD are recon-

ﬁgured into the SSD format and put into the trained SSD-ELM

model, then the estimated location of the TD will be calculated.

1262 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 2, FEBRUARY 2016

For STI-ELM and STI-WELM, as mentioned in Section IV.

B, only WiFi RSS ﬁngerprints collected by the RD at the Q

RPs are adopted for building up the STI-ELM model and STI-

WELM model. Therefore, the training process of these two

approaches are much faster than RSS-ELM and SSD-ELM,

which require to train the WiFi RSS ﬁngerprints at all the 40

ofﬂine calibration points. In our experiments, we select Qto be

13 because the wweight value of these QRPs are larger than

wth =0.01. Therefore, the size of training database is largely

reduced from 500 ×40 to 500 ×13. The performance of three

activation functions: radial basis function (RBF) G(a,b,x)=

e−bx−a2, sine function G(a,b,x)=sin(ax +b)and hard-

limit transfer (hardlim) function G(a,b,x)=hardli m(ax +

b)are analyzed by leveraging the ofﬂine WiFi RSS ﬁnger-

prints database. The hardlim function is chosen since it provides

the best performance among the three activation functions.

Another critical parameter for the performance of the ELM

based approaches is the number of hidden nodes L. The ﬁve-

fold cross-validation method is employed with a range from 1

to 100 and a step size of 2 in order to determine the optimal

L. After comprehensive evaluations on both localization accu-

racy and repeatability, Lis selected to be 23 for both STI-ELM

and STI-WELM. Based on our experimental results, these two

approaches only spend 0.056s on average to calculate the out-

put weights βfor the (500 ×13 =6500)WiFi RSS ﬁngerprints

during the training process.

A guideline for selecting the type of activation function and

the number of hidden nodes in the STI-WELM hidden layer,

both of which are the critical parameters for the performance

of the STI-WELM approach, is listed as follows: the suggested

default activation function for the STI-WELM approach is the

hardlim function, whose performance is better than others in

general; as for the optimal number of hidden nodes, the ﬁve-

fold cross-validation method is employed with a range from 0

to 100 and a step size of 2 based on the empirical tuning.

The weight matrix Wof STI-WELM is calculated accord-

ing to our proposed weighting scheme as introduced in

Section IV.B. Similar to the KNN experiments, there are

20 different combinations of reference device and testing

device because 5 mobile devices are employed in the ELM

experiments.

The speciﬁc average localization errors of each combina-

tion of reference device and testing device when RSS-ELM,

SSD-ELM, STI-ELM and STI-WELM are adopted are demon-

strated in Table VI respectively. It can be seen from Table VI

that its localization performance trumps other three approaches

signiﬁcantly in every combination. It is also noteworthy that

the performance of STI-ELM is better than RSS-ELM and

SSD-ELM. The mean localization accuracies of RSS-ELM

and SSD-ELM are almost the same. The distance error dis-

tribution of the four approaches when each mobile device is

leveraged as the reference device are present in Fig. 5. As

observed in Fig. 5, STI-WELM provides the most accurate

indoor positioning service among the four approaches, which

is consistent with the results demonstrated in Table VI.

In summary, STI-WELM enhances the precision of indoor

positioning by 39.89% over RSS-ELM, 33.53% over SSD-

ELM and 11.46% over STI-ELM respectively. Table VII

TAB L E V I

DETAILED AVERAGE LOCALIZATION ERRORS (IN METER)UNDER

VARIOUS SITUATIONS (ELM)

summarizes the performance of each approach. Therefore,

the proposed STI-WELM can provide more robust, fast and

accurate indoor positioning service than other approaches con-

sistently, and alleviate the effect of heterogeneous issue among

different devices remarkably. Furthermore, another noteworthy

point is that the performance of both ELM and WELM is better

than KNN provided that the same type of the location ﬁnger-

print is adopted. This claim is supported by Fig. 4 and Fig. 5,

in which the curves produced by ELM and WELM based algo-

rithms are smoother than KNN based ones, i.e., the ELM and

WELM based approaches are more robust to outliers.

In addition, iPad Air and Fujitsu Laptop obtain the best

overall localization accuracy among all the devices considered,

which is contributable to their relative high transmission pow-

ers; see the resulting RSS values in relation to different devices

in Fig. 1.

4) Performance evaluation of STI-WELM under the inﬂu-

ence of the number of APs: The aforementioned section has

demonstrated the superiority of STI-WELM to alleviate the

effect of heterogeneous devices for indoor localization when

all the APs in the testbed were leveraged. In this subsection,

we further analyze the performance of STI-WELM under the

inﬂuence of the number of APs.

We compare the performance of STI-WELM with RSS-ELM

and STI-ELM when the number of APs is altered. The training

ZOU et al.: ROBUST IPS BASED ON THE PROCRUSTES ANALYSIS AND WELM 1263

Fig. 5. Comparison of distance error distributions for different methods (ELM and WELM).

