A Fast and Precise Indoor Localization Algorithm Based on an Online Sequential Extreme Learning Machine

Abstract

Nowadays, developing indoor positioning systems (IPSs) has become an attractive research topic due to the increasing demands on location-based service (LBS) in indoor environments. WiFi technology has been studied and explored to provide indoor positioning service for years in view of the wide deployment and availability of existing WiFi infrastructures in indoor environments. A large body of WiFi-based IPSs adopt fingerprinting approaches for localization. However, these IPSs suffer from two major problems: the intensive costs of manpower and time for offline site survey and the inflexibility to environmental dynamics. In this paper, we propose an indoor localization algorithm based on an online sequential extreme learning machine (OS-ELM) to address the above problems accordingly. The fast learning speed of OS-ELM can reduce the time and manpower costs for the offline site survey. Meanwhile, its online sequential learning ability enables the proposed localization algorithm to adapt in a timely manner to environmental dynamics. Experiments under specific environmental changes, such as variations of occupancy distribution and events of opening or closing of doors, are conducted to evaluate the performance of OS-ELM. The simulation and experimental results show that the proposed localization algorithm can provide higher localization accuracy than traditional approaches, due to its fast adaptation to various environmental dynamics.

Full text

Sensors 2015,15, 1804-1824; doi:10.3390/s150101804 OPEN ACCESS
sensors
ISSN 1424-8220
www.mdpi.com/journal/sensors
Article
A Fast and Precise Indoor Localization Algorithm Based on an
Online Sequential Extreme Learning Machine †
Han Zou *, Xiaoxuan Lu, Hao Jiang and Lihua Xie
School of Electrical and Electronics Engineering, Nanyang Technological University, 50 Nanyang Ave,
Singapore 639798, Singapore; E-Mails: xlu010@e.ntu.edu.sg (X.L.); jiangh@ntu.edu.sg (H.J.);
elhxie@ntu.edu.sg (L.X.)
†This paper is an extended version of the paper entitled “An Online Sequential Extreme Learning
Machine Approach to WiFi Based Indoor Positioning”, presented at 2014 IEEE World Forum on
Internet of Things (WF-IoT), Seoul, Korea, 6–8 March 2014.
*Author to whom correspondence should be addressed; E-Mail: zouhan@ntu.edu.sg;
Tel.: +65-6790-4242; Fax: +65-6790-5868.
Academic Editor: Kourosh Khoshelham
Received: 20 November 2014 / Accepted: 8 January 2015 / Published: 15 January 2015
Abstract: Nowadays, developing indoor positioning systems (IPSs) has become an
attractive research topic due to the increasing demands on location-based service (LBS)
in indoor environments. WiFi technology has been studied and explored to provide
indoor positioning service for years in view of the wide deployment and availability of
existing WiFi infrastructures in indoor environments. A large body of WiFi-based IPSs
adopt fingerprinting approaches for localization. However, these IPSs suffer from two
major problems: the intensive costs of manpower and time for offline site survey and the
inflexibility to environmental dynamics. In this paper, we propose an indoor localization
algorithm based on an online sequential extreme learning machine (OS-ELM) to address
the above problems accordingly. The fast learning speed of OS-ELM can reduce the
time and manpower costs for the offline site survey. Meanwhile, its online sequential
learning ability enables the proposed localization algorithm to adapt in a timely manner
to environmental dynamics. Experiments under specific environmental changes, such as
variations of occupancy distribution and events of opening or closing of doors, are conducted
to evaluate the performance of OS-ELM. The simulation and experimental results show that
the proposed localization algorithm can provide higher localization accuracy than traditional
approaches, due to its fast adaptation to various environmental dynamics.

