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Refinement of Localization Results in Wireless
Networks Using Weighted Universal Improvement
Schemes
Oleksandr Artemenko, Andreas Mitschele-Thiel
Faculty of Computer Science and Automation
Technische Universit¨
at Ilmenau
98693 Ilmenau, Germany
Email: {Oleksandr.Artemenko, Mitsch}@tu-ilmenau.de
Mykola Kuznietsov
Institute of Computer Systems
Odessa National Polytechnic University
65044 Odessa, Ukraine
Email: kuznetsov@ics.opu.ua
Abstract—In this paper, we present an extension of our concept
of the Universal Improvement Scheme (UnIS) investigated in
our previous work. The main focus of UnIS is to improve the
localization results of unknown wireless nodes, aka mobiles, in the
network with prepositioned reference nodes, aka anchors. The
UnIS algorithm uses some additional information known a priori
about the network. This information is represented by distances,
known before the experiment, between couples of mobile nodes
being localized.
In this work, the optimization of the UnIS algorithm is
proposed. According to our previous observations, we introduce
a novel weighted UnIS (W-UnIS) approach that uses different
weighting criteria to achieve a higher improvement ratio. We
compare the effectiveness of W-UnIS scheme to its predecessor
using the data collected in a deployed wireless sensor network
testbed. The obtained results indicate that the localization error
can be reduced significantly using our new W-UnIS approach.
I. INTRODUCTION
A. Motivation
Wireless communications have already become a very im-
portant part of our everyday life. According to this, hundreds
of new applications emerge every week defining higher and
higher requirements on hardware and software. Localization is
one of the most crucial issues for many such applications. To
keep it simple and cheap, but nevertheless accurate and robust,
is still a big challenge for thousands of researchers all over
the world that try to improve the location estimation process.
According to the literature, there are schemes that can be
applied for the refinement of the localization results. The
majority of these schemes is based on the history collected
during the location estimation process. Here, the amount
of various filters can be listed: Kalman Filter [1], LaSLAT
(Bayesian filter) [2], Particle Filter [3], Map-filtering [4], Rao-
Blackwellized particle filter [5], Gaussian Mixture Filter [6],
etc. The common problems of filters are that they need many
continuously measured data sequences and appropriate results
are given only after some time of operation (e.g., LaSLAT:
60 seconds of tracking [2]). In some situations, fast start-up
time with only little available data is required (e.g., disaster
scenarios). According to the requirements mentioned above,
alternative systems or additional algorithms are essential for
some ad-hoc network environments.
In our previous work, new possibilities to improve the lo-
calization results have been presented, implemented, simulated
and evaluated on the real testbed. All proposed solutions use
some additional information known a priori about the network.
This information is represented by distances, known before the
experiment, between couples of mobile nodes being localized.
From [7], a practical application example of this idea is
the usage of known distances between nodes attached to an
object being monitored or tracked (e.g., several wireless nodes
attached to an automated robot that is used in some specific
industrial process and needs to be localized). If the distances
between pairs of these nodes are static, they can be measured
a priori and used in the improvement process to enhance the
accuracy of the localization results of each node. This idea has
been investigated in our previous work [7]. In this work, we
proposed an Universal Improvement Scheme (UnIS) that uses
known distances between nodes and improves the localization
results significantly.
To further increase the robustness and accuracy of our
previous algorithm, we propose with this work an optimization
of the improvement process. Based on our observations, we
introduce a novel weighted UnIS (W-UnIS) scheme that uses
different weighting criteria to achieve a higher improvement
ratio. We compare the effectiveness of W-UnIS scheme to its
predecessor using the data obtained in a deployed wireless
sensor network testbed.
B. Paper Organization
The remainder of this paper is organized as follows. In
section II, we briefly describe the basic Universal Improvement
Scheme (UnIS) and its extensions derived from UnIS as a
part of our previous work. Section III introduces new W-UnIS
schemes and their mathematical models. Thereafter, section IV
describes the developed testbed, received results and analysis
of them. Finally, Section V concludes this paper.