TAB L E V I I

SUMMARY OF AVERAGE LOCALIZATION ERRORS (IN METER) (ELM)

Fig. 6. Comparison of mean localization error between different approaches

under the inﬂuence of the number of APs.

TABLE VIII

SUMMARY OF AVERAGE LOCALIZATION ERRORS (IN METER)UNDER THE

INFLUENCE OF THE NUMBER OF APS

processes of these approaches are the same as is introduced in

Section V.B.3). We consider all the 20 different combinations of

reference device and testing device for this experiment as well,

since 5 different mobile devices are utilized in total. The overall

performance in terms of mean localization errors between these

approaches under different numbers of APs is demonstrated in

Fig. 6 and Table VIII.

As shown in Table VIII, the mean localization errors of all

the three approaches decrease as the number of APs in-use

1264 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 2, FEBRUARY 2016

increases. It can be easily observed that STI-WELM outper-

forms RSS-ELM and STI-ELM in every situation. The per-

formance of RSS-ELM is the worst in all situations since it

leverages the raw RSS data of testing device and the large local-

ization error is caused by device heterogeneity. On the contrary,

after the operations of translation and uniformly scaling in STI,

the newly constructed TDS

newis more relevant to the RSS ﬁn-

gerprints stored in the reference device database. This is the

main reason why both STI-ELM and STI-WELM are superior

to RSS-ELM. By considering the relative importance of each

RSS sample according to its corresponding STI value in the

reference device database and leveraging our proposed weight-

ing scheme, the localization accuracy of STI-WELM is higher

than that of STI-ELM in general. To be speciﬁc, the mean

localization error of STI-WELM is at the same level with STI-

ELM when only three APs are leveraged. However, as shown

in Fig. 6, it reduces signiﬁcantly when the required number of

APs is between 4 and 6, and keeps the mean localization error

at a low level when the number of APs is more than 7.

In summary, as long as no less than three APs are available

in indoor environments, the STI-based localization approaches

outperform RSS-based localization approaches. Furthermore,

STI-WELM, which integrates the advantages of both STI

and WELM, can overcome the heterogeneity issue of mobile

devices for indoor localization and provide high localization

accuracy consistently even only a few APs are available in

indoor environments.

D. Implementation of the Proposed IPS for Real Location-

based Service

Since both the theoretical and experimental analysis have

veriﬁed the superiority of the proposed IPS in terms of accuracy

and robustness, we have implemented our IPS in the fol-

lowing four different indoor environments: Internet of Things

Lab (600m2) in Nanyang Technological University (NTU),

Lecture Theater 22 (500m2) in NTU, the Center for Berkeley

Education Alliance for Research in Singapore (BEARS) head-

quarter (1500m2), and the Center for Research in Energy

Systems Transformation (CREST) Lab (400m2) in University

of California, Berkeley. It turns out that our system is able

to provide satisfactory LBS across heterogeneous devices in

these places, including indoor positioning, indoor navigation,

real-time occupancy distribution monitoring and indoor geo-

fencing, and has been fully operational for more than one year.

For instance, [44] provides a video demo about our indoor nav-

igation service on Google Glass, which is the mobile device

(distinct from the reference device: iPad) to be localized. As

shown in the video, by leveraging our proposed STI-WELM

localization algorithm, our IPS offers high localization accu-

racy and seamless indoor navigation across heterogeneous

devices.

VI. CONCLUSION

In this paper, we presented a robust and precise IPS by

introducing STI, which is a new type of ﬁngerprints and embod-

ies more reliable and robust location signatures compared to

traditional location ﬁngerprints in the presence of heteroge-

neous devices and changing indoor environments. We also

proposed a novel weighting scheme by taking into considera-

tion of the relative importance of each RSS sample according

to its corresponding STI value, for the WELM training process.

On these grounds, we proposed the STI-WELM scheme which

inherits the advantages of both STI and WELM. According

to our experimental results, the STI-WELM scheme enhances

the precision of indoor positioning by 39.89% over RSS-ELM,

33.53% over SSD-ELM and 11.46% over STI-ELM, respec-

tively, which conﬁrms the superiority of the STI approach to

the traditional RSS ﬁngerprints as well as the recently devel-

oped SSD approach. In addition, our IPS has been deployed in

various types of indoor environments, such as lab, ofﬁce space

and lecture theater, and turns out to provide satisfactory LBS.