Sensors 2015,15 1805
Keywords: indoor localization; online sequential extreme learning machine; WiFi
1. Introduction
The widespread usage of mobile devices and the popularity of social networks have spurred
extensive demands on location-based service (LBS) in recent years. In outdoor environments, GPS
has dominated the LBS market with excellent localization performance. However, due to the lack of line
of sight (LoS) transmission channels between satellites and a receiver, GPS is not capable of providing
positioning service with sufficient localization accuracy in indoor environments [1]. Hence, developing
an indoor positioning system (IPS) to provide reliable and precise indoor positioning and navigation has
become a hot research topic recently. Various wireless communication technologies have been studied
and developed to provide indoor positioning and navigation services in the past two decades [2–5].
Unlike other wireless technologies, such as ultra-wideband (UWB) and radio frequency identification
(RFID), which require the deployment of extra infrastructure, the existing IEEE 802.11 (WiFi) network
infrastructures, such as WiFi routers, are widely available in large numbers of commercial and residential
buildings, and nearly every mobile device now is equipped with a WiFi receiver. As such, it is low-cost
and practical to develop a WiFi-based IPS to provide LBS in an indoor environment [6–11].
Fingerprinting-based localization algorithms are widely adopted for WiFi-based indoor positioning,
since the received signal strengths (RSS) can be measured easily from mobile devices [7–12].
However, the existing WiFi-based IPSs adopting the fingerprinting approach suffer from two major
problems. One is that the site survey involves intensive costs of both time and manpower during the
offline calibration phase. In order to achieve sufficient localization accuracy, the WiFi RSS fingerprints
from different access points (APs) need to be measured at a huge number of calibration points. The other
one is that the existing fingerprinting-based approaches are not robust to environmental dynamics [6,13].
Since the WiFi RSS fingerprint database is built up during the offline phase, it cannot reflect the real-time
radio map of the WiFi signals well once the environment is altered during the online localization phase.
Environmental factors, such as presence of humans, opening and closing of doors and variations of
humidity, can interfere with the propagation of WiFi signals severely [6]. This will lead to serious
localization errors in the estimation of the target if the same WiFi RSS fingerprint database is adopted.
In this paper, we propose an indoor localization algorithm based on an online sequential extreme
learning machine (OS-ELM) to address the above two problems accordingly. Originating from the
batch learning extreme learning machine (ELM), OS-ELM inherits the advantage of ELM, which
can provide good generalization performance at an extremely fast learning speed [14]. In addition,
OS-ELM has an online sequential learning ability that does not require retraining when new data are
received [15]. Another noteworthy point of OS-ELM is that, different from other online sequential
learning algorithms, such as stochastic gradient descent back-propagation (SGBP) [16] and growing
and pruning RBF network (GAP-RBF) [17], which require specific types of hidden nodes and can only
handle data one-by-one (learning only one training sample at each time), OS-ELM is able to adapt to
various types of hidden nodes and can learn data one-by-one or chunk-by-chunk with a varying chunk
size. Therefore, WiFi RSS fingerprints can be collected and updated more flexibly for OS-ELM online

Sensors 2015,15 1806
sequential learning. In addition, the fast learning speed of OS-ELM greatly reduces time consumption
and manpower costs for the offline site survey. More importantly, the online sequential learning ability of
OS-ELM permits the entire system to provide sufficient localization accuracy, even under environmental
dynamics. A preliminary version of this paper was presented at the 2014 IEEE World Forum on the
Internet of Things (WF-IoT) Conference [18]. In addition to the results in [18], a more elaborate
description of the OS-ELM approach is presented in this paper. Furthermore, a simulation is conducted
and demonstrated, as well. Besides overall performance evaluation and comparison between OS-ELM
and existing fingerprinting-based approaches, experiments under specific environmental changes, such
as variations of occupancy distribution and events of opening or closing of doors, are also conducted to
evaluate the performance of OS-ELM in this paper.
The rest of the paper is organized as follows. In Section 2, we review related works. Section 3 provides
the proposed localization algorithm. The simulation results and evaluation of OS-ELM are presented in
Section 4. In Section 5, a system overview of our WiFi-based IPS is provided firstly, followed by the
experimental results and performance evaluation of the proposed localization algorithm. We conclude
the work in Section 6.
2. Related Works
Indoor localization algorithms have been extensively studied, and a number of approaches has been
proposed over the past two decades [2,3]. These algorithms can be classified into two categories:
model-based approaches and fingerprinting-based approaches.
2.1. Model-Based Approaches
Model-based approaches use geometrical models, such as time of arrival (ToA) [19] and time
difference of arrival (TDoA) [20], to estimate the position of the target [21,22]. Several model-based
approaches employing radio propagation models have been investigated in [23]. The log-distance path
model, which estimates the RSS value based on the propagation distances, is one of the most popular
models. For instance, weighted path loss (WPL) [24] can achieve a 2-m localization accuracy on
RFID-based IPS. The AP locations and floor plans are also leveraged to improve the estimation of the
RSS value for model-based approaches [7].
However, establishing a sophisticated indoor radio propagation model is very difficult, due to the
irregular signal propagation in an indoor environment. Moreover, model-based approaches also suffer
from the interference from different materials and mobile obstacles.
2.2. Fingerprinting-Based Approaches
A large body of existing IPSs adopt the other type of localization algorithms, namely the
fingerprinting-based approaches, which usually involve two phases: an offline training phase and an
online localization phase. During the offline training phase, a site survey dedicated to collecting the WiFi
RSS fingerprints from different APs at some known locations is performed in the indoor environment,
and consequently, a WiFi RSS fingerprint database is built up. During the online localization phase, when

