An Efficient Directed Localization Recursion Protocol for Wireless Sensor Networks

Abstract

The establishment of a localization system is an important task in wireless sensor networks. Due to the geographical correlation between sensed data, location information is commonly used to name the gathered data and address nodes and regions in data dissemination protocols. In general, to estimate its location, a node needs the position information of at least three reference points (neighbors that know their positions). In this work, we propose a different scheme in which only two reference points are required in order to estimate a position. To choose between the two possible solutions of an estimate, we use the known direction of the recursion. This approach leads to a recursive localization system that works with low-density networks (increasing by 40 percent the number of nodes with estimates in some cases), reduces the position error by almost 30 percent, requires 37 percent less processor resources to estimate a position, uses fewer beacon nodes, and also indicates the node position error based on its distance to the recursion origin. No GPS-enabled node is required, since the recursion origin can be used as a relative coordinate system. The algorithm's evaluation is performed by comparing it with a similar localization system; also, experiments are made to evaluate the impact of both systems in geographic algorithms.

Full text

An Efficient Directed Localization Recursion
Protocol for Wireless Sensor Networks
Horacio Antonio Braga Fernandes de Oliveira, Azzedine Boukerche,
Eduardo Freire Nakamura, and Antonio Alfredo Ferreira Loureiro
Abstract—The establishment of a localization system is an important task in wireless sensor networks. Due to the geographical
correlation between sensed data, location information is commonly used to name the gathered data and address nodes and regions in
data dissemination protocols. In general, to estimate its location, a node needs the position information of at least three reference
points (neighbors that know their positions). In this work, we propose a different scheme in which only two reference points are required
in order to estimate a position. To choose between the two possible solutions of an estimate, we use the known direction of the
recursion. This approach leads to a recursive localization system that works with low-density networks (increasing by 40 percent the
number of nodes with estimates in some cases), reduces the position error by almost 30 percent, requires 37 percent less processor
resources to estimate a position, uses fewer beacon nodes, and also indicates the node position error based on its distance to the
recursion origin. No GPS-enabled node is required, since the recursion origin can be used as a relative coordinate system. The
algorithm’s evaluation is performed by comparing it with a similar localization system; also, experiments are made to evaluate the
impact of both systems in geographic algorithms.
Index Terms—Network architecture and design, algorithm/protocol design and analysis, wireless sensor networks, localization,
GPS free.
Ç
1INTRODUCTION
WIRELESS sensor networks (WSNs) [1], [2], [3], [4], [5] are
composed of a large number of sensor nodes used to
monitor an area of interest. This type of network has become
popular due to its applicability in several areas such as the
environmental, medical, industrial, and military fields.
Despite the fact that the main goal of a WSN is to monitor
an area of interest, several secondary objectives or pre-
requisites have to be achieved in order to reach the main
objective (Fig. 1). To cite a few, these prerequisites include
data dissemination [6], [7], time synchronization [8], [9], [10],
[11], mobile location management [12], media access control
[13], security [14], and density control [15].
The definition of a localization system for sensor nodes
[16], [17], [18], [19], [20], [21], [22], [23], [24], [25] is also one
of the prerequisites needed in order for many applications of
WSNs to become viable. The localization problem consists of
identifying the physical location (e.g., latitude, longitude,
and altitude) of the sensor nodes. The importance of this
problem arises from the need to name the gathered data [26]
and associate events with their location of occurrence [27]. In
addition, some routing algorithms use location information
to improve their performance, an example of which is the
Geographical and Energy-Aware Routing (GEAR) algo-
rithm [28] that optimizes the process of finding sources by
using geographically scoped queries. However, depending
on the accuracy of location information, such queries may
not reach the correct nodes.
In a recursive localization system, such as Recursive
Position Estimation (RPE) [21] or the Ad Hoc Localization
System (AHLoS) [18], a node estimates its location based on
the position information of three reference nodes (neighbors
that know their positions). Once its position is estimated, the
node becomes a reference and broadcasts its own location
information to assist other nodes in estimating their positions.
In this work, we propose a different recursive localization
system: Directed Position Estimation (DPE). The main idea of
DPE is to make the recursion of such systems follow a
determined and known direction. In this way, a node can
estimate its position using only two reference neighbors. This
approach leads to a localization system that can work in a
low-density sensor network. In addition, the controlled way
in which the recursion is made also leads to a system with
fewer errors that are also more predictable. This method
requires fewer resources than the triangulation, trilateration,
or multilateration methods.
IEEE TRANSACTIONS ON COMPUTERS, VOL. 58, NO. 5, MAY 2009 677
.H.A.B.F. de Oliveira is with the PARADISE Research Laboratory, School of
Information Technology and Engineering (Site), University of Ottawa,
800 King Edward Avenue, Ottawa, ON K1N 6N5, Canada, and also with
the Department of Computer Science, Federal University of Minas Gerais,
Av. Antonio Carlos, 6627, Pampulha, 30123-970, Belo Horizonte, MG,
Brazil, and the Department of Computer Science, Federal University of
Amazonas, Av. Gen. Rodrigo Octavio, 3000, Coroado, 69077-000, Manaus,
AM, Brazil. E-mail: horacio@dcc.ufam.edu.br, horacio@site.uottawa.ca.
