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
Index Terms—Indoor positioning system (IPS), device hetero-
geneity, Procrustes analysis, weighted extreme learning machine
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:
H. Zou, X. Lu, H. Jiang, and L. Xie are with the School of Electrical
and Electronics Engineering, Nanyang Technological University, Singapore
(e-mail: firstname.lastname@example.org; email@example.com; firstname.lastname@example.org; elhxie@
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
Color versions of one or more of the ﬁgures in this paper are available online
Digital Object Identiﬁer 10.1109/TWC.2015.2487963
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 .
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 –
. 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 – 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 .
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
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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 –. 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.
–) 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)
, 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 , , , machine learn-
ing based schemes ,  and so on, to improve their robust-
ness. Furthermore, considering the fact that Extreme Learning
Machine (ELM) ,  provides good generalization per-
formance at an extremely fast learning speed, we integrate the
weighted version of ELM, termed WELM , 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
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  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 , , . Furthermore, other approaches
adopt machine learning methods, including neural networks
, Back-propagation (BP) , support vector machine for
regression (SVR) , compressed sensing , factor graphs
, kernel estimation , ,  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
, . In , , 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 .
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 , , 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
, . To handle the device heterogeneity issue encoun-
tered by the WiFi ﬁngerprinting-based IPS, different schemes
were proposed –, .
One effective but time-consuming solution is to manually
adjust RSS values for distinct testing devices by a linear trans-
formation method , , . Various transformation func-
tions, such as Kullback-Leibler divergence , time-space
sampling , Gaussian ﬁt sensor model , 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 , 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 , 
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 . Unsupervised learning methods such
as online regression and expectation-maximization have been
leveraged to learn the mapping function . 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
, . 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 , . In , , 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
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
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
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  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
Then, in the uniformly scaling step, we have
TDS =[P1−TDS,P2−TDS,..., Pn−TDS]/ˆσ, (2)
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,
RDS, is chosen for matching with the RSS vector
from the TD. To evaluate the similarity between the two original
curves in terms of their shapes, the Procrustes distance between
the two vectors
RDS, termed signal tendency index
(STI), is computed as follows
where ·denotes the Euclidean norm.
After elementary mathematical operations (see Appendix A),
we can obtain
where ρdenotes the sample Pearson product-moment correla-
tion coefﬁcient (PPMCC)  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. –), 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 , we have
P(dj)(dBm)=10 log τ2
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
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
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 . 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
=10 log τ2
1256 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 2, FEBRUARY 2016
with j=2,...,n. As suggested in , 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
Using the STI method, the average RSS from all the APs,
denoted by TDS, can be formulated as follows
pGpTp)+10 log GMD
and the translating RSS associated with the j-th AP is
=10 log(τ 2
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
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 , 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
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
+(α +α) ⎛
⎝−10 log dj+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  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 , . Furthermore, it is able to
deal with data of imbalanced distributions by incorporating the
information of imbalance dataset .
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
i] is a vector of RSS received
from nAPs in the environment, and training target ti=(t1
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
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
G(a1,b1,x1) ... G(aL,bL,x1)
. ... .
G(a1,b1,xM) ... G(aL,bL,xM)
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,  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
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
. The solution of the output weight vector βis analyti-
cally determined using the Moore-Penrose generalized inverse
H. Dependent on the size of training samples, there are two
versions of solutions of β:
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
. 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.
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
3. Construct the weight matrix Wof STI-WELM
4. Establish the trained STI-WELM model for online localiza-
First of all, we calculate the STI value sibetween TDS and
i. Since a smaller siindicates that RDS
iis more sim-
ilar with TDS, we further deﬁne a weight value wifor each
i, which is calculated as follows:
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.
newis calculated based on the following formula,
It can be seen from the above equation that TDS
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  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
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
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 . At each point, the mobile device was
put on a 1.65-meter-high plastic cart for collecting WiFi RSS
B. Comparison between RSS, SSD and STI as Location
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
STI results in more stable and reliable location ﬁngerprints than
C. Experimental Results and Evaluation
Two well-known localization algorithms, namely K Nearest
Neighbor (KNN)  and extreme learning machine (ELM)
, 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  that KNN-based approaches are
superior to Bayesian Inference (BI) based approaches 
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
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 .
It has been shown in  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 .
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.:
Since we utilize 5 mobile devices in our experiments, there
are 20 different combinations of reference device and testing
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
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
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.
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
D. Implementation of the Proposed IPS for Real Location-
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,  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
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.
RDS, we deﬁne
Then, we can have
ZOU et al.: ROBUST IPS BASED ON THE PROCRUSTES ANALYSIS AND WELM 1265
 B. Buchli, F. Sutton, and J. Beutel, GPS-Equipped Wireless Sensor
Network Node for High-Accuracy Positioning Applications.NewYork,
NY, USA: Springer, 2012, pp. 179–195.
 H. Liu, H. Darabi, P. Banerjee, and J. Liu, “Survey of wireless indoor
positioning techniques and systems,” IEEE Trans. Syst. Man Cybern. C,
Appl. Rev., vol. 37, no. 6, pp. 1067–1080, Nov. 2007.