Sensors 2015,15 1807
a user sends a location query containing his or her current WiFi RSS fingerprint, the location of the user
will be estimated by matching the measured fingerprint with the fingerprints stored in the database, and
the location associated with the matching fingerprint will be returned as his or her location estimation.
A majority of these approaches leverage RF signals for RSS fingerprinting. To name a few,
Horus [8] is based on WiFi signals, while LANDMARC [25] utilizes RFID signals; FM radio [26],
geomagnetisms [27,28] and GSM signals [29] are also adopted as fingerprints for indoor localization.
Although fingerprinting-based approaches require a site survey to build up a fingerprint database
during the offline phase, they can provide a higher localization accuracy than model-based approaches
in general [2].
One of the disadvantages of existing fingerprinting-based approaches is the high calibration cost, as
a labor-intensive offline site survey is required to build up the RSS fingerprint database. Moreover, the
static database is vulnerable to environmental dynamics. The offline site survey needs to be reconstructed
when any environmental factor is altered, which involves extensive maintenance costs and efforts.
3. An Indoor Localization Algorithm
3.1. Preliminary on OS-ELM
ELM is a type of machine learning algorithm based on a single-hidden layer feedforward neural
network (SLFN) architecture. OS-ELM on the basis of ELM was developed for SLFNs with additive
hidden nodes [15]. Assume there are Narbitrary distinct training samples (xi,ti)∈Rn×Rm, where
xare the training inputs and tare the training targets. If a SLFN with Lhidden nodes can approximate
these Nsamples with zero error, there exist βi,aiand bi, such that:
fL(xj) =
L
X
i=1
βiG(ai, bi,xj) = tj, j = 1,2, . . . , N (1)
where aiand biare the learning parameters of the hidden nodes, βiis the output weight and G(ai, bi,xj)
is the activation function, which gives the output of the i-th hidden node with respect to the input xj.
If the hidden node is additive, G(ai, bi,xj) = g(ai·xj+bi), bi∈R, where aiis the input weight vector,
biis the bias of the i-th hidden node and ai·xjdenotes the inner product of the two.
The OS-ELM algorithm contains two phases: an initialization phase and a sequential learning
phase. One special property of OS-ELM is that it can learn data one-by-one or chunk-by-chunk
(a block of data) with a fixed or varying chunk size [15]. Suppose the network has Lhidden nodes
and the data ℵ={(xi,ti)|xi∈Rn,ti∈Rm, i = 1, . . . , N }are presented to the network sequentially.
In the initialization phase, rank(H0) = Lis required to ensure that OS-ELM can achieve the same
learning performance as ELM, where H0denotes the hidden output matrix for the initialization phase.
The number of training data required in the initialization phase, N0, has to be equal to or greater than L,
i.e.,N0≥L. If N0=N, the performance of OS-ELM is the same as batch ELM. Therefore, batch ELM
is a special case of OS-ELM when all of the data are used in the initialization phase.
Initialization phase: a small chunk of training data ℵ0is used to initialize the learning, where
ℵ0={xi,ti}N0
i=1 ⊆ ℵ and N0≥L.
Step 1: Randomly assign the input parameters: input weights aiand bias bi,i= 1, . . . , L.

Sensors 2015,15 1808
Step 2: Calculate the initial hidden layer output matrix H0=



G(a1, b1,x1). . . G(aL, bL,x1)
.
.
.. . . .
.
.
G(a1, b1,xN0). . . G(aL, bL,xN0)


N0×L
(2)
Step 3: Estimate the initial output weight β(0). Since T0= [t1,...,tN0]T
N0×m, the problem is
equivalent to minimizing kH0β−T0k. Noticing that H†= (HTH)−1HT[14], the optimal solution
is given by β(0) =P0HT
0T0, where P0= (HT
0H0)−1and K0=P−1
0=HT
0H0.
Step 4: Set k= 0, where kis a parameter indicating the number of chunks of data that are presented
to the network.
Sequential learning phase: present the (k+ 1)-th chunk of new observations
ℵk+1 ={(xi,ti)}Σk+1
j=0 Nj
i=(Σk
j=0Nj)+1, where Nk+1 denotes the number of observations in the (k+ 1)-th chunk.
Step 1: Compute the partial hidden layer output matrix Hk+1 =




G(a1, b1,x(Σk
j=0Nj)+1 ). . . G(aL, bL,x(Σk
j=0Nj)+1 )
.
.
.. . . .
.
.
G(a1, b1,xΣk+1
j=0 Nj). . . G(aL, bL,xΣk+1
j=0 Nj)



Nk+1×L
(3)
Step 2: Calculate the output weight β(k+1) . We have Tk+1 = [t(Σk
j=0Nj)+1,...,tΣk+1
j=0 Nj]T
Nk+1×m.
Moreover,
Kk+1 =Kk+HT
k+1Hk+1 (4)
β(k+1) =β(k)+K−1
k+1HT
k+1(Tk+1 −Hk+1β(k))(5)
In order to avoid inverting matrices, such as K−1
k+1 in Equation (5) in the recursive process, the
Woodbury formula [30] is applied to transform the equations as follows:
K−1
k+1 =K−1
k−K−1
kHT
k+1(I+Hk+1K−1
kHT
k+1)−1Hk+1K−1
k(6)
Since Pk+1 =K−1
k+1,
Pk+1 =Pk−PkHT
k+1(I+Hk+1PkHT
k+1)−1Hk+1Pk(7)
β(k+1) =β(k)+Pk+1HT
k+1(Tk+1 −Hk+1β(k))(8)
Step 3: Set k=k+ 1. Go to Step 2 in this online sequential learning phase.
3.2. OS-ELM-Based Indoor Localization Algorithm
The proposed OS-ELM approach considers the localization problem as a regression problem.
For WiFi RSS fingerprint calibration process, OS-ELM only requires a relative sparse radio map of WiFi
RSS during the offline phase, which trumps the traditional fingerprinting-based localization algorithms.
These WiFi RSS fingerprints and their physical locations are adopted as training inputs and training
targets, respectively, to build up an initial OS-ELM model for online localization.