.A. Boukerche is with the PARADISE Research Laboratory, School of
Information Technology and Engineering (Site), University of Ottawa,
800 King Edward Avenue, Ottawa, ON K1N 6N5, Canada.
E-mail: boukerch@site.uottawa.ca.
.E.F. Nakamura is with the Department of Computer Science, Federal
University of Amazonas, Av. Gen. Rodrigo Octavio, 3000, Coroado,
69077-000, Manaus, AM, Brazil, and Center of Analysis, Research and
Technological Innovation Foundation (FUCAPI), Av. Gov. Danilo de
Matos Areosa, 381, Distrito Industrial, 69075-351, Manaus, AM, Brazil.
E-mail: eduardo.nakamura@fucapi.br.
.A.A.F. Loureiro is with the Department of Computer Science, Federal
University of Minas Gerais, Av. Antonio Carlos, 6627, Pampulha,
30123-970, Belo Horizonte, MG, Brazil. E-mail: loureiro@dcc.ufmg.br.
Manuscript received 31 May 2007; revised 8 May 2008; accepted 20 May
2008; published online 11 Dec. 2008.
Recommended for acceptance by G. Constantinides.
For information on obtaining reprints of this article, please send e-mail to:
tc@computer.org, and reference IEEECS Log Number TC-2007-05-0194.
Digital Object Identifier no. 10.1109/TC.2008.221.
0018-9340/09/$25.00 ß2009 IEEE Published by the IEEE Computer Society
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In the proposed scheme, GPS-enabled nodes may or may
not be used. If no GPS is available, the recursion origin can
be used as a relative coordinate system. This approach can
be useful for routing algorithms that use location informa-
tion. Some GPS-enabled beacons can be used to transform
the relative coordinate system into a global one when events
need to be associated with their geographic location.
This work makes three contributions to the area of
localization systems in WSNs. The main contribution is the
proposal and empirical evaluation of DPE. Second, we
propose the division of localization systems into three
distinct components. We show how each of these compo-
nents can affect the final localization error and conclude
that they should be studied and analyzed separately. Third,
the effects of the localization errors on geographic algo-
rithms are analyzed. We simulate two known geographic
algorithms [29], [15] that have not been analyzed in the
presence of real localization errors (i.e., using the positions
resulting from a proposed localization algorithm).
The rest of this work is organized as follows: Section 2
presents an overview of the localization systems for WSNs
and shows how these systems can be divided into compo-
nents. Section 3 describes the proposed schema, DPE, which
is evaluated though simulations in Section 4. In Section 5, we
discuss other solutions that are available for the localization
problem. Section 6 presents our conclusions and future
directions.
2MAIN COMPONENTS OF LOCALIZATION SYSTEMS
IN WIRELESS SENSOR NETWORKS
The localization problem consists in finding the geographic
location of nodes in a WSN. The location of a node can be
computed by a central unit (the sink node) [17] or in a
distributed manner [20], [21], [18], [22], the latter of which
is more common in WSNs. In the next section, we will
briefly define our network model, as well as the localization
problem in WSNs, while in Section 2.2, we will show the
components on which localization systems are based.
2.1 Problem Statement
A WSN can be composed of nnodes, with a communication
range of r, that are distributed in a two-dimensional squared
sensor field Q¼½0;s½0;s. For the sake of simplification,
we consider symmetric communication links, i.e., for any
two nodes uand v,ureaches vif and only if (iff) vreaches u
with the same signal strength w. Thus, we represent the
network by the euclidean graph G¼ðV;EÞwith the
following properties:
.V¼fv1;v
2;...;v
ngis the set of sensor nodes.
.hi; ji2Eiff vireaches vj, i.e., the distance between vi
and vjis less than r.
.wðeÞris the weight of edge e¼hi; ji, i.e., the
distance between viand vj.
In this paper, the term broadcast is used to indicate a node
sending a message to all of its neighbors in a single packet,
while the term flooding is used to indicate the case where all
nodes receiving a packet retransmit it once to all of their
neighbors (using broadcast). Thus, the communication cost
of a broadcast is only Oð1Þ, while the communication cost of
flooding is OðnÞ.
Some terms can be used to designate the state of a node.
Definition 1 (unknown nodes—U). Also known as free or
dumb nodes, this term refers to the nodes in the network that do
not know their localization information. To allow these nodes to
estimate their positions is the main goal of a localization system.
Definition 2 (settled nodes—S). These nodes were initially
unknown nodes that have managed to estimate their positions
by using the localization system. The number of settled nodes
and the estimated position error of these nodes are the main
parameters for determining the quality of a localization system.
Definition 3 (beacon nodes—B). Also known as landmarks or
anchors, these are nodes that do not need a localization system
in order to estimate their physical positions. Their localization
is obtained by manual placement or by external means such as
GPS. These nodes form the basis of most localization systems
for WSNs.
678 IEEE TRANSACTIONS ON COMPUTERS, VOL. 58, NO. 5, MAY 2009
Fig. 1. Several areas of the WSNs that work together in order to achieve one common goal: to monitor an area of interest.
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Definition 4 (reference nodes—R). These are the nodes from
which localization information will be used by unknown nodes
to estimate their locations. A reference node must also be a
beacon or settled node.
The localization problem can then be defined as follows:
Definition 5 (localization problem). Given a multihop
network G¼ðV;EÞand a set of beacon nodes Band their
positions ðxb;y
bÞ, for all b2B, we want to find the position
ðxu;y
uÞof as many u2U as possible, transforming these
unknown nodes into settled nodes—S.
