Energy-efficient mobile tracking in heterogeneous networks using node selection

Abstract

Range-based positioning is capable of achieving better accuracy in heterogeneous networks, where mobile nodes enabled with multiple radio access technologies are allowed to deploy not only the faraway access points but also high spatial density peer nodes as anchor nodes. However, due to peer node energy supply constraint and network capacity constraint, an efficient cooperation strategy is required. In this paper, we propose a cooperation method to track the position of a moving target with high accuracy and reduce the energy consumption and signaling overhead via node selection. It is demonstrated by simulation that in a specific practical scenario, the proposed method is capable of reducing the signaling overhead by about 34% to within 0.5-m degradation of accuracy compared to exhaustive cooperation. We also evaluate the achievable performance averaged over randomly located node configurations and compare the proposed scheme with the mostly used nearest-node selection algorithm in terms of accuracy and cost.

Full text

R E S E A R C H Open Access
Energy-efficient mobile tracking in heterogeneous
networks using node selection
Senka Hadzic
1
, Du Yang
1*
, Manuel Violas
1,2
and Jonathan Rodriguez
1
Abstract
Range-based positioning is capable of achieving better accuracy in heterogeneous networks, where mobile nodes
enabled with multiple radio access technologies are allowed to deploy not only the faraway access points but also high
spatial density peer nodes as anchor nodes. However, due to peer node energy supply constraint and network capacity
constraint, an efficient cooperation strategy is required. In this paper, we propose a cooperation method to track the
position of a moving target with high accuracy and reduce the energy consumption and signaling overhead via node
selection. It is demonstrated by simulation that in a specific practical scenario, the proposed method is capable of
reducing the signaling overhead by about 34% to within 0.5-m degradation of accuracy compared to exhaustive
cooperation. We also evaluate the achievable performance averaged over randomly located node configurations and
compare the proposed scheme with the mostly used nearest-node selection algorithm in terms of accuracy and cost.
Keywords: Heterogeneous network; Anchor selection; Accuracy indicator
1 Introduction
Indoor localization via wireless signals is increasingly be-
coming a prominent feature for intelligent services and
applications. Range-based positioning first estimates the
Euclidian distance between the target node and several
position-known anchor nodes via received signal strength
(RSS), time of arrival (ToA), or other distance-dependent
signal metrics and then derives the target node coordi-
nates by exploiting the geometrical relationship between
distances and coordinates. In the context of noncoopera-
tive homogeneous network, the number of anchor nodes
such as Wi-Fi access points are small and far away from
each other, which limits the localization accuracy.
In the context of heterogeneous network, a multi-Radio
Access Technology (RAT) aided mobile device is capable of
communicating not only with the access points (APs) but
also with peer nodes such as fixed ZigBee/Bluetooth sensors
or other mobile nodes if cooperation is supported. The
spatial density of peer nodes is typically much higher than
APs, so by exploiting these nodes as anchor nodes, we could
significantly decrease the distance estimation error and
improve the range-based positioning accuracy. However,
peer nodes are energy-constrained. Unlike the APs, they are
not supposed to be always in transmission mode broadcast-
ing their coordinates. In order to cooperate with peer nodes,
training sequences and extra packets are required for dis-
tance estimation and location information exchange, which
results in signaling overhead and energy consumption.
Hence, an efficient cooperation strategy is required so as to
achieve the required positioning accuracy and to minimize
the resultant energy consumption and traffic overhead.
In this paper, we investigate a heterogeneous network
containing fixed location-known Wi-Fi APs covering the
area of interest and sufficient number of connected multi-
modal (Wi-Fi and ZigBee) peer nodes. The goal is to esti-
mate the position of a moving node with required accuracy.
We propose a cooperation method to reduce the signaling
overhead via anchor node selection. The main idea is to se-
lect a subset of anchor nodes for location estimation. As
the mobile moves, the selected subset remains the same
until the required accuracy drops to within a minimum
threshold, at which point the reselection process is trig-
gered. Compared to exhaustive cooperation, the proposed
method is capable of reducing 34% signaling overhead to
within 0.5-m degradation of accuracy in a specific practical
scenario. We also evaluate the achievable performance av-
eraged over randomly located node configurations and
compare the proposed scheme with the mostly used
* Correspondence: duyang@av.it.pt
1
Instituto de Telecomunicações, Campus Universitário de Santiago, Aveiro
3810-193, Portugal
Full list of author information is available at the end of the article