Sensors 2015,15 1809
Furthermore, by leveraging the online learning ability of OS-ELM, WiFi RSS fingerprints can also
be collected at some known locations during the online phase to reflect the environmental dynamics.
Once new WiFi RSS fingerprints have been collected, they will be integrated into the initial OS-ELM
model to update and generate a revised OS-ELM model. During the online phase, when a user sends a
location request with his or her current WiFi RSS fingerprint, the fingerprint will be fed into the latest
revised OS-ELM model, and then, the estimated location will be calculated.
The methodology and framework of the proposed OS-ELM approach are demonstrated in Figure 1.
The processes of the three main phases of the OS-ELM approach are presented as follow:
Figure 1. Methodology of the online sequential extreme learning machine
(OS-ELM) approach.
3.2.1. Offline Calibration Phase
Suppose ℵ0WiFi RSS fingerprints are collected at some known locations during the offline calibration
phase. These WiFi RSS fingerprints and their corresponding physical locations are adopted as the
training inputs xand the training targets t, respectively, for OS-ELM offline training. Similar to the
initialization phase of OS-ELM, the initial OS-ELM model will be trained as mentioned in Section 3.1.
The detailed steps are illustrated below:
Step 1: Randomly assign the input parameters: input weights aiand input bias bi.
Step 2: Calculate the initial hidden layer output matrix H0.
Step 3: Estimate the initial output weight β(0) .
Step 4: Set k= 0, where kindicates the number of updating times of WiFi RSS fingerprints that are
collected during the online calibration phase.
Additionally, the activation function Gand the number of hidden nodes Lneed to be carefully tuned
in order to guarantee that the initial OS-ELM model can provide sufficient localization accuracy for

Sensors 2015,15 1810
the users before any WiFi RSS fingerprints are collected at any online calibration points during the
online phase. The five-fold cross-validation method with a range from zero to 1000 and a step size of
50 is employed to select the optimal number of hidden nodes L. A guideline for selecting the type of
activation functions and the number of hidden nodes is presented in Section 5.
3.2.2. Online Sequential Learning Phase
The main purpose of the online sequential learning phase of OS-ELM is to make the localization
algorithm more robust and be able to adapt to various environmental changes. Unlike other online
sequential learning algorithms, which can only handle data one-by-one, OS-ELM can learn data
one-by-one or chunk-by-chunk with a varying chunk size.
Therefore, WiFi RSS fingerprints can be collected and updated more flexibly for OS-ELM online
sequential learning. These newly collected WiFi RSS fingerprints and their corresponding physical
locations will be adopted as training samples, and they will be updated chunk-by-chunk to revise the
initial OS-ELM model during the online sequential learning phase. Suppose ℵk+1 WiFi RSS fingerprints
have been collected during the (k+1)-th online calibration; the revised OS-ELM model will be obtained
by the following steps:
Step 1: Calculate the partial hidden layer output matrix Hk+1 .
Step 2: Calculate the output weight β(k+1) .
Step 3: Set k=k+ 1 for the next online calibration.
3.2.3. Online Localization Phase
Before any WiFi RSS fingerprints are collected at any known locations during the online phase, the
initial OS-ELM model will be used to provide estimated locations of users when they send location
queries with their real-time WiFi RSS fingerprints.
When more WiFi RSS fingerprints are collected at some known locations during the online calibration
phase, the OS-ELM model is updated and revised. It will be used to provide the estimated location of
the user.
4. Simulation Results and Evaluation
We develop a simulation environment using MATLAB R2013a in order to evaluate the performance
of the proposed OS-ELM approach before any experiment is conducted. The simulation is running on a
PC, which has a Intel Core i5-2400 3.10-GHz CPU and 8 GB RAM. As shown in Figure 2, we assume a
20 m ×20 m room, where four WiFi access points are installed at the four corners of the room. The most
commonly-used path loss model for indoor environment is the International Telecommunication Union
(ITU) indoor propagation model [31]. Since it provides a relation between the total path loss P L (dBm)
and distance d(m), it is adopted to simulate the WiFi signals generated from each WiFi access point.
The indoor path loss model can be expressed as:
P L(d) = P L0−10αlog(d) + Xσ(9)

Sensors 2015,15 1811
where P L0is the pass loss coefficient, and it is set to be −40 dBm in our simulation. Xσrepresents a
zero-mean normal random noise with standard deviation σ= 0.5, and αis the path loss exponent.
Figure 2. Positions of the WiFi access points, offline calibration points, online calibration
points and online testing points in the simulated field.
During the offline calibration phase, αis set to be two in Scenario I, and simulated WiFi RSS
fingerprints from the four WiFi routers are collected at 10 randomly selected offline calibration points for
OS-ELM offline training, with 200 WiFi RSS fingerprints collected at each point. The hardlim function
G(a, b, x) = hardlim(ax +b)is chosen as the activation function, and 380 hidden nodes are selected
and put in the hidden layer during the offline training. The initial OS-ELM model is obtained after
a 0.219-s training process. In order to imitate the environmental dynamics in the room, we set αto
be 2.5 in Scenario II and 3.5 in Scenario III, respectively. WiFi RSS fingerprints are collected at five
online calibration points and five online testing points under each scenario. Two hundred WiFi RSS
fingerprints are collected at each point, and the positions of these points are distinct. The positions of
the offline calibration points, the online calibration points and the online testing points are demonstrated
in Figure 2. The updated WiFi RSS fingerprints at the online calibration points are adopted as online
training samples and leveraged to revise the initial OS-ELM model.
We evaluate the performance of OS-ELM with each online sequential learning updated based on the
WiFi RSS fingerprints collected at the 10 online testing points. The distance error is used to measure the
localization accuracy of the proposed OS-ELM 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=p(x−x0)2+ (y−y0)2(10)
Table 1illustrates the performance of OS-ELM with each online sequential learning update in terms
of training time, testing time and average localization accuracy. The comparison of the cumulative
percentile of error distances between the initial OS-ELM and the two updated OS-ELM is presented