 Y. Gu, A. Lo, and I. Niemegeers, “A survey of indoor positioning systems
for wireless personal networks,” IEEE Commun. Surveys Tuts., vol. 11,
no. 1, pp. 13–32, Mar. 2009.
 G. Deak, K. Curran, and J. Condell, “A survey of active and pas-
sive indoor localisation systems,” Comput. Commun., vol. 35, no. 16,
pp. 1939–1954, 2012.
 H. Zou, L. Xie, Q.-S. Jia, and H. Wang, “Platform and algorithm devel-
opment for a RFID-based indoor positioning system,” Unmanned Syst.,
vol. 2, no. 3, pp. 279–291, 2014.
 P. Bahl and V. N. Padmanabhan, “Radar: An in-building RF-based user
location and tracking system,” in Proc. 19th Annu. Joint Conf. IEEE
Comput. Commun. Soc. (INFOCOM), 2000, vol. 2, pp. 775–784.
 M. Youssef and A. Agrawala, “The horus WLAN location determina-
tion system,” in Proc. 3rd Int. Conf. Mobile Syst. Appl. Serv., 2005,
 S.-H. Fang, T.-N. Lin, and K.-C. Lee, “A novel algorithm for multipath
ﬁngerprinting in indoor WLAN environments,” IEEE Trans. Wireless
Commun., vol. 7, no. 9, pp. 3579–3588, Sep. 2008.
 S.-H. Fang, Y.-T. Hsu, and W.-H. Kuo, “Dynamic ﬁngerprinting combina-
tion for improved mobile localization,” IEEE Trans. Wireless Commun.,
vol. 10, no. 12, pp. 4018–4022, Dec. 2011.
 A. Mahtab Hossain, Y. Jin, W.-S. Soh, and H. N. Van, “SSD: A robust
RF location ﬁngerprint addressing mobile devices’ heterogeneity,” IEEE
Trans. Mobile Comput., vol. 12, no. 1, pp. 65–77, Jan. 2013.
 J.-G. Park, D. Curtis, S. Teller, and J. Ledlie, “Implications of device
diversity for organic localization,” in Proc. IEEE INFOCOM, 2011,
 S.-H. Fang, C.-H. Wang, S.-M. Chiou, and P. Lin, “Calibration-free
approaches for robust Wi-Fi positioning against device diversity: A per-
formance comparison,” in Proc. IEEE 75th Veh. Technol. Conf. (VTC
Spring), 2012, pp. 1–5.
 C. Figuera, J. L. Rojo-lvarez, I. Mora-Jimnez, A. Guerrero-Curieses,
M. Wilby, and J. Ramos-Lpez, “Time-space sampling and mobile device
calibration for WiFi indoor location systems,” IEEE Trans. Mobile
Comput., vol. 10, no. 7, pp. 913–926, Jul. 2011.
 A. Haeberlen, E. Flannery, A. M. Ladd, A. Rudys, D. S. Wallach, and
L. E. Kavraki, “Practical robust localization over large-scale 802.11 wire-
less networks,” in Proc. 10th Annu. Int. Conf. Mobile Comput. Netw.,
2004, pp. 70–84.
 M. B. Kjrgaard, “Indoor location ﬁngerprinting with heterogeneous
clients,” Pervasive Mobile Comput., vol. 7, no. 1, pp. 31–43, 2011.
 F. Della Rosa, H. Leppakoski, S. Biancullo, and J. Nurmi, “Ad-hoc
networks aiding indoor calibrations of heterogeneous devices for ﬁn-
gerprinting applications,” in Proc. Int. Conf. Indoor Positioning Indoor
Navigat. (IPIN), 2010, pp. 1–6.
 A. W. Tsui, Y.-H. Chuang, and H.-H. Chu, “Unsupervised learning for
solving RSS hardware variance problem in WiFi localization,” Mobile
Netw. Appl., vol. 14, no. 5, pp. 677–691, 2009.
 F. Dong, Y. Chen, J. Liu, Q. Ning, and S. Piao, A Calibration-Free
Localization Solution for Handling Signal Strength Variance.NewYork,
NY, USA: Springer, 2009, pp. 79–90.
 H. Wang, S. Sen, A. Elgohary, M. Farid, M. Youssef, and
R. R. Choudhury, “No need to war-drive: Unsupervised indoor local-
ization,” in Proc. 10th Int. Conf. Mobile Syst. Appl. Serv., 2012,
 A. Rai, K. K. Chintalapudi, V. N. Padmanabhan, and R. Sen, “Zee: Zero-
effort crowdsourcing for indoor localization,” in Proc. 18th Annu. Int.
Conf. Mobile Comput. Netw., 2012, pp. 293–304.
 Y. Jiang et al., “Ariel: Automatic Wi-Fi based room ﬁngerprinting for
indoor localization,” in Proc. ACM Conf. Ubiquitous Comput., 2012,
 V. Radu and M. K. Marina, “HiMLoc: Indoor smartphone localization
via activity aware pedestrian dead reckoning with selective crowdsourced
WiFi ﬁngerprinting,” in Proc. Int. Conf. Indoor Positioning Indoor
Navigat. (IPIN), 2013, pp. 1–10.