© 2014 Hadzic et al.; licensee Springer. This is an open access article distributed under the terms of the Creative Commons
Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction
in any medium, provided the original work is properly cited.
Hadzic et al. EURASIP Journal on Wireless Communications and Networking 2014, 2014:2
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nearest-node selection algorithm [1] in terms of accuracy
and cost.
The rest of the paper is organized as follows: in the
next section, we present the state of the art solutions in
anchor selection. In Section 3, we propose our target
scenario. The proposed method is detailed in Section 4.
Simulation results and discussion are given in Section 5,
and finally, Section 6 concludes the paper.
Notation: we use unhighlighted letters for scalar variables,
highlighted lowercase letters for vectors, and highlighted up-
percase letters for matrix. ( )
T
and ( )
−1
represent matrix
transportation and inversing. E ( ) and var ( ) represent the
expectation and variance of a random variable. Variables
with a hat
^
:ðÞrepresent estimated values directly from esti-
mators or from computations using estimated values. Vari-
ables without a hat represent the true value.
2 Related work
The accuracy of positioning algorithm is influenced by
both measurement noise and relative node geometry [2,3].
The Geometric Dilution of Position (GDOP) [4] captures
the relative node geometry aspect, while the Cramer-Rao
Lower Bound (CRLB) captures both aspects. They are
often used as positioning accuracy indicators [5,6]. Besides
positioning accuracy, some works [7-9] apply concepts
from coalitional games and utility functions and select an-
chor nodes according to a cost function jointly consider-
ing power consumption and localization performance.
Most of the previous works related to anchor node
selection are in the context of homogeneous network,
especially sensor network [3,8-11]. Anchor node selection
in heterogeneous network is less addressed [5,6]. The au-
thors in [7] considered iterative cooperative localization
among static nodes having imperfect position information.
The algorithm in [5] includes both transmit and receive
censoring. Transmit censoring prevents broadcast of
unreliable position estimates, while receive censoring dis-
cards inadequate links for position estimation. All censor-
ing decisions are distributed and based on a modified
CRLB. In [6], unreliable links are consecutively discarded
based on CRLB analysis. A comparison of different selec-
tion criteria, namely CRLB and GDOP, and analysis of
their correlation with localization error in both coopera-
tive and noncooperative scenarios have been given in [12].
Here, the mobile scenario has been studied, so the selec-
tion criteria are used for predicting the best set of anchor
nodes.
An important aspect in localization is energy saving.
The use of coalitional games has been proposed in [8]
with the purpose of determining which nodes can stay
in sleep mode while only a subset participates in the po-
sitioning algorithm. In [1], experiments were performed
to increase the energy efficiency of a localization system
in wireless sensor networks. The idea is to use the clos-
est anchor nodes, and the remaining ones stay in semi-
active state. Besides radio localization, there are also
works that consider multimedia (camera) sensors for en-
ergy aware target tracking [13].
Compared to previous works, this paper investigates
mobile tracking in a heterogeneous network with the
following novel contributions:
1. The proposed method exploits the knowledge of
indoor layout to improve the RSS-based distance
estimation accuracy.
2. We propose a new positioning accuracy indicator
for linear weighted least square (LWLS) estimator
and demonstrate that it outperforms the estimated
CRLB positioning accuracy indicator.
3 Target scenario
The target indoor scenario is illustrated in Figure 1, which
shows a heterogeneous network containing three types of
nodes: Wi-Fi APs, peer nodes, and mobiles. Peer nodes and
mobiles are equipped with both Wi-Fi and ZigBee modules.
APs and peer nodes both know their positions, which are
served as anchor nodes. However, they are different in two
aspects: (1) APs are spatially separated, covering long dis-
tance, while peer nodes are densely packed with short-
distance coverage; (2) APs periodically broadcast its position
information, while peer nodes do not due to power supply
constraints. We are interested in the scenario having dense
nodes so that the moving multi-RAT mobile is always able
to communicate with APs and more than three peer nodes.
For the target mobile, we denote the set of reachable
APs as N
AP
, the set of reachable peer nodes as N
P
, the
set of potential anchor nodes for selection as N
A
⊆
(N
AP
∪N
P
) and their locations as x
n
=[x
n
,y
n
]
T
(n∈N
A
)in
two-dimensional space. We assumed that there is at least
one AP (|N
AP
|≥1) and at least three reachable peer nodes
(|N
P
|≥3). The AP associated with the target node is called
connected AP. The target node position is denoted as x=
[x,y]
T
. The distance between the nth anchor and the tar-
get node is denoted as dn¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
xn−xðÞ
2þyn−yðÞ
2
q. The es-
timated distance using ranging technical such as RSS/
TOA is denoted as
^
dnwith mean value E
^
dn