Sensors 2015,15 1812
in Figure 3. It can be easily spotted from Table 1that the average localization accuracy of OS-ELM
becomes better when more WiFi RSS fingerprints at various online calibration points have been learned
online. The latest updated OS-ELM can provide 1.794 m, which enhances the precision of indoor
localization by 42.18% over the performance of the initial OS-ELM. Furthermore, the online sequential
learning of OS-ELM is very efficient. It only spends 0.014 s on average to calculate the output weights
βfor 1000 newly-received WiFi RSS fingerprints in each online sequential learning update.
Table 1. Simulation results of OS-ELM.
Number of Calibration Points (Offline + Online) Training Time (s) Testing Time (s) Accuracy (m)
10 + 0 0.219 0.015 3.103
10 + 5 0.148 0.014 2.563
15 + 5 0.139 0.014 1.794
Figure 3. Cumulative percentile of error distance.
Based on the simulation results and evaluation, we can conclude that OS-ELM can provide higher
localization accuracy due to its efficient online sequential learning ability when the indoor environment
is altered during the online phase.
5. Experimental Results and Performance Evaluation
5.1. System Overview
We conducted extensive experiments to evaluate the performance of the proposed OS-ELM approach.
The testbed is Internet of Things Laboratory at School of Electrical and Electronic Engineering, Nanyang
Technological University. The area of the test-bed is around 580 m2(35.1 m ×16.6 m). Thirty six
graduate students and 15 undergraduate students work and study in this lab regularly.

Sensors 2015,15 1813
The layout of the testbed is shown in Figure 4. Eight D-Link DIR-605L WiFi Cloud Routers are
utilized as WiFi access points for our experiments. In order to collect WiFi RSS fingerprints from
multiple access points simultaneously, an Android application that can collect data once per second is
developed. As shown in Figure 5, this Android app is installed on a Samsung I929 Galaxy SII mobile
phone. We leveraged this mobile phone to collect the WiFi RSS fingerprints at the offline calibration
points, online calibration points and online testing points. After that, all of this information was sent to
a process server running on a PC. The performance evaluation was conducted on the server side.
Figure 4. Positions of the WiFi access points, offline calibration points, online calibration
points and online testing points in the test-bed.
Figure 5. The test mobile device Samsung I929 and developed Android apps.
The initial OS-ELM model was built by the following steps. During the offline phase, 30 offline
calibration points were selected, and 1000 WiFi RSS fingerprints were collected at each point.
The positions of these 30 offline calibration points are demonstrated in Figure 4. The grid spacing
between two adjacent locations of the calibration points was chosen to be larger than 1.25 m based on
the analysis in [32]. By leveraging these 30,000 WiFi RSS fingerprints and their physical positions as

Sensors 2015,15 1814
training inputs and training targets accordingly, the initial OS-ELM model was constructed. During the
online phase, we continued to collect WiFi RSS fingerprints at several online calibration points and
online testing points for five days. In each day, two distinct online calibration points and two distinct
online testing points were selected in order to reflect the environmental dynamics. The positions of
these total 10 online calibration points and 10 online testing points are also presented in Figure 4.
One thousand WiFi RSS fingerprints are collected at each point. Unlike [18], which only tested the
performance of OS-ELM in the corridors in the testbed, as shown in Figure 4, the positions of the online
calibration points and online testing points were selected on the tables and cubicles, as well as in the
testbed to acquire a more comprehensive performance evaluation of the proposed OS-ELM approach.
5.2. Selection of Parameters for the Initial OS-ELM Model
Based on the analysis in Section 3.2, the type of activation function and the number of hidden nodes
in the OS-ELM hidden layer are two key parameters affecting the performance of OS-ELM during the
initialization phase, which is accordingly the offline calibration phase in our case.
5.2.1. Selection of the Type of Activation Function Gfor the Initial OS-ELM Model
By using the 30,000 WiFi RSS fingerprints we collected during the offline calibration phase,
we evaluate the performance of three different activation functions: radial basis function (RBF)
G(a, b, x) = e−b||x−a||2, sine function G(a, b, x) = sin(ax +b)and hard-limit transfer (hardlim) function
G(a, b, x) = hardlim(ax +b), with different numbers of hidden nodes.
It can be seen from Figure 6that as the number of hidden nodes increases, the performances in terms
of the mean localization accuracy of the sine function and hardlim function become better. On the
contrary, the performance of RBF is the worst and appears to be irrelevant with respect to the number
of hidden nodes. Since the performance of the hardlim function is the best among the three activation
functions, it is chosen as the activation function for the initial OS-ELM model and also for the online
sequential learning of OS-ELM.
Figure 6. Localization accuracy regarding different activation functions and different
numbers of hidden nodes.