2.2 The Basic Components of Localization Systems
In this work, we propose the division of localization systems
into three distinct components (Fig. 2): distance estimation,
position computation, and localization algorithm. Each of
these components can affect the final error of a localization
system separately. For example, a localization system should
achieve better results if the Time Difference of Arrival (TDoA)
method is used instead of the Received Signal Strength
Indicator (RSSI) method to estimate distances. The same
principle applies to the other components. These components
can be seen as subareas of the localization problem that need
to be studied separately. The following sections define these
components.
2.2.1 Distance Estimation
This component is responsible for estimating the distances
between two nodes. This information is used by the other
components of the localization system. Some techniques used
to estimate distances include RSSI (Fig. 3a) [30], [31], Time of
Arrival (ToA—Fig. 3b) [32], and TDoA (Fig. 3c) [33], [34], [35].
2.2.2 Position Computation
This component is responsible for computing a node’s
position based on the information available (e.g., distances
and positions of neighbors). Some of the techniques used to
compute positions include trilateration (Fig. 4a), multi-
lateration (Fig. 4b), and triangulation (Fig. 4b).
2.2.3 Localization Algorithm
This is the main component of a localization system. It
defines how the available information is manipulated in
order to allow the nodes in the sensor network to estimate
their positions. Some algorithms include the Ad Hoc
Positioning System (APS) [20], RPE [21], and the DPE scheme
proposed in this work.
A recursive localization algorithm is an algorithm that
extends position estimation throughout the sensor network.
A node that has at least three reference neighbors can estimate
its own location through trilateration. Then, this node
becomes a reference by broadcasting its location and helping
other nodes to estimate their own locations. To start the
recursion, usually, a fraction of all nodes (e.g., 5 percent) can
determine their positions (e.g., GPS-enabled nodes). An
example of such a system is RPE. The RPE algorithm can be
divided into four phases, as depicted in Fig. 5. In the first
phase, beacon nodes start broadcasting their position
information so that they can be used as reference nodes. In
the second phase, a node estimates its distance to the
reference nodes by using, for example, the RSSI. In the third
phase, the node computes its position by using, for example,
trilateration and becomes a settled node. In the final phase,
the node becomes a reference and broadcasts its estimated
position to assist its neighbors with their position estimations.
3THE DIRECTED POSITION ESTIMATION ALGORITHM
By adding some restrictions to a recursive localization system,
we can make the localization recursion start from a single
point and follow a determined and known direction (Fig. 6a).
DE OLIVEIRA ET AL.: AN EFFICIENT DIRECTED LOCALIZATION RECURSION PROTOCOL FOR WIRELESS SENSOR NETWORKS 679
Fig. 2. The division of localization systems into three distinct components:
distance estimation, position computation, and localization algorithm.
The arrows indicate the dependency relations, i.e., the information flow
from one component to another.
Fig. 3. Distance estimation methods. Some methods like RSSI provide very inaccurate distance estimation, while others like TDoA provide accurate
estimation but require extra hardware in order to work. (a) RSSI: the signal is sent with a determined strength that decreases as the distance to the
receptor increases. (b) ToA: the time that the signal takes to leave the sender and reach the receptor is estimated. The distance is derived from this
time. (c) TDoA: the difference of the time of arrival of two signals sent simultaneously is estimated to derive the distance.
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Once this behavior is guaranteed, it is possible to estimate a
node’s position using only two reference neighbors.
When a node has the position information of only two
reference neighbors, a pair of possible points results from
the position computation procedure: one is the correct
position of the unknown node, and the other is a wrong
estimate (Fig. 6b). The decision of which point to use is a
crucial factor of the proposed scheme. A wrong choice may
lead to an error of almost twice the communication range.
Once the direction of the localization recursion is kept
stable, it is easy to choose between the two possible solutions:
the most distant point from the recursion origin is the right
position of the unknown node.
3.1 The DPE Algorithm
In this section, we will show how the proposed scheme
operates. The algorithm is divided into four phases (Fig. 7).
In the first phase, the beacon nodes start the recursion. In
680 IEEE TRANSACTIONS ON COMPUTERS, VOL. 58, NO. 5, MAY 2009
Fig. 4. Position computation methods. The method used depends on the information and processor resources available. (a) Trilateration: the position
is the intersection of three circles formed by the positions and the estimated distances to three reference nodes. (b) Multilateration: uses the same
principle as trilateration, but more than three references points can be used, and an overdetermined system is computed. (c) Triangulation: the angle
of arrival of the received signal is estimated, and the node position is computed through trigonometrical relations.
Fig. 5. Example and phases of RPE.
Fig. 6. (a) The beacon structure doing a directed localization recursion. (b) A position estimate using only two reference neighbors. A pair of possible
solution result from the system. The right position of the node is the most distant point from the recursion origin.
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the second phase, a node determines its (two) reference
points. In the third phase, the node estimates its position
and then becomes a reference by sending this information
to its neighbors (fourth phase).