and vari-
ance var
^
dn

. The estimated target location is denoted as
^
x¼^
x;
^
y½
T. We employed root mean squared error (RMSE)
to represent the positioning accuracy, which is formulated as
RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
tr C^
x
ðÞ
p¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E^
x−xðÞ
2þ^
y−yðÞ
2

qð1Þ
The notation C^
Xrepresents the covariance matrix of
estimated vector ^
x. The required accuracy is denoted as
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RMSE
req
(in meters). Our goal is to select a subset of
nodes N
S
(N
S
⊆N
A
) having a fixed cardinality |N
S
| such
that (1) the required accuracy can be achieved or
approached as close as possible and (2) the remaining
unselected anchors could remain silent so as to save en-
ergy consumption and reduce traffic overhead.
4 Proposed method
4.1 General description
The proposed method is illustrated in Figure 2. At the be-
ginning (t= 0), the target mobile node transmits training
sequence at its highest transmit power and seeks for as-
sistance from all reachable peer nodes. Peer nodes meas-
ure the related signal parameters such as RSS/ToA and
transmit measurement results to connected AP. (If peer
nodes cannot communicate with the AP, the measurement
results are sent via the target node). Upon receiving the
measurements, the connected AP performs distance esti-
mation and then chooses the best set of anchors, N
S
, over
all possible combinations which is expected to achieve the
smallest RMSE. The estimation result ^
xand the chosen
set N
S
are transmitted to the target node.
As the target node moves on, it periodically transmits
training sequences and seeks assistance from those se-
lected peer nodes. Upon receiving the measurements,
the connected AP will estimate the achievable RMSE
using the selected set of anchors. If the required accur-
acy is satisfied, the estimation result ^
xusing this chosen
set N
S
is transmitted to the target node. Otherwise, a re-
selection process is triggered, and a new set of N
S
an-
chors providing the best accuracy will be chosen.
In addition, the indoor layout map is assumed to be
available at the AP, which will be used to improve the
RSS-based distance estimation by exploiting the know-
ledge of location-dependent channel parameters such as
path loss, shadowing, and line-of-sight (LoS)/non-line-
of-sight (NLoS) conditions. The coordinates of all an-
chor nodes are also recorded and updated at the AP to
avoid the overhead traffic caused by exchanging location
information between peer nodes and target nodes.
4.2 Positioning accuracy indicator
The pseudocode of the proposed method is summarized
in Algorithm 1. The key aspect is positioning accuracy
estimation. In this section, we will detail two positioning
accuracy indicators: estimated CRLB denoted as CRLB
^
Target Mobile Peer Nodes Connected AP
Knowledge assisted
distance estimation
Location Estimation
Received Estimated
location
anchor
selection
periodically transmit
training sequence to
selected peer-nodes
Measurement at
selected nodes
No
Calculate
Measurement at all peer
nodes
Knowledge assisted
distance estimation
Yes
transmit training
sequence to all peer-
nodes
t=0
x
RMSE
RMSE < =RMSEreq
Figure 2 Illustration of the proposed method.
AP1
AP2
AP3
Peer-nodes
Target
Mobile
Mobile trajectory
Figure 1 Heterogeneous network. It contains location-known
access points, peer nodes serving as anchor nodes, and one multi-RAT
target mobile moving according to a certain trajectory.
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and estimated RMSE for LWLS estimator denoted as
RMSE
^
LWLS . In the next section, we will compare these
two indicators in terms of their correlation with the true
RMSE.
4.2.1 Estimated CRLB (CRLB
^
)
The goal of range-based positioning is to estimate target
coordinates xbased on the observation of distance vec-
tor
^
d. In estimation theory, CRLB is defined as the lower
bound on variance of any unbiased estimator, which is
formulated as
RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
tr C^
X