0
1
2
3
4
5
012345
y
x
A(0;5)
B(0;0) C(5;0)
12
X
&
13
X
&
3
ˆ
h
2
ˆ
h
1
ˆ
h
3
h2
h
1
h
12
d
13
d
23
d
12
d
12
X
P
&
- Real positions of nodes
- Estimated positions of
mobile nodes
ij
X
&
- An improvement vector
ij
X
P
&
- A correction vector
Fig. 1. P-UnIS improvement example for a network with three anchors and
three mobiles
II. PREVIOUS WORK
After the initial position calculation step of the localization
process is complete and the first estimates of nodes’ positions
are available, the so called postimprovement step can be
conducted to increase the accuracy of the location estimation.
To do this, we apply UnIS refinement [7] that uses distances
between mobiles, known a priori (e.g., d12,d13 ,d23 between
mobile nodes h1,h2and h3in Fig. 1).
The basic step in the improvement is represented by pair-
wise recalculations of position coordinates using the known
distances between pairs of mobile nodes (e.g., reference dis-
tance d12 between real coordinates h1and h2in Fig. 1). At the
beginning of the localization, each node estimates its distances
to the given anchors separately and calculates its own virtual
coordinates (ˆ
h1,ˆ
h2,ˆ
h3in Fig. 1) using one of the well-known
calculation methods like trilateration. After the localization of
each node, the refinement process is being conducted. One
of the possible refinement methods could be the “shifting” of
calculated coordinates of two mobile nodes to/from each other
if the computed distance between them is bigger/smaller than
the corresponding reference distance dknown a priori.
Considering the simple pairwise refinement idea mentioned
above, the following steps will be executed to improve the
estimated virtual position of the node ˆ
h1in Fig. 1:
•According to the pair {ˆ
h1,ˆ
h2},wemoveˆ
h1along the
improvement vector υ12 so that
(ˆ
h1+υ12 )−(ˆ
h2−υ12 )=d12.
•Thereafter, the improvement vector υ13 for the pair
{(ˆ
h1+υ12 ),ˆ
h3}will be calculated in the same way as
υ12 and will be applied as the next improvement step so
that
((ˆ
h1+υ12 )+υ13 )−(ˆ
h3−υ13 )=d13.
In Fig. 1, vector υ12 represents the movement of coordinates
ˆ
h1and ˆ
h2until the distance between them is equal to the
reference distance d12. In such a way, the algorithm uses
pairwise computations to refine the estimated coordinates of
the mobile nodes and operates in a sequential way proceeding
from one pair of mobiles to another.
To make system converge to some certain state, UnIS
operates in an iterative way, i.e. each pair of mobile nodes
goes through the improvement process many times. For this,
it was essential to add a step size parameter μto the mathe-
matical model of the algorithm. A new movement vector, aka
correction vector, is given then by μυij (e.g., μυ12 in Fig. 1).
According to the idea above, the general description of the
UnIS refinement is as follows. Let Nrepresent all the mobile
nodes in the network. Then, the first improvement step for the
node ˆ
hi∈N, with respect to its neighbor ˆ
hj∈N, includes
the calculation of the corresponding refinement vector υij and
the estimation of new ˆ
hi[n+1] position:
υij =ˆ
hj−ˆ
hi−di,j
2ˆ
hj−ˆ
hi(ˆ
hj−ˆ
hi),(1)
ˆ
hi[n+1]=ˆ
hi[n]+μυij
=ˆ
hi[n]+μˆ
hj−ˆ
hi−di,j
2ˆ
hj−ˆ
hi(ˆ
hj−ˆ
hi),(2)
where di,j is a corresponding reference distance between
nodes hiand hj, and μis a step size parameter.
According to this basic idea, many new extensions from
UnIS have been derived [7]. To evaluate different UnIS
schemes, simulations and experiments have been conducted.