 C. Laoudias, D. Zeinalipour-Yazti, and C. G. Panayiotou, “Crowdsourced
indoor localization for diverse devices through radiomap fusion,”
in Proc. Int. Conf. Indoor Positioning Indoor Navigat. (IPIN), 2013,
 J. C. Gower, “Generalized procrustes analysis,” Psychometrika, vol. 40,
no. 1, pp. 33–51, 1975.
 L. M. Ni, Y. Liu, Y. C. Lau, and A. P. Patil, “Landmarc: Indoor location
sensing using active RFID,” Wireless Netw., vol. 10, no. 6, pp. 701–710,
 G.-B. Huang, Q.-Y. Zhu, and C.-K. Siew, “Extreme learning machine:
Theory and applications,” Neurocomputing, vol. 70, no. 1, pp. 489–501,
 G.-B. Huang, H. Zhou, X. Ding, and R. Zhang, “Extreme learning
machine for regression and multiclass classiﬁcation,” IEEE Trans. Syst.
Man Cybern. B, Cybern., vol. 42, no. 2, pp. 513–529, Apr. 2012.
 W. Zong, G.-B. Huang, and Y. Chen, “Weighted extreme learning
machine for imbalance learning,” Neurocomputing, vol. 101, pp. 229–
 M. Brunato and R. Battiti, “Statistical learning theory for location ﬁnger-
printing in wireless lans,” Comput. Netw., vol. 47, no. 6, pp. 825–845,
 E. A. Martnez, R. Cruz, and J. Favela, Estimating User Location in a
WLAN Using Backpropagation Neural Networks. New York, NY, USA:
Springer, 2004, pp. 737–746.
 Z.-l. Wu, C.-H. Li, J.-Y. Ng, and K. Leung, “Location estimation via
support vector regression,” IEEE Trans. Mobile Comput., vol. 6, no. 3,
pp. 311–321, Mar. 2007.
 C. Feng, W. S. A. Au, S. Valaee, and Z. Tan, “Received-signal-strength-
based indoor positioning using compressive sensing,” IEEE Trans.
Mobile Comput., vol. 11, no. 12, pp. 1983–1993, Dec. 2012.
 C.-T. Huang, C.-H. Wu, Y.-N. Lee, and J.-T. Chen, “A novel indoor
RSS-based position location algorithm using factor graphs,” IEEE Trans.
Wireless Commun., vol. 8, no. 6, pp. 3050–3058, Jun. 2009.
 A. Kushki, K. N. Plataniotis, and A. N. Venetsanopoulos, “Kernel-
based positioning in wireless local area networks,” IEEE Trans. Mobile
Comput., vol. 6, no. 6, pp. 689–705, Jun. 2007.
 Y. Jin, W.-S. Soh, and W.-C. Wong, “Indoor localization with channel
impulse response based ﬁngerprint and nonparametric regression,” IEEE
Trans. Wireless Commun., vol. 9, no. 3, pp. 1120–1127, Mar. 2010.
 H. Zou, L. Xie, Q.-S. Jia, and H. Wang, “An integrative weighted path
loss and extreme learning machine approach to RFID based indoor posi-
tioning,” in Proc. 4th IEEE Int. Conf. Indoor Positioning Indoor Navigat.
(IPIN’13), 2013, pp. 1–5.
 H. Zou, X. Lu, H. Jiang, and L. Xie, “A fast and precise indoor localiza-
tion algorithm based on an online sequential extreme learning machine,”
Sensors, vol. 15, no. 1, pp. 1804–1824, 2015.
 H. Cheng, F. Wang, R. Tao, H. Luo, and F. Zhao, “Clustering algorithms
research for device-clustering localization,” in Proc. Int. Conf. Indoor
Positioning Indoor Navigat. (IPIN), 2012, pp. 1–7.
 M. B. Kjrgaard and C. V. Munk, “Hyperbolic location ﬁngerprinting: A
calibration-free solution for handling differences in signal strength (con-
cise contribution),” in Proc. 6th Annu. IEEE Int. Conf. Pervasive Comput.
Commun. (PerCom’08), 2008, pp. 110–116.
 S. L. Jackson, Research methods and statistics: A critical thinking
approach. Cengage Learning, 2015.
 T. S. Rappaport, Wireless Communications: Principles and Practice.
Englewood Cliffs, NJ, USA: Prentice-Hall, 1996, vol. 2.
 A. E. Hoerl and R. W. Kennard, “Ridge regression: Biased estimation
for nonorthogonal problems,” Technometrics, vol. 12, no. 1, pp. 55–67,
 K. Kaemarungsi and P. Krishnamurthy, “Analysis of WLANS received
signal strength indication for indoor location ﬁngerprinting,” Pervasive
Mobile Comput., vol. 8, no. 2, pp. 292–316, 2012.
 H. Zou. (2015). Indoor Navigation on Google Glass [Online]. Available:
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.