q≥ffiffiffiffiffiffiffiffiffiffiffiffi
CRLB
p:ð2Þ
Supposed that the log-likelihood function of coordi-
nates xgiven the distance vector
^
dis equal to the nat-
ural logarithm of the probability density function of
^
d
given x, formulated as ℓðxj
^
dÞ¼ln pð
^
djxÞ

, the CRLB
is calculated as
CRLB ¼1
tr FxðÞðÞ
;FxðÞ¼−E
∂2ℓxj
^
d

∂x2
0
@1
A:ð3Þ
The Fisher information matrix F(x) is a function of the
second derivation of the likelihood function. If F(x)con-
tains any unknown parameters, they are replaced by their
estimated values, and the resultant bound is called esti-
mated CRLB, which is denoted as CRLB
^
. For example, the
CRLB of RSS-based ranging in a two-dimensional space
derived in [12,14] is a function of the true distances d
n
,
which are in practice unknown. Hence, it is only feasible
to calculate the estimated CRLB
^
using
^
dn.
4.2.2 RMSE for linear weighted least square estimator
If the LWLS estimator is used, we can have a closed-
form expression of ^
xas
^
x¼ATC−1
^
bA

−1
ATC−1
^
b
^
b:ð4Þ
Matrix Ais a function of anchor coordinates X
n
, vector
^
bis a function of distance estimates
^
dnas well as anchor
coordinates X
n
,and C−1
^
bis the inverse of covariance
matrix of
^
b. Hence, the covariance matrix C^
xalso has a
close-form expression as
C^
x¼ATC−1
^
bA