Sensors 2015,15 1815
5.2.2. Selection of the Number of Hidden Nodes Lfor the Initial OS-ELM Model
Another critical parameter for the performance of the OS-ELM approach is the number of hidden
nodes Lin the initial OS-ELM hidden layer, after the hardlim function is chosen as the activation
function. The five-fold cross-validation method is employed with a range from 0 to 1000 and a step
size of 50 in order to determine the optimal L. As observed in Figure 6, the performances in terms of the
localization accuracy of the hardlim function become relatively stable when Lis increased to 600.
In addition to the evaluation of the localization accuracy, the repeatability (REP) of the initial
OS-ELM with a different number of hidden nodes is also evaluated by leveraging the 30,000 WiFi
RSS fingerprints that we collected during the offline calibration phase. REP is measured by the standard
deviation of localization errors over the rrepeated realizations, and this measure is proposed based on the
fact that ELM with the same parameters and in the same training dataset may draw quite different results.
A smaller value of REP is desired in general. The mean localization error ¯eand REP are calculated based
on the following equations:
¯e=1
r
r
X
m=1
em(11)
REP =v
u
u
t
1
r
r
X
m=1
(em−¯e)(12)
rin our experiment is selected as 50. Figure 7demonstrates the repeatability of the initial OS-ELM,
which is measured by the standard deviation of localization error with a range of hidden nodes from
zero to 1000 and a step size of 50. As observed from Figure 7, the standard deviation of localization
errors decreases when the number of hidden nodes is increased. After comprehensive evaluations on
both localization accuracy and repeatability, Lis selected to be 950.
Figure 7. Deviation of distance error with different numbers of hidden nodes.

Sensors 2015,15 1816
A guideline for selecting the type of activation function and the number of hidden nodes in the
OS-ELM hidden layer, both of which are the critical parameters for the performance of the OS-ELM
approach, is listed as follows: the suggested default activation function for the OS-ELM approach is
the hardlim function, whose performance is better than others generally in terms of simulation and
experimental results. As for the optimal number of hidden nodes, the five-fold cross-validation method
is employed with a range from 0 to 1000 and a step size of 50 based on the empirical tuning.
5.3. Comparison between OS-ELM and Other Methods
Three well-known algorithms, RADAR K nearest neighbor (KNN) [7], fuzzy K nearest neighbor
(Fuzzy KNN) [33] and batch ELM [14], are chosen to compare with the proposed OS-ELM approach.
It has been shown in [34,35] that the performance of batch ELM in terms of the offline training time,
the online testing time and the average localization accuracy is better than classical machine learning
algorithms, such as the back-propagation (BP) algorithm and the support vector machine for regression
(SVR) algorithm. Therefore, we choose batch ELM to be compared with the proposed OS-ELM.
Considering the wide usage of KNN and fuzzy KNN as classical localization algorithms, we also include
them in the comparison.
Unlike OS-ELM, which can update and revise the initial OS-ELM model sequentially during the
online phase, KNN, fuzzy KNN and batch ELM can only utilize the data collected during the offline
phase. In order to make a fair comparison, we collected WiFi RSS fingerprints, not only at the 30 offline
calibration points, but also at the 10 online calibration points, to build up the WiFi RSS fingerprints
offline database during the offline calibration phase. One thousand WiFi RSS fingerprints were collected
at each point. The hardlim function and 950 hidden nodes in the hidden layer were chosen for batch ELM
offline training, which are the same as for the initial OS-ELM offline training. The batch ELM model
was obtained by leveraging the WiFi RSS fingerprints and their corresponding locations stored in the
database. During the online phase, after feeding the WiFi RSS fingerprints into the batch ELM model,
this model will output the estimated location of the target. For KNN and fuzzy KNN, the value of Kwas
chosen empirically based on the data stored in the database. 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 detail methodologies of these are presented in [7,33].
The comparison of performances will be conducted as follows. First of all, we evaluate the
performances of KNN, fuzzy KNN, batch ELM and OS-ELM without online sequential learning based
on the WiFi RSS fingerprints we collected at the 10 online testing points during the online localization
phase. Table 2demonstrates the performance comparison between KNN, fuzzy KNN, batch ELM and
OS-ELM in terms of the training time, the testing time and the average localization accuracy. As shown
in Table 2, although the localization accuracy of the initial OS-ELM is slightly worse than that of batch
ELM, the offline training time of OS-ELM is less than that of batch ELM by 30.01%, which evidently
reduces the time and manpower costs for the offline site survey. The testing times of KNN, fuzzy KNN,
batch ELM and OS-ELM are almost the same.