3.1.1 Phase 1—Starting the Recursion from a
Single Point
First, we need to ensure that the recursion starts from a
single location. To accomplish this task, we use the beacon
structure depicted in Fig. 6a in which four beacons are at
a given distance (e.g., 5 m) from a central point (the
recursion origin) and the angle between each pair of
neighbor beacons is known (e.g., 90 degrees). Then, the
base of the relative coordinate system is formed by the
positions of the recursion origin (0, 0), the first beacon
node (5, 0), and the second beacon node (0, 5). To start the
recursion, the beacon nodes send a packet containing their
position information, as depicted in Fig. 7a and shown in
Algorithm 1 in lines 3-7.
Algorithm 1. DPE Localization Algorithm
.Variables:
1: positionsi¼; {Set of received positions.}
2: referencesi¼; {Set of reference nodes.}
.Input:
3: msgi¼nil.
Action:
4: If ni2Bthen {If this node is a beacon node.}
5: ðxi;y
iÞ:¼getGpsP ositionðÞ;
6: Send positionðxi;y
iÞto all nj2Neigi.
{Start the recursion.}
7: end if
.Input:
8: msgi¼positionðxk;y
kÞsuch that
distk¼distanceEstimationðmsgiÞ.
Action:
9: if ni2Uthen {If this node is an unknown node.}
10: positionsi:¼positionsi[fðxk;y
k; distkÞg;
11: [Re]Start waitT imer.
12: end if
.Input:
13: waitT imer timeout.
Action:
14: if sizeðpositionsiÞ>¼2then
{If there is enough positions.}
15: referencesi:¼chooseT woBestP ositionsðpositionsiÞ
{Select pair of References.}
16: ðxi;y
iÞ:¼mostDistantFromOrigin
ðintersectCirclesðref erencesiÞÞ;
{Compute Position.}
17: Send positionðxi;y
iÞto all nj2Neigi.
{Become a reference node.}
18: end if
3.1.2 Phase 2—Selecting Which Pair of References
to Use
Unknown nodes receiving positioning packets store the
received data (lines 8-12) and wait for a determined time
(waitT imer in Algorithm 1) for more localization packets.
When a node has received location information from two or
more reference neighbors (beacons or settled nodes), it can
estimate its own position (Fig. 7b). The choice of which pair
of nodes to use (when there are more than two references) is
also an important issue in the DPE algorithm. We are
interested in the pair of references that leads to the right
solution. Thus, instead of merely selecting the nodes with
lower residual errors (see the next section), we select the
pair of nodes with the largest distance between them and
that is closest to the recursion origin (line 15). This selection
can be done easily by comparing the distances between the
received positions of the reference nodes and the known
recursion origin (0, 0 in this case). It is important to choose
distant reference nodes to facilitate the process of estimating
the position, which is the next phase of the DPE algorithm.
3.1.3 Phase 3—Estimating the Position
The third phase is to estimate the position of the node, as
depicted in Fig. 7c and shown in line 16 of Algorithm 1. This
DE OLIVEIRA ET AL.: AN EFFICIENT DIRECTED LOCALIZATION RECURSION PROTOCOL FOR WIRELESS SENSOR NETWORKS 681
Fig. 7. Phases of DPE. (a) First, the beacon structure starts the recursion by broadcasting the position information of the beacon nodes. (b) A node
chooses its two reference points and estimate the distances to these points. (c) The position computation is done. (d) This node broadcasts its newly
estimated position in order to help the other nodes in estimating their own positions.
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position is estimated, as shown in Fig. 6b, by intersecting the
two circles and choosing the most distant point from the
recursion origin (which has the position 0, 0). This is an
advantage of the DPE algorithm, as it uses fewer processor
resources (about 20 flops) than other methods like the least
squares method (about 32 flops for three references). In
this phase, we need to determine whether the solution is
consistent enough to ensure that we choose the right position
(as explained in “Avoiding the Wrong Solution” further in
this section).
When a node has the position information of only two
beacons and no other position information about any other
reference nodes (e.g., other beacons or settled nodes), it is not
possible to guarantee which solution is correct since the
node could be either inside or outside the beacon structure.
In these cases, we cannot simply accept the most distant
solution; instead, we wait for more information from another
beacon or from a newly settled node (which will be used as a
reference node) and then use the residual error (see the next
section) to choose the correct position. This shows the
importance of having a consistent beacon structure.
3.1.4 Phase 4—Becoming a Reference Node
When a node estimates its position, it can become a
reference node by sending a broadcast packet with its
position and its residual error. This phase, depicted in
Fig. 7c and shown in line 17 of Algorithm 1, characterizes
the recursive behavior of the system.
Quantifying the Position Error. The residual error can be
used as a measure of confidence in the estimated position. The
residual error for an estimated position ð^
x; ^
yÞis defined as
residual ¼X
i2refset ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðxi^
xÞ2þðyi^
yÞ2
qdi

2
;ð1Þ
where ðxi;y
iÞis the ith reference position, and diis the
distance measured by means of the RSSI. In other words, the
residual error is the sum of the squared differences between
the distance using the estimated position and the distance
acquired using the RSSI measurement. Beacon nodes have
no residual errors associated with their positions.
Avoiding the Wrong Solution. Even though the recursion
starts from a single point, the direction of the recursion can
still become wrong, resulting in an erroneous position
estimate. To assure the correct estimation and maintain the
right direction of the recursion, we need to avoid two possible
scenarios:
1. when one of the two reference nodes is more distant
to the recursion origin than the unknown node
(Fig. 8a) and
2. when the two reference nodes are aligned to the line
of the recursion origin (Fig. 8b).