−1
:ð5Þ
In the case when C−1
^
bis a function of (unknown) true
distances d
n
, the estimated version C−1
^
b
^
using
^
dnis
employed. We derive the location accuracy indicator for-
mulated as
RMSE
^
LWLS ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ATC−1
^
b
^
A−1
"#
1;1þ"ATC−1
^
b
^
A−1#2;2
v
u
u
tð6Þ
5 Simulation results and analysis
Although the proposed method is not constrained by
ranging techniques, RSS-based distance estimation is
used in our simulation for its universal applicability and
ease of implementation. Using the unbiased distance es-
timator, the estimated distance squared for the nth an-
chor can be formulated as [15]
d2
n
^
¼e−2rn
α−2λ2
n
α2
ð7Þ
It has zero mean and a variance of var d2
n
^
¼d4
ne4λ2
n
α−1
.
In detail, r
n
=ln(P
n,r
)−ln(X
n
)−ln(P
n,t
), λ2
n¼0:01 ln 10ðÞ
2
σ2,andP
n,y
and P
n,t
represent time-averaged received and
transmitted signal strength from the nth anchor; αis the
path loss exponent, and X
n
denotes the summation of all
other losses (e.g., wall penetration loss). X
n
is assumed to
Algorithm 1 Algorithm cooperative scheme with
anchor selection at the time (t), given the
previous selected anchor set N
S(t-1)
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be perfectly compensated using the knowledge of layout
map. We express the location accuracy indicators described
in Section 4 as follows. Using the unbiased RSS-based
distance estimator, the estimated CRLB is formulated as
CRLB
^
RSS ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
bX
N
n¼1
d−2
n
^
X
N−1
n¼1X
N
m¼nþ1
dt⊥n;m
^
dn;m
d2
n
^
d2
n;m
0
@1
A
2;
v
u
u
u
u
u
u
u
u
t
ð8Þ
where d
n,m
is the distance between the nth and mth an-
chors, and the term dt⊥n;m
^
is the estimated shortest dis-
tance from the target to the segment connecting the nth
and mth anchors. The term baccounts for channel con-
ditions and is calculated as b¼10α
σln10.
Using the best linear unbiased estimator proposed in [15],
the estimated RMSE is formulated as Equation 6 using
A¼
−2x1−2y11
−2x2
⋮
−2y2
⋮
1
⋮
−2xn−2yn1
0
B
B
B
@
1
C
C
C
A
;
C−1
^
b
^
¼
var d2
1
^

^
0
⋱
0 var d2
n
^

^
0
B
B
B
B
@
1
C
C
C
C
A
−1
ð9Þ
In the rest of this section, we describe the simulation
for (a) the specific scenario from Figure 3 and (b) gener-
alized scenarios with randomly distributed anchors and
averaged performances over 10 different constellations.
We generated the setups in MATLAB (Mathworks, Inc.,
Natick, MA, USA) and then determined the channel
conditions based on the WINNER tool.
5.1 A specific scenario
We consider a practical scenario illustrated in Figure 3,
which consists of one Wi-Fi AP and seven peer nodes.
The target moves from the corridor to a room. Along
the movement trajectory, propagation conditions be-
tween the target and the other nodes change (LoS or
NLoS) as modeled by the WINNER II channel [16].
The target node moves at the speed of 1 m/s. We trace
the location of the target node every 1 s (T
s
=1 s), which
results in 38 footprints. The WINNER model [16] for in-
door scenario at a carrier frequency of 2.4 GHz is used to
simulate the channel between AP/peer nodes and target
node. The path loss parameter αis set to α
LoS
=1.85 and
α
NLoS
=3.68. The variance of zero-mean log-normal sha-
dowing σ
2
is set to σ2
LoS ¼2dB and σ2
NLoS ¼5dB,respect-
ively. The true location RMSE is averaged over 1,000
independent shadowing samples. Setting |N
s
|andRMSE
req
in different values, we simulate the following four schemes:
Scheme 1. |N
S
|=|N
AP
|+|N
P
|, RMSE
req
= 0. This is
equivalent to exhaustive cooperation, where all
reachable APs and peer nodes are used for location
estimation at every sampling time.
Figure 3 Simulation scenario. It consists of one Wi-Fi access point, seven peer nodes, and one target mobile node moving from the
corridor to a room.
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Scheme 2. |N
S
| = 3, RMSE
req
= 0, using CRLB
^
RSS in
Equation 8as indicator and LWLS/ML location
estimator.
Scheme 3. |N
S
| = 3, RMSE
req
= 0, using RMSE
^
LWLS
in Equations 6and 9as indicator and LWLS
location estimator.
Scheme 4. |N
S
| = 3, RMSE
req
= 1 and 2, using
RMSE
^
LWLS in Equations 6and 9as indicator and
LWLS location estimator.
5.1.1 Location accuracy indicator comparison
Using the parameters set for Scheme 2, three out of eight
anchors, which provide the lowest value of CRLB
^
RSS ,are
chosen at each sampling time. The true RMSEs using the
LWLS estimator and maximum likelihood (ML) estimator
are compared to the indicated value CRLB
^
RSS in Figure 4.
The ML estimator is the optimal RSS-based position esti-
mator; however, it is computationally very demanding,
and we use it for benchmark purposes. It is demonstrated
that from the 15 sample onward, where the anchor nodes
are dense and distributed in variable directions, the indi-
cated RMSE using CRLB
^
RSS has a good correlation with
the true RMSE using the ML estimator but is much lower
than the true RMSE using the LWLS estimator. In the first
few samples, the CRLB
^
values are low, but the true RMSE
using either linear or ML estimators are very high. The
reason is that the closest three anchors are not in line with
the target but almost collinear with each other. In this situ-
ation, the assumption ℓðxj
^
dÞ¼ln pð
^
djxÞ