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Table 2. Comparison between OS-ELM and other methods.
Approaches Number of Calibration Points Training Time Testing Time Accuracy
(Offline + Online) (s) (s) (m)
KNN 40 + 0 - 0.108 3.098
Fuzzy KNN 40 + 0 - 0.117 2.728
Batch ELM 40 + 0 11.574 0.113 2.581
OS-ELM
30 + 0 8.101 0.113 2.615
30 + 2 1.204 0.111 2.487
32 + 2 1.213 0.114 2.346
34 + 2 1.182 0.109 2.219
36 + 2 1.226 0.115 2.091
38 + 2 1.229 0.117 1.973
During the online phase, since we collected WiFi RSS fingerprints at two different online calibration
points at each time, the performance of OS-ELM with each online sequential learning update is also
presented in Table 2. As observed from Table 2, the average localization accuracy of OS-ELM becomes
better when more WiFi RSS fingerprints at different online calibration points have been learned online.
In addition, another noteworthy point is that the online sequential learning time of OS-ELM is quite fast.
It only spends 1.2108 s on average to calculate the output weights βfor 2000 newly-received WiFi RSS
fingerprints in each online sequential learning update.
As observed from Table 2, the average localization accuracy by using KNN, fuzzy KNN and batch
ELM is, respectively, 3.098 m, 2.728 m and 2.581 m. In contrast, with online sequential learning of WiFi
RSS fingerprints at 10 different online calibration points, OS-ELM can provide a localization accuracy of
1.973 m, which enhances the precision of indoor localization by 36.31%, 27.68% and 23.56% over KNN,
fuzzy KNN and batch ELM, respectively. The comparison of the cumulative percentile of error distances
between KNN, fuzzy KNN, batch ELM and the latest updated OS-ELM is presented in Figure 8. Figure 9
demonstrates the distance error distribution of the four approaches. The distance error distribution of
OS-ELM, as shown in Figure 9d, ranges mainly within 2.5 m. On the contrary, the distance error
distributions of KNN in Figure 9a, fuzzy KNN in Figure 9b and batch ELM in Figure 9c are much
more scattered.
Figure 8. Cumulative percentile of error distance for different methods.

Sensors 2015,15 1818
(a) (b)
(c) (d)
Figure 9. Comparison of the distance error distribution for different methods. (a) KNN;
(b) fuzzy KNN; (c) batch ELM; (d) OS-ELM.
In summary, based on our experimental results and analysis, we can conclude that OS-ELM can
provide higher localization accuracy consistently with a fast online sequential learning speed to adjust to
various environmental dynamics than existing approaches, such as KNN, fuzzy KNN and batch ELM.
5.4. Performance Evaluation of OS-ELM under Specific Environmental Dynamics
Variations of occupancy distribution and events of opening and closing of doors have been observed
as two major environmental factors that could severely affect the localization accuracy of WiFi-based
IPS, since they change frequently over time in the indoor environment [6]. Besides the general
performance evaluation of the proposed OS-ELM approach, as shown in [18] and the above sections,
we also conducted experiments to evaluate how well OS-ELM adapts to some specific environmental

Sensors 2015,15 1819
dynamics. During each experiment, we measured the localization accuracy of the system when only one
environmental factor was altered, while others remained unvaried.
5.4.1. Impact of Human Presence and Movements
This experiment aims to determine how well the proposed OS-ELM approach can adjust to the
interferences of human presence and movements while other environmental factors are kept unchanged.
The experiment was conducted in the conference room in the testbed, since it is easier to create and
manage the variation of the occupancy distribution for performance evaluation in this relatively small
space. As shown in Figure 1, the location of the conference room is the left upper corner of the testbed.
The area of the conference room is around 22 m2(6.3 m ×3.5 m).
The experiment was conducted based on the following steps. First of all, we continued to collect
WiFi RSS fingerprints at five offline calibration points for one day when nobody was in the conference
room. After that, the batch ELM model and the initial OS-ELM model were built up based on the
collected WiFi RSS fingerprints and their corresponding positions. We put the testing mobile device
on the conference table to evaluate the performances of the batch ELM and the OS-ELM under the
non-human interference condition in the first place. As shown in Table 3, the batch ELM and the
OS-ELM provide similar localization accuracy under the non-human interference condition, which is
2.203 m and 2.183 m, respectively.
Table 3. Impact of human presence and movements on localization accuracy.
Localization Accuracy (m) Non-Human Interference With Human Interference
Batch ELM 2.203 3.106
OS-ELM 2.183 2.197
Then, we evaluate the performance of both batch ELM and OS-ELM with human interference.
The position of the online testing point was unchanged. However, five people intentionally sat around
the table for 6 h. The purpose is to use human bodies to disturb or block the WiFi signal transmission
between the test mobile device and the multiple WiFi access points. Meanwhile, WiFi RSS fingerprints
were collected at three online calibration points to update and revise the OS-ELM model.
After conducting the experiment for 6 h, the average localization accuracies of the two approaches
are calculated and demonstrated in Table 3. It can be seen from Table 3that the performance of
batch ELM becomes worse with human interference. Its performance decay is 41.99% compared
with non-human interference. The main reason is that the batch ELM model was constructed under
non-human interference, which cannot reflect the variation of occupancy distribution adaptively during
the online phase. On the contrary, by leveraging the information collected at the online calibration points,
OS-ELM can nicely capture the event of human presence and movements and take this environmental
change into the online localization process sequentially. As shown in Table 3, the average localization
accuracy provided by OS-ELM under the human interference circumstance is 2.197 m, almost the same
as the non-human interference scenario. It enhances the precision of indoor localization by 29.27% over
batch ELM under the same condition.