In both cases, we cannot guarantee which of the two
possible solutions of the estimation is correct, and scenarios
like these indicate that the direction of the recursion has
become incorrect. In these cases, the unknown node may
wait for other reference nodes and then use this new
information to estimate its position.
To detect these two scenarios using only local informa-
tion, we need to compare the distances from the two
possible solutions to the recursion origin to the distances
from the reference nodes to the recursion origin. In the first
scenario (Fig. 8a), we can see that the distances from the two
possible solutions to the recursion origin are smaller than
the distance from Reference Node 2 to the same point. In the
second scenario (Fig. 8b), the distances from the two
possible solutions are greater than the distance from the
reference nodes. Thus, to avoid both scenarios, we need to
check two conditions: 1) whether the distance to the
recursion origin of one of the possible solutions is greater
than the distance of the most distant reference node and
2) whether the distance of the other possible solution is
smaller than the distance of the most distant reference node,
as shown in Fig. 6b. In other words, we want the most
distant reference node to be between the two possible
solutions.
When an unknown node has more than two reference
neighbors, it can use the residual error to check the position
estimate. A node can detect an inconsistency when one of
thepossiblesolutionshasthelargerdistancetothe
recursion origin but it also has a higher residual error
when compared to the other possible solution. The ideal
682 IEEE TRANSACTIONS ON COMPUTERS, VOL. 58, NO. 5, MAY 2009
Fig. 8. Scenarios that could lead to wrong position estimates or to the loss of the recursion direction. (a) An unknown node computing its position
when one of the two reference nodes is more distant to the recursion origin than this node. (b) An unknown node computing its position when the two
reference nodes are aligned to the line of the recursion origin.
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case is that the most distant solution, which is considered
the right position of the node, has the lower residual error.
3.2 Complexity Analysis
In this section, we will briefly analyze the complexity of our
algorithm in terms of communication requirements, pro-
cessor resources, and time consumption:
.Communication complexity. In the DPE algorithm,
beacon nodes (from the beacon structure) start the
recursion by broadcasting their localization packets.
Neighboring nodes that were able to estimate their
positions broadcast packets containing their esti-
mated positions in order to be used as references by
the unknown nodes. This recursion continues until
all nodes have estimated their positions. In this
scheme, each node will send only one packet during
the whole algorithm execution. Thus, the commu-
nication complexity of our algorithm is only OðnÞ,
where nis the number of nodes in the network. We
can see the DPE algorithm as single directed flood-
ing from the recursion origin toward the network
borders.
.Computational complexity. As mentioned before and
shown in Fig. 6b, in the DPE algorithm, a position is
computed by intersecting the two circles formed by
two references and choosing the most distant solu-
tion from the recursion origin. These procedures are
quite simple and can be done using a fixed number of
only 20 flops in each node.
.Time complexity. The execution time of our algorithm
is proportional to the network size and to the time
that a node waits for more packets from its
neighbors (waitT imer in Algorithm 1). In our
experiments, which will be presented in the next
section, we use a waitT imer of 0.5 second. We also
implement a random transmission time of half this
waitTimer in order to avoid collisions. Even with all
of these relative superestimated timers, we have a
time complexity of about 1.7 seconds per hop, which
shows that the algorithm can finish quickly even in
large-scale networks.
4PERFORMANCE EVALUATION
In this section, we evaluate our proposed scheme, DPE, and
compare it to RPE [21], a similar recursive scheme that uses
random distributed beacons and at least three reference
neighbors to estimate a position.
4.1 Methodology
The evaluation is performed through simulations using the
Ns-2 simulator [36]. The communication range is fixed at
15 m for all nodes. For RPE, 5 percent of the nodes are
beacons, while for DPE, we have only four beacons, as
depicted in Fig. 6a. Two scenarios are evaluated for DPE: In
the first scenario, the beacon structure is deployed at the
center of the sensor field, while in the second scenario, it is
deployed at the border. We can see these scenarios as the best
and worst cases of deployment. A random deployment of
the beacon structure generates intermediate results between
the two scenarios. To simulate the RSSI inaccuracy, each
range sample is disturbed by a normal distribution with the
actual distance as the mean and 10 percent of this distance as
the standard deviation. Each point in the graphs represents
the average of 33 random topologies of 150 sensor nodes in a
70 70 m2sensor field. The error bars represent the
confidence interval for 95 percent of confidence.
4.2 Geographic Distribution of the Error
An illustration of how the position errors are distributed
along the sensor field is provided in Fig. 9. Fig. 9a depicts
the error distribution resulting from RPE, where the peaks
indicate nodes that are distant from their real position.
Compared to the original RPE algorithm, Figs. 9c and 9e
show that DPE reduces the number of peaks and also
maintains a controlled increase in the error, so that the more
distant from the recursion origin a node is, the greater is its
position error. Therefore, the distance to the recursion
origin can be used as an indication of the position error.
This behavior occurs as a consequence of the directed
recursion and the method used to choose the reference
nodes in the second phase of DPE.
4.3 Error Directions and Correlations
The two points obtained by the real position of a node and
its estimated position can define an error vector with a
magnitude and a direction. Basically, the correlation
between the errors of two nodes is the level of linear
dependence of their error vectors.