does not hold
anymore. In fact, given
^
d, the log-likelihood function of x
achieves two peak values: one at the true location, and the
other at the mirror location symmetric to the approximate
line connecting these to the near collinear anchors. Hence,
CRLB
^
gives false accuracy estimation. It chooses the close,
but near collinear anchors, which results in high position-
ing error.
Using similar parameters, Figure 5 compares the indicator
^
RMSELWLS and the true RMSE. Again, three out of eight an-
chors, which provide the lowest value of RMSE
^
LWLS ,are
chosen at each sampling time. The results show that the indi-
cated RMSE using RMSE
^
LWLS has a good correlation with the
true RMSE using the LWLS estimator at all samples. Near
collinear anchors are avoided during the first few samples.
Based on these two figures, we could conclude that
RMSE
^
LWLS is a better RMSE indicator than CRLB
^
, which
can avoid choosing near collinear anchors, and provides
Figure 4 Comparison of the CRLB indicators and the true RMSE
when using Scheme 2.
Figure 5 Comparison between indicator RMSE
^
LWLS and the true
RMSE when using Scheme 3.
Figure 6 Comparison of achievable accuracy RMSE between
exhaustive cooperation (Scheme 1) and the proposed method
(Scheme 4).
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a more accurate estimation of the achievable RMSE
LWLS estimator deployed. Hence, we will use the
RMSE
^
LWLS indicator and LWLS estimator to evaluate
the proposed method.
5.1.2 Exhaustive cooperation versus the proposed method
We simulate the proposed method and compare its
RMSE to those using exhaustive cooperation. The
parameters are summarized in Scheme 4 and Scheme 1,
respectively. As shown in Figure 6, the degradation of
accuracy is negligible. When using the proposed method
with RMSE
req
= 2, the average RMSE is about 0.53 m
higher than exhaustive cooperation. However, the total
traffic overhead reduction is about 34% as shown in
Figure 7. More explicitly, the proposed method does
not always require a message from all anchors (in
green). It only occasionally requires additional control
packets from the AP (in blue) to invoke the reselection
process. Compared to exhaustive cooperation, the
overall transmit overhead over 38 samples is reduced
by 34% using the proposed method. The energy used
to spend on this traffic overhead is saved.
5.2 Generalized scenario
In order to extend the validity of the results presented
for the specific scenario from Figure 3, we evaluated the
proposed method in more generalized scenarios. We
consider a mobile moving across a 25-m × 10-m room.
The number of anchors in the room is 20, where one of
them is the access point (|N
AP
| = 1) and the remaining
ones are peer nodes (|N
P
| = 19). We generated 10 setups
having anchor nodes randomly distributed over the
room, while the target node follows the same trajectory
from the bottom left to the upper right. The averaged
performance that sat 30 sampled locations along the tra-
jectory is evaluated.
Again, the WINNER model for indoor scenario at a
carrier frequency of 2.4 GHz are used with the path loss
0 5 10 15 20 25 30
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Trac ki ng samp le
RMSE (m)
3 of 7
5 of 7
7 of 7
3 of 14
7 of 14
3 of 20
20 of 20
Figure 8 Comparison of different combinations of |N
S
| and |N
A
| using the proposed algorithm (averaged localization accuracy).
Figure 7 Comparison of traffic overhead between exhaustive
cooperation (Scheme 1) and the proposed method (Scheme 4).
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parameter αset to α
LoS
= 1.85 and α
NLoS
= 3.68. The
variance of zero-mean log-normal shadowing σ
2
is set to
σ2
LoS ¼2dB and σ2
NLoS ¼5dB, respectively. The true lo-