Sensors 2015,15 1820
To conclude, OS-ELM can provide high localization accuracy consistently when the occupancy
distribution is altered due to its fast adaptation.
5.4.2. Impact of Opening/Closing of Doors
Besides the variation of occupancy distribution, another environmental factor that affects the
performance of WiFi-based IPS badly is the events of opening and closing of doors. Therefore, we also
conducted an experiment to evaluate how well the proposed OS-ELM approach can adjust to opening
and closing of doors while other environmental factors were kept unchanged.
The experiment was conducted based on the following steps. We collected WiFi RSS fingerprints at
15 offline calibration points, which were near the four doors inside the testbed for one day under the
all-door-open condition firstly. The batch ELM model and the initial OS-ELM model were built up by
leveraging the collected WiFi RSS fingerprints and their corresponding positions. Then, we determined
the performance of these two approaches near the door area. It can be seen from Table 4that both
batch ELM and OS-ELM can provide nearly 2.15-m localization accuracy on average when all doors
are opened.
Table 4. Impact of opening/closing doors on localization accuracy.
Localization Accuracy (m) All Doors are Opened All Doors are Closed
Batch ELM 2.214 4.203
OS-ELM 2.107 2.085
After that, we continued the experiment to assess the performance of these two approaches under the
all-door-close condition. We closed the four doors within the testbed for 6 h and collected WiFi RSS
fingerprints at the same online testing points as under the all-door-open condition. WiFi RSS fingerprints
were also collected at the 10 online calibration points in the testbed simultaneously for updating the
OS-ELM model.
The average localization accuracy of batch ELM and OS-ELM under the all-door-close condition is
presented in Table 4. As shown in Table 4, the average localization accuracy of batch ELM is 4.203 m
when all doors are closed, which is 47.32% worse than the all-door-open condition. This reveals that
batch ELM is not capable of providing a sufficient and satisfactory indoor positioning service when the
status of doors is different from the offline calibration phase.
In contrast, the performance of OS-ELM is more stable and robust when the status of doors is
altered. It can be seen in Table 4that the average localization accuracy provided by OS-ELM under
the all-door-close condition is 2.085 m, which is roughly the same as the all-door-open condition.
Moreover, it enhances the precision of indoor localization by 50.39% over batch ELM. The main reason
that OS-ELM can consistently provide the indoor positioning service under different status of doors
is due to its online sequential learning ability. By leveraging the information collected at the online
calibration points, OS-ELM can sequentially update its model to adjust the influence from opening or
closing doors.

Sensors 2015,15 1821
Thus, the experimental results leads to the same conclusion that OS-ELM can provide higher
localization accuracy steadily under various environmental dynamics, regardless of the impact from
human presence or movements or the influence from changing the status of doors.
6. Conclusions and Future Work
In this paper, we proposed an indoor localization algorithm based on OS-ELM to address the two
challenging problems of the existing WiFi-based IPS: the intensive costs of manpower and time for
offline site survey and the inflexibility to environmental dynamics. Both our simulation analysis and
experimental studies have shown that OS-ELM can tackle the problems satisfactorily. The fast learning
speed of OS-ELM obviously reduced the time consumptions and manpower costs for the site survey
during the offline calibration phase. In addition, the online sequential learning ability of OS-ELM
made it possible to reflect and adapt to the environmental changes in a timely manner. Furthermore,
WiFi RSS fingerprints can be collected and updated more flexibly, since OS-ELM can learn data with
a varying chunk size. Experiments under specific environmental dynamics, such as variations of the
occupancy distribution and events of opening or closing doors, were also conducted. In summary,
OS-ELM can provide high localization accuracy with a fast online sequential learning speed under
various environmental changes and achieve superior performance to the existing approaches.
Future work can be focused on the following directions. Firstly, since we only conducted experiments
in the lab environment, experiments in other indoor scenarios, such as lecture theaters or shopping
centers, need to be conducted to make the performance evaluation of OS-ELM more conclusive.
Secondly, mobile devices with different brands or equipped with different WiFi chipsets as the one used
in the experiments will incur degraded localization accuracy. Therefore, how to improve OS-ELM to
overcome the heterogeneous issue among mobile devices is quite attractive.
Acknowledgments
This research is partially funded by the Republic of Singapore National Research Foundation
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.
BEARS has been established by the University of California, Berkeley, as a center for intellectual
excellence in research and education in Singapore.
This research is also partially funded by the Republic of Singapore National Research
Foundation through grants: NRF2011NRF-CRP001-090, NRF2013EWT-EIRP004-012 and NSFC
NSFC 61120106011.
Author Contributions
Han Zou proposed the OS-ELM-based localization algorithm and expanded the conference version
to a journal version. Han Zou and Xiaoxuan Lu conducted the simulation and experiments. Hao Jiang
developed the Android app for the experiment. Lihua Xie supervised the work and revised the paper.

Sensors 2015,15 1822
Conflicts of Interest
The authors declare no conflict of interest.
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