Therefore, an error is not defined only by the distance
between the calculated and actual position of a node. This
error is also defined by its direction. Analyzing and
knowing the correlation between the errors’ directions
obtained by the localization algorithms can be very useful,
especially in algorithms like the geographic routing algo-
rithms that can be influenced by the error correlation levels.
Figs. 9b, 9d, and 9f depict the true location of nodes with
an error vector pointing to the estimated position for RPE
and DPE (scenarios 1 and 2). These results use the same
information used by those explained in the previous
section. Squared points indicate the beacon nodes.
A behavior can be observed in these graphics: nodes that
are close to each other have correlated errors. This informa-
tion is very important since it shows that a node’s localization
error cannot be simulated only by using, for example, a
normal distribution with random directions. Even a localiza-
tion scheme with a GPS receiver at each sensor node results in
correlated errors [31], and ignoring these correlations can
result in inconsistent experiments, especially in routing
algorithms. This behavior shows the importance of using
real localization systems to simulate geographic algorithms,
as is done in this work.
4.4 The Error Distribution
The distribution of position errors among the sensor nodes
depicted in Figs. 10a and 10b. Fig. 10a depicts the probability
distribution of the nodes’ position error. The cumulative
error, depicted in Fig. 10b, identifies the percentage of nodes
(y-axis) with an error smaller than a parameterized value
(x-axis). A sharp curve means that the majority of nodes has
a small error.
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We can see that the best results are achieved by the
DPE algorithm with controlled recursion and its choice of
references (RPE chooses the references with smaller residual
errors). Another aspect that decreases the localization error
in comparison to the RPE algorithm is the fact that the
DPE algorithm requires fewer reference nodes and, thus,
fewer RSSI estimations, making this algorithm less suscep-
tible to these inaccurate distance estimations. From the
graph, it is also possible to see how the position of the
beacon structure (scenarios 1 and 2) can affect the position
error of the nodes.
4.5 The Impact of the Network Density
The impact of the network density is evaluated by
increasing the network density from 0.005 to 0.1 nodes=m2.
The increase in this value results in more neighbors and,
potentially, more reference points for estimating a node’s
position. In low-density networks, the number of settled
nodes (nodes that have estimated their positions) decreases
since the nodes do not have enough reference neighbors to
estimate their own position (and thus, they do not become
references). Fig. 11a shows that DPE can work in lower
density networks compared to RPE. In low densities such as
684 IEEE TRANSACTIONS ON COMPUTERS, VOL. 58, NO. 5, MAY 2009
Fig. 9. Geographic distribution of the error (a) using the RPE algorithm, (c) using DPE in the first scenario, and (e) using DPE in the second scenario.
Also, the corresponding correlation of the error (b) using the RPE algorithm, (d) using DPE in the first scenario, and (f) using DPE in the second
scenario.
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0.01 and 0.015 nodes=m2, the number of settled nodes
increases by almost 40 percent. In Fig. 11b, we can see the
position error decreasing as the network density increases.
4.6 The Impact of the RSSI Inaccuracy
The distance estimated using RSSI measurements is not
accurate. Depending on the environment, such an inaccu-
racy may lead to greater errors in the estimated positions.
We evaluate this impact by adding some noise to the real
distances. This noise is generated by a normal distribution
with the actual distance as the mean and a percentage of
this distance as the standard deviation [37], [21].
Fig. 11c compares the increase in the standard deviation
of the normal distribution (used to simulate the noise)
from 0 to 25 percent of the actual distance in the RPE and
DPE algorithms. This figure shows that the DPE algorithm
DE OLIVEIRA ET AL.: AN EFFICIENT DIRECTED LOCALIZATION RECURSION PROTOCOL FOR WIRELESS SENSOR NETWORKS 685
Fig. 10. Simulation results. (a) Probability distribution of the error. (b) Cumulative error.
Fig. 11. Simulation results. (a) Impact of the network density in the error. (b) Impact of the network density in the number of settled nodes. (c) Impact
of the RSSI inaccuracy.
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seems to be more influenced by the RSSI inaccuracy,
although it still has better results in most cases.
4.7 The Impact of the Network Scale
Scalability is evaluated by varying the network size from
100 to 350 nodes with a constant density of 0.03 nodes=m2.
Thus, the sensor field is resized according to the number of
sensor nodes. The number of beacons in the RPE algorithm
is always 5 percent of the nodes. Thus, this number
increases as the number of nodes is increased. Fig. 12a
compares the RPE algorithm to the DPE algorithm when
only one beacon structure (with four beacons) is used by the
DPE method. We can see the error increasing more quickly
in the DPE algorithm when the number of beacons remains
constant but the number of nodes increases. On the other
side, when we add another beacon structure (with four
beacons) for each group of 100 nodes (e.g., two structures for
200 nodes), the error remains almost constant as depicted in
Fig. 12b. In this last case, we can see that the DPE algorithm
decreases the error by at least 30 percent.
4.8 Deducing a Node’s Position Error by Its
Distance to the Recursion Origin
As previously mentioned (and shown in Figs. 9c and 9e), in
the DPE algorithm, we can estimate the position error of a
node by knowing its distance to the recursion origin. This
error is depicted in Fig. 13a using 0.05, 0.10, and 0.15 of the
distance as the standard deviation of the RSSI noise. A similar
result, depicted in Fig. 13b, shows the positioning error with
reference to the number of hops to the recursion origin, which
seems to be a more reliable source for deducing the nodes’
positioning error. It is important to note that it is not possible
to make this deduction in RPE since the beacon nodes are
deployed randomly and there is no recursion origin.