cation RMSE is averaged over 1,000 independent shadow-
ing samples. We simulate the following two schemes:
Proposed algorithm: using RMSE
^
LWLS in Equations 6
and 9as indicator and LWLS location estimator,
RMSE
req
= 0.6 m, and various combinations of |N
S
|
and |N
A
|(|N
S
|, |N
A
|) = {(3,7), (3,14), (3,20), (5,7),
(7,7), (7,14), (20,20)}.
Nearest-three-node selection algorithm used in [1].
5.2.1 Comparison of different combination of |N
S
| and |N
A
|
The averaged localization accuracy using the proposed
algorithm with different combinations of |N
S
| and |N
A
|
are shown in Figure 8. First of all, the required accuracy,
RMSE
req
= 0.6 m, is achieved for all settings from track
sample 5 to 27, when the target moves in the central
area of the room surrounded with sufficient number of
anchor nodes. By contrast, when the target moves in the
edge of the room corresponding to samples 1 to 5 and
27 to 30, the accuracy requirement is only always
achieved if (|N
S
|, |N
A
|) = (20,20). It is because at edge
areas, the number of reachable anchors is limit and they
are not 360° spread. Also, as expected, the accuracy im-
proves by increasing the number of selected nodes |N
S
|
or the cardinality of potential selection set |N
A
|. How-
ever, the performances using the three selected nodes
out of 7, 14, and 20 are very similar. The accuracy is sig-
nificantly improved when both |N
S
| and |N
A
| are in-
creased such as (5,7) and (7,14).
Figure 9 illustrates the traffic overhead accumulated
from 30 tracking samples and averaged over 10 different
setups. The traffic overhead consists of one message
from |N
S
| selected nodes at each tracking sample, one
message from AP, and |N
A
|−|N
S
| messages from peer
nodes at some tracking sample when reselection is acti-
vated. Figure 8 shows that selecting five nodes of seven
candidates achieve the smallest traffic overhead, while
selecting three nodes results in higher traffic overhead
because it triggers more often reselection.
Deploying the parameters stated in [17], we compare
the energy consumption in Table 1. More explicitly, we
assume that each message lasts for 1 ms and adopt the
typical value of 32 mW (15 dBm) as transmit power of
peer nodes and 63 mW (18 dBm) as transmit power of
APs [17]. The total energy required for transmitting the
averaged traffic shown in Figure 9 is calculated, assum-
ing that each message lasts 1 ms. Again, it demonstrates
that the (5,7) combination achieves the smallest energy
consumption.
5.2.2 Nearest-nodes algorithm versus the proposed method
As a benchmark, we used the approach of choosing the
three closest nodes, as in [1], which is popular because
of its simplicity. Although it has the lowest signaling
overhead and power consumption as shown in Figure 9
and Table 1, we can see from Figure 10 that the accuracy
requirement is much worse compared to the proposed
algorithm. The main reason for this is that by choosing
simply three nodes with the strongest RSSI, we run the
Table 1 Energy consumption for overhead messages
Case Proposed algorithm with
different combination
of |N
S
| and |N
A
|
Nearest-three
nodes
20 of 20 3 of 20 3 of 7 5 of 7
Energy (mJ) 19.2 16.315 5.903 3.661 1.92
Using (1) the proposed algorithm with different combination of |N
S
|and |N
A
|
and the nearest-three-node selection algorithm in [16].
0
100
200
300
400
500
600
msg from APs
msg from peer nodes
total msgs
3 of 20
20 of 20 5 of 73 of 7 3 of 20
Figure 9 Averaged traffic overhead. Using (1) the proposed algorithm with different combination of |N
S
| and |N
A
| and (2) the nearest-three-node
selection algorithm in [1].
Hadzic et al. EURASIP Journal on Wireless Communications and Networking 2014, 2014:2 Page 8 of 10
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risk to choose three collinear nodes, or almost collinear,