APPENDIX A

DERIVING (4)

Regarding

RDS, we deﬁne

RDS =PR

1−RDS,PR

2−RDS,...,PR

n−RDS/ˆσ,

(19)

where

RDS =

n

i=1

PR

i,(20)

ˆσR=

1

n

n

i=1

(PR

i−RDS)2.(21)

Then, we can have

TDS−

RDS2

=

n

j=1Pj−TDS

ˆσ−

PR

j−RDS

ˆσR2

=

n

j=1⎛

⎝Pj−TDS

1

nn

i=1(Pi−TDS)2

−

PR

j−RDS

1

nn

i=1(PR

i−RDS)2

⎞

⎠

2

=

n

j=1⎛

⎝(Pj−TDS)2

1

nn

i=1(Pi−TDS)2+

(PR

j−RDS)2

1

nn

i=1(PR

i−RDS)2

−

2(Pj−TDS)( PR

j−RDS)

1

nn

i=1(Pi−TDS)21

nn

i=1(PR

i−RDS)2⎞

⎠

=n

j=1(Pj−TDS)2

1

nn

i=1(Pi−TDS)2+n

j=1(PR

j−RDS)2

1

nn

i=1(PR

i−RDS)2

−

2n

j=1(Pj−TDS)( PR

j−RDS)

1

nn

i=1(Pi−TDS)21

nn

i=1(PR

i−RDS)2

=2n−

2nn

j=1(Pj−TDS)( PR

j−RDS)

n

i=1(Pi−TDS)2n

i=1(PR

i−RDS)2

=2n(1−ρ)

ZOU et al.: ROBUST IPS BASED ON THE PROCRUSTES ANALYSIS AND WELM 1265

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https://www.youtube.com/watch?v=vJ4kJu4ivdE

Han Zou (S’11) received the B.Eng. (ﬁrst class

Hons.) degree from Nanyang Technological

University, Singapore, in 2012, and is currently

pursuing the Ph.D. degree at the School of Electrical

and Electronic Engineering, Nanyang Technological

University. He is also a Graduate Student Researcher

with Berkeley Education Alliance for Research,

Singapore Limited (BEARS), Singapore. His

research interests include mobile computing, Internet

of Things, wireless sensor networks, indoor posi-

tioning and navigation systems, and indoor human

activity sensing and inference.

1266 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 2, FEBRUARY 2016

Baoqi Huang (S’10–M’11) received the B.E. degree

in computer science from Inner Mongolia University

(IMU), Hohhot, China, the M.S. degree in com-

puter science from Peking University, Beijing, China,

and the Ph.D. degree in information engineering

from the Australian National University, Canberra,

A.C.T., Australia, in 2002, 2005, and 2012, respec-

tively. From May 2013 to April 2014, he worked

as a Research Fellow with Nanyang Technological

University, Singapore. He is with the College of

Computer Science, IMU, where he is currently a

Professor. His research interests include source localization, wireless sen-

sor networks, and mobile computing. He was a recipient of the Chinese

Government Award for Outstanding Chinese Students Abroad in 2011.

Xiaoxuan Lu received the B.E. degree in automation

engineering from Nanjing University of Aeronautics

and Astronautics, Nanjing, China, and the M.E.

degree in electrical and electronic engineering from

Nanyang Technological University, Singapore, in

2013 and 2015, respectively. He is currently pur-

suing the Ph.D. degree in computer science at the

University of Oxford, Oxford, U.K. His research

interests focus on Internet of Things and machine

learning techniques for sensor networks.

Hao Jiang (M’14) received the B.E and Ph.D.

degrees from the School of Information Science

and Engineering, Xiamen University, Xiamen, China,

in 2008 and 2013, respectively. He is currently

a Postdoctoral Research Fellow with the School

of Electrical and Electronic Engineering, Nanyang

Technological University, Singapore. His research

interests include localization system, sensor network,

ﬁber optic sensor, and evolutionary algorithm.

Lihua Xie (S’91–M’92–SM’97–F’07) received the

B.E. and M.E. degrees in electrical engineering

from Nanjing University of Science and Technology,

Nanjing, China, and the Ph.D. degree in electri-

cal engineering from the University of Newcastle,

Callaghan, N.S.W., Australia, in 1983, 1986, and

1992, respectively. Since 1992, he has been with

the School of Electrical and Electronic Engineering,

Nanyang Technological University, Singapore, where

he is currently a Professor and served as the Head

of the Division of Control and Instrumentation, from

July 2011 to June 2014. He held teaching appointments with the Department of

Automatic Control, Nanjing University of Science and Technology, from 1986

to 1989 and Changjiang Visiting Professorship with South China University

of Technology, Guangzhou, China, from 2006 to 2011. His research interests

include robust control and estimation, networked control systems, multiagent

networks, and unmanned systems. He has served as an Editor of the IET Book

Series in Control and an Associate Editor of a number of journals includ-

ing the IEEE TRANSACTIONS ON AUTOMATIC CONTROL,Automatica,the

IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, and the IEEE

TRANSACTIONS ON CIRCUITS AND SYSTEMS-II. He is a Fellow of IFAC.