4.9 The Influence of the Beacon Structure
Some features of the beacon structure, like the number of
beacons and their distance to the center, can affect the final
localization error of the DPE algorithm. Fig. 13c depicts the
localization error by varying the number of beacons in the
beacon structure, showing that having fewer than four
nodes can increase this error, while having more than four
does not help in decreasing it.
One of the main problems in the existing geographic
algorithms is that most of them do not consider localization
inaccuracies, which are present even in the simplest solutions
such as using GPS receivers. This section has two main goals:
1) to compare the performance of the geographical algorithms
when using our proposed DPE algorithm and RPE as the
source for localization information and 2) to show the effect of
inaccurate position information on the geographic algo-
rithms. The next section shows the effect of the localization
systems on the routing algorithms, while Section 4.11 shows
the effect on density control algorithms.
Fig. 13d shows the localization error in relation to
beacons’ distance to the center of the beacon structure. The
more distant the beacons are, the less recursion the system
will have, thereby decreasing the localization error. How-
ever, a large structure may not be feasible.
4.10 The Effect on Geographic Routing Algorithms
Geographic algorithms have become more popular, espe-
cially in sensor networks, due to their ability to use the
known positions of nodes to reduce communication. An
example of this class of algorithms is the geographic routing
algorithms [29], [38], [39]. These algorithms have low route
discovery overhead, and basically, a node only needs to
store information about its neighbors. For these reasons,
geographic routing is the protocol of choice for many
emerging applications in sensor networks [40].
One of the main drawbacks of the proposed geographic
algorithms is that most of them do not consider the
localization inaccuracy, which is present even when we
use a GPS receiver at each sensor node. In this work, we
analyze the effects of the localization errors in two types of
geographic algorithms: the geographic routing and density
control algorithms (next section).
To analyze the effects of the localization inaccuracy on
the geographic routing algorithms, we simulated the GEAR
algorithm [29] using the node position provided by the
localization systems RPE and DPE (scenarios 1 and 2).
686 IEEE TRANSACTIONS ON COMPUTERS, VOL. 58, NO. 5, MAY 2009
Fig. 12. Simulation results. (a) Impact of the network scale using only one beacon structure. (b) Impact of the network scale using more than one
beacon structure.
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GEAR is an example of the algorithm Greedy Forward
[41]
1
that uses an associated cost for each node to allow
the packet to be forwarded around holes and also to
distribute the routing work among the nodes.
GEAR uses geographic regions to disseminate the sink’s
interests [41]. Furthermore, this interest is received not by
only one node but by a set of nodes in a certain region. A
node decides whether it should receive a packet depending
on whether it is inside or outside the region. Depending on
the localization error, the routing algorithm can make a
right or wrong decision:
.Right decision. A node that should receive the packet
has received it, or a node that should not receive the
packet did not receive it.
.Wrong decision. A node that should receive the
packet did not receive it, or a node that should not
receive a packet did receive it.
Fig. 14a depicts the difference between the right decisions
and the wrong decisions taken by the GEAR algorithm using
the RPE and DPE (scenarios 1 and 2) algorithms. This
graphic shows how a simple procedure like a node deciding
whether it is inside or outside a region can become erroneous
in the presence of localization errors. As we can see, in many
cases, the precision of the packet delivery is less than
50 percent.
In the Greedy Forward mechanism, each node chooses
the nearest neighbor to the destination node. In the presence
of localization errors, these choices can be wrong. Fig. 14b
depicts the fraction of wrong choices made by the GEAR
when using the localization algorithms. This graphic shows
how the choices at each node can be wrong in the presence
of localization errors. This effect results in larger paths from
the sink to the region of interest.
4.11 The Effect on Density Control Algorithms
Another class of algorithms that can use node position
information to increase its performance is the density
control algorithm [15]. These algorithms are also important
to sensor networks since they allow redundant nodes to be
turned off.
To analyze the effects of the localization inaccuracy on
density control algorithms, we simulated the Geographical
Adaptive Fidelity (GAF) algorithm [15], a known protocol
that uses the positions of nodes to decide whether a node
should be awake or turned off. We also used the node
position information provided by the localization systems
RPE and DPE (scenarios 1 and 2).
GAF divides the sensor field into grids so that every
node in one grid can reach every node in the neighboring
grids. In this way, only one node needs to stay awake in
each grid. To compute its grid, a node uses its known
position. The computation of this grid can become wrong in
the presence of localization errors. Fig. 15a depicts the
DE OLIVEIRA ET AL.: AN EFFICIENT DIRECTED LOCALIZATION RECURSION PROTOCOL FOR WIRELESS SENSOR NETWORKS 687
1. In this routing algorithm, the packet is forwarded to the neighbor
nearest to the destination node.
Fig. 13. Simulation results. Error in relation to changes in (a) the distance to the recursion origin, (b) the number of hops to the recursion origin,
(c) the number of beacons, and (d) the distance of the beacons to the recursion origin.
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fraction of nodes that computed their grids correctly in the
presence of localization errors. As we can see, a localization
algorithm with fewer errors is capable of providing better
performance to the GAF algorithm.
Two problems arise from the wrong grid calculation.