which is an ill-conditioned scenario and yields large er-
rors. This prenominal has been overlooked in [1], where
anchor nodes are regularly placed. It is a reasonable as-
sumption in sensor network as considered in [1] but no
longer valid in our heterogeneous network.
Finally, we summarize our analysis in terms of per-
formance trade-offs in Table 2. In this sense, ‘cost’is re-
lated to communication overhead, energy consumption,
search complexity, and computational complexity. For
accuracy metrics, we used the mean RMSE. For the
communication overhead metric, we use the number of
messages which are exchanged in the anchor selection
process. The search complexity is the number of pos-
sible search space size, and the computational complex-
ity arises from matrix inversions that have to be
performed in WLS localization algorithm. The proposed
algorithm provides the flexibility of achieving different
trade-offs by manipulating the value of |N
S
|and|N
A
|.
6 Conclusions
In this paper, we proposed a cooperation method for
range-based positioning in a heterogeneous network via
node selection in order to reduce communication and
energy cost. Inactive nodes do not waste energy while
collecting, processing, and communicating measure-
ments. We analyzed a specific scenario and generalized
one that corresponds to realistic indoor environments.
We presented an extensive study of different setups in
order to determine the best trade-off between desired
accuracy and cost. In our future work, we aim at obtain-
ing experimental results of the proposed method. An-
other extension will be to consider more practical
scenarios and to investigate moving peer nodes and
Table 2 Analysis of performance trade-offs
Performance metric Mean
RMSE
(m)
Communication overhead Size of search
space
Computational complexity
(packet number) (size of A in Equation 4)
The nearest-three nodes 2.109 60 1 3 × 3
Proposed algorithm 20 of 20 0.2975 600 1 20 × 20
3 of 20 0.5424 465 1,140 3 × 3
3 of 7 0.5716 136 21 3 × 3
5 of 7 0.4501 128 35 5 × 5
0 5 10 15 20 25 30
0
1
2
3
4
5
6
7
8
Trackin
g
sample
RMSE (m)
nearest 3
3 of 7
3 of 20
20 of 20
Figure 10 Comparison of the nearest-three-node selection algorithm to the proposed algorithm in terms of averaged
localization accuracy.
Hadzic et al. EURASIP Journal on Wireless Communications and Networking 2014, 2014:2 Page 9 of 10
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imperfect prior knowledge of anchor locations. These
virtual anchors are the result of error propagation in the
localization procedure.
Competing interests
The authors declare that they have no competing interests.
Acknowledgements
The research leading to these results was partly funded from the European
Community's Seventh Framework Programme [FP7/2007-2013] under grant
agreement n° 264759 [GREENET], n° 248894 [WHERE2], and funding from FEDER
through Programa Operacional Factores de Competitividade –COMPETE and
from National funds from FCT (Portugal) –Fundação para a Ciência e a
Tecnologia under the project PTDC/EEA-TEL/119228/2010 –SMARTVISION.
Senka Hadzic would like to acknowledge the support of the FCT - Portugal
through the scholarship SFRH/BD/61023/2009.
Author details
1
Instituto de Telecomunicações, Campus Universitário de Santiago, Aveiro
3810-193, Portugal.
2
Universidade de Aveiro, Aveiro, Portugal.
Received: 23 July 2013 Accepted: 8 December 2013
Published: 4 January 2014
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doi:10.1186/1687-1499-2014-2
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heterogeneous networks using node selection. EURASIP Journal on
Wireless Communications and Networking 2014 2014:2.
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