The best improvement ratio was obtained by the scheme
“P-UnIS Sequential Selective-DESC”. We observed that se-
quential schemes are much more flexible than parallel ones
and consider changes in the nodes’ positions during the
improvement process. Further flexibility is introduced by the
selection feature. A correct criterion applied for organizing a
nodes’ sequence can result in a better improvement ratio (e.g.,
descending order in [7]).
Additionally, we observed in our experiments one weak
aspect when one node with a very inaccurate position estimate
“pulled” all the remaining nodes to a wrong place during the
improvement. This happened because the step size parameter
μwas considered to be static during the refinement process.
However, it can be very profitable to modify the mathematical
model correspondingly to make this parameter adaptive which
can lead to even better improvements. Representing the main
contribution of this paper, this phenomenon will be investi-
gated in this work.
III. OPTIMIZATION OF UNIS
In this work, we introduce a weighted UnIS (W-UnIS)
approach that uses adaptive step size parameter instead of
static one
μadaptive =ωμ, (3)
where ωis a weighting function that reflects the accuracy level
of the produced location estimate. The node, which position
was estimated more accurately, has bigger weight (bigger mass
inertia) during the refinement process and obtains, as a result,
a smaller correction vector. To rate the accuracy level of the
obtained localization result, one of the following aspects can
be considered:
•From [7], the accuracy level Aiin location estimation of
the node iis inversely proportional to a Mean Absolute
Error εin distance estimation between the i-th node and
its neighbors according to reference distances known a
priori:
Ai∝1
εi
.(4)
•From [8], the accuracy level Aiin location estimation
of the node iis inversely proportional to a quality of
obtained reference signals:
Ai∝1
signal qualityi
.(5)
Next, we describe every aspect in detail and present the
weighting functions that have been derived.
A. Mean Absolute Distance Error (MADE)
To define a Mean Absolute Distance Error εiof the node
i, we use initial estimates of the nodes positions ˆ
has well as
the information, known a priori, about the reference distances
dbetween these nodes:
εi=1
|Ni|
j∈Ni
|ˆ
hj−ˆ
hi−di,j |,(6)
where di,j is a reference distance between nodes iand j, and
Nirepresents all the neighbors of the mobile node i.
As mentioned above, the main idea of the W-UnIS approach
is to increase the weight of those nodes which positions are
likely to be more accurate and decrease the weight of the nodes
which positions are likely to be less accurate. According to this
idea, we developed several weighting functions that are given
as follows:
ω1(εi)= εi
max{εi,ε
1,ε
2,...,ε
Ni},(7)
ω2(εi)=minεi
εj
,1,(8)
ω3(εi)=1−min{εi,ε
1,ε
2,...,ε
Ni}
εi
,(9)
where Nirepresents all the neighbors of the mobile node i,
εiis its MADE, and εjis a MADE of the neighbor node j.
B. Link Quality
According to [8], the quality of the signal affects the pro-
duced location estimation error significantly. If we assume that
the nodes with stronger signals from anchors produce more
accurate localization results than the ones with weaker signals,
then giving these nodes bigger weights in the refinement
process will positively affect the improvement ratio.
In our evaluation, we use Link Quality Indicator (LQI) to
measure the quality of the obtained signals. In contrast to
Signal Strength Indicator and according to the IEEE 802.15.4
specification [9] (E.2.3), “The LQI (see 6.7.8) measures the
received energy and/or SNR (Signal to Noise Ratio) for each
received packet.” It is important to notice that smaller LQI
values, unlike the signal strength, indicate a better quality of
the signal and vice versa.
With respect to this, every node iduring the initial localiza-
tion process computes a mean Link Quality value liaccording
to the obtained signals from reference nodes so that
li=1
|Ki|
j∈Ki
lqij,
where Kirepresents all the reference nodes that are in
communication range of the node i, and lqi are corresponding
Link Quality values of signals from reference nodes that are
estimated at the node i. According to this, we define a fitness
function based on the Link Quality value lifor the i-th node
as follows:
f(li)=1−min{li,l
1,l
2,...,l
Ni}
li
,(10)
where Nirepresents all the neighbors of the node i.
Considering the fact that LQI-based optimization refers
to statistic results only, it cannot be used as a standalone
parameter. For this, it is essential to keep history of the
estimated LQI data and conduct corresponding filtering. Since
we try to avoid filters, we will combine two functions: ω3(εi)
that reflects the Mean Absolute Distance Error in (9) and f(li)
that considers the signal quality in (10).
Both of the functions are equally important for the improve-
ment. Applying a Weighted Sums optimization technique, the
new weighting function will be
ω4(εi,l
i)=1
2ω3(εi)+1
2f(li).(11)
To evaluate all weighting functions introduced in (7)-(9) and
(11), they were integrated in our emulation environment that
will be introduced next.
IV. EVALUATION
For the evaluation of the weighting functions, the data
collected in our previous work has been used to emulate the
real environment. To enable a fair comparison of different
approaches, all algorithms had the same input.
A. Evaluation Environment
The core of the evaluation environment is represented by
the data collected in our experimental testbed that will be
described next.
1) Network deployment: The experimental testbed was
deployed in one of the office rooms in the building #11 at
the University of Applied Sciences in Erfurt, Germany. This
room is equipped with standard furniture including chairs,
bookshelves, and desks. It has two windows and represents
a dynamic measurement environment where people may walk
in and out of the room during the normal operation of the
network, thus modifying the characteristics of the actual radio
propagation channel.
0
1
2
3
4
5
012345
y
x
A(0;5)
B(0;0) C(5;0)
2
h4
h6
h8
h10
h
1
h3
h5
h7
h9
h
Fig. 2. Real positions of anchors A, B and C as well as ten unknown nodes
from h1to h10
The deployed localization system consists of the following
main elements (Fig. 2): (i) three anchor nodes with known
coordinates A [0;5], B [0;0] and C [5;0] used for the local-
ization of unknown wireless sensor nodes; (ii) ten unknown
nodes that need to be localized.
To obtain explicit results, the full information about the
distances in meters between all mobile nodes was provided in
the form of a matrix D=[di,j ]N×Npresented in [7], where
N=10is a total number of the unknown nodes and di,j is a
reference distance between the i-th and j-th node.
2) Hardware platform: For the measurement campaign, the
wireless sensor nodes ZEBRA2411 from senTec Elektronik
GmbH were used. These modules are based on the chip set
ZRP1 developed by Freescale Semiconductor [10]. The nodes
operate in the 2.4GHz ISM frequency band and allow wireless
communication over a distance of more than 1000m (line-of-
sight). ZEBRA contains a micro-controller, a High Frequency
(HF) circuitry and a chip antenna with low noise ampli-
fier (LNA) and power amplifier (PA) stages. An integrated
Freescale HCS08 MCU serves as a base band controller and
operates at 8MHz. A SMAC (Simple Media Access Control)
protocol [11], which is based on the IEEE 802.15.4 standard,
has been applied for communication between nodes. For the
programming of nodes, we use the Metrowerks CodeWarrior
development environment from Freescale.
3) Path loss model: According to the process of localiza-
tion, we need to estimate distances from the observed LQI
values and then use these distances for the position calculation
step. There are a lot of studies which propose various models,
even for indoor scenarios. The model which has been applied
in this work was found in [12] and adapted to the LQI
estimates produced with our hardware platform. So, the path
loss Lat distance dis
L(d)=Ld0+Lp+10γlog10 d
d0+χ, d ≥d0(12)
where Ld0=72is the path loss at d0=0.1m, γlog10 d
d0is
the average path loss with reference to d0,γ=3.1is the path
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
0 5 10 15 20 25 30
average localization error, m
number of refinement rounds
=1
Ό
Ύ
Ώ
Fig. 3. Average localization error
loss exponent and Lp=2.4is the penetration loss and both are
functions of the measured scenario and working environment;
and χ=3.6is the log-normal shadow fading. For the given
scenario, the equation (12) and the corresponding parameters
mentioned above produce the least-square error path loss log-
distance model according to the collected LQI values.
The trilateration algorithm has been applied to calculate
initial positions according to the estimated three distances from
anchors.
4) Step size parameter: In our previous work, we observed
that the P-UnIS algorithm produces the best improvement ratio
with the step size in the range from 0.01 to 0.4 and performs
best with the step size μ=0.2, which is common for all
numbers of rounds.
In this work the step size μadaptive is designed to be variable
(see (3)) and includes a weight value ω∈[0,1]. According to
this and considering the basic value μ=0.2in (3), we get
μadaptive ∈[0,0.2].
According to this setup, we conducted a measurement
campaign that took approximately 24 hours. The location
estimation of each mobile node was performed every second
according to newly observed LQI values. All the LQI data pro-
duced in the experiment was stored for the further emulation
purposes.
Now, the picture of the evaluation platform is complete.
Next, we present the evaluation results of different optimiza-
tion functions presented above.
B. Evaluation Results
Using the data obtained in the testbed, we evaluated weight-
ing functions proposed above: ω1(7), ω2(8), ω3(9), ω4(11).
To present the effectiveness of the methods, the standard P-
UnIS improvement with static step size (i.e. w=1) has been
used as a benchmark (Fig. 3). 30 iteration steps were applied
every time for the improvement of nodes positions.
The key observations can be stated as follows:
•As a part of the W-UnIS algorithm, all the introduced
functions produce better results than the previous P-
UnIS improvement with ω=1, according to the average
localization error (Fig. 3). This supports the idea of using
the Mean Absolute Distance Error (MADE) to weight the
nodes positions.
1
10
0 5 10 15 20 25 30
average MADE, m
number of refinement rounds
=1
Ό
Ύ
Ώ
Fig. 4. Average Mean Absolute Distance Error (MADE)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.1 1 10
probability
CDF of MADE, m
unimproved
=1
Ό
Ύ
Ώ
Fig. 5. Cumulative Distribution Function (CDF) of the MADE Eiaccording
to (6)
•The best results are presented by ω4weighting function.
ω4reflects the quality of the received signals from the
anchors additionally to the information about MADE.
•Figure 4 shows how the MADE values change during
the refinement according to different approaches. It is
obvious that the best trend here is represented by static
weight ω=1. Although this method does not reach the
best accuracy in the location estimation, it minimizes the
MADE value and, as a result, brings the nodes close to
the original relative positioning.
•Figure 5 presents the comparison of the initial localiza-
tion (unimproved results) and the proposed improvement
schemes with respect to the accumulated MADE value of
all mobiles in the network. Due to the big uncertainty in
indoor signal propagation, unimproved location estima-
tion presents more than ten times bigger distance error
than the proposed improvement technique.
•The same as for P-UnIS, the major drawback of W-UnIS
is represented by the need in the estimation of distances
between unknown nodes, which is not always possible
and depends on the working scenario.
V. C ONCLUSION AND FUTURE WORK
As the main contribution in this paper, we introduced
the novel optimization strategy in improving the localization
results for the networks with known distances between mobile
nodes.
It was shown that adding weights to the estimated nodes
positions yields 22% higher improvement ratio as compared
to the previous refinement technique (0.573 m average local-
ization error against 0.713 m, respectively).
In contrast to the existing improvement techniques that were
discussed at the beginning of this paper, our algorithm does not
require continuously measured data sequences and significant
improvement is provided directly after first initial position
estimations.
In our future work, we are going to continue investigation
of different optimization techniques to gain even better local-
ization results. Additionally, we are going to do a scalability
analysis of our algorithm.
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