First, nodes that should be sleeping remain awake. Second,
nodes that should be awake are turned off. The last problem
seems to be more critical, since part of the sensor field could
become uncovered by sensor nodes. Fig. 15b depicts the
fraction of grids that become uncovered by nodes after the
execution of the GAF algorithm. As we can see, in many
cases, more than 30 percent of the grids were uncovered by
a sensor node, which is impractical in most scenarios.
5RELATED WORK
Cricket [33] combines active beacons and passive ultrasonic
receivers to provide a localization system. Cricket is
designed for mobile nodes in an indoor environment, but it
may be used with static nodes. The active beacons broadcast
their location information over a radio frequency channel
together with ultrasonic pulses. The other nodes use the
TDoA method to estimate the distance to a beacon. In the
Cricket solution, beacon nodes need to be placed statically to
cover all of the sensor field, i.e., a beacon grid is built to cover
the whole sensor field. In the DPE algorithm, the beacon
structure can be strategically placed or deployed with the
regular nodes. Thus, the DPE algorithm is more suitable for
outdoor environments. TDoA, used by Cricket, can also be
used by DPE to enhance its distance measurements resulting
in better position estimates.
GPS-less localization [42] uses a fixed number of beacons
with overlapping regions of coverage. The beacon nodes
broadcast radio signals periodically. The other nodes use
connectivity information to determine their proximity to a
subset of beacon nodes and localize themselves to the
centroid of the selected beacons. The principal drawbacks of
a GPS-less localization is that regular nodes must be in the
communication range of at least three beacon nodes, just like
in the Cricket solution, and that it requires a beacon grid that
covers the whole sensor field. This approach leads to a larger
number of beacon nodes compared to the DPE algorithm.
APS [20] is a distributed hop-by-hop positioning algo-
rithm that works as an extension of distance vector routing
and GPS positioning to provide a localization system in
which a limited fraction of nodes have the self-location
capability. In APS, each beacon broadcasts a correction
factor to help other nodes deal with the propagated errors.
These correction factors indicate the difference between
multihop distances that a beacon obtains using its own
688 IEEE TRANSACTIONS ON COMPUTERS, VOL. 58, NO. 5, MAY 2009
Fig. 14. Simulation results of the GEAR experiments. (a) Precision of the interest delivery. (b) Precision of the hop selection.
Fig. 15. Simulation results of the GAF experiments. (a) Wrong grid allocation. (b) Grid coverage.
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known position. This technique needs a similar number of
beacon nodes compared to DPE, but the localization error is
larger because APS uses the number of hops (or the sum of
RSSI) to estimate the distances from the beacons.
RPE [21] recursively computes the node location informa-
tion without the need for strategic beacon placement. A
similar algorithm is the Localization using Sweeps [43].
These approaches are very similar to DPE, but it uses beacons
that are randomly deployed. A number of beacons (usually
5 percent of the nodes) must be deployed to ensure that at
least in one place, an unknown node will have three or more
beacon neighbors so that the recursion can start. Since there is
no known direction to the recursion, an unknown node needs
at least three reference nodes to estimate its own location
using trilateration. Both RPE and DPE have the problem of
propagating the position error throughout the network.
However, in DPE, this error is reduced by selecting the best
reference neighbors, and it can also be somewhat indicated
by the distance of the node from the recursion origin.
AHLoS [18] is designed to provide a localization system to
a special node, called Medusa, that requires four ultrasound
transmitters and four receivers. Although AHLoS works
both indoors and outdoors, the additional hardware
increases the network cost. This system also has a recursive
behavior and can thus take advantage of the proposed
DPE scheme.
GPS-free positioning [44] proposes a distributed infra-
structure-free localization algorithm that does not rely on
GPS. The key point of the algorithm is to show that it is
possible to build a relative coordinate system without
centralized knowledge of the network topology. The
DPE algorithm also uses a relative coordinate system that
is automatically known by all of the settled nodes to be
the recursion origin. No extra packets are needed to
discover or elect a coordinate system in DPE.
Some experiments with geographic routing algorithms in
the presence of localization errors have been presented in
[45] and [40]. In [45], the Target Estimation and Object
Tracking algorithms are also analyzed with localization
errors. However, in both cases, the localization error is
simulated only by disturbing the real positions of the nodes
with a fraction of the localization range. One contribution of
this work is to show that this type of error simulation is not
realistic, since it does not consider the correlation and
distribution of the error. Furthermore, to the best of our
knowledge, this paper is the first to evaluate these geo-
graphic algorithms using real proposed localization systems.
An approach to divide localization systems into phases
has been proposed by Langendoen and Reijers [37], who
identified three distinct phases in localization systems:
determine the distances to beacons, derive positions, and
refine positions. In this work, we do not divide the
localization systems into phases but rather into compo-
nents, which, we believe, can be more widely applied to a
greater number of proposed localization systems. While
the phase classification proposed in [37] can only be
applied to distributed localization systems, we believe that
the component classification proposed in this work can be
used in almost any localization system.
6FINAL REMARKS
This work has presented the DPE algorithm, a directed
recursive localization system for WSNs. We have shown
how this method allows an unknown node to correctly
estimate its position based on the location information of
only two reference neighbors and the direction of the
recursion. The simulation experiments have shown that
compared to RPE [21], the DPE algorithm works in lower
density sensor networks, reduces location errors due to its
reference selection phase, requires fewer processor re-
sources, uses fewer beacon nodes, and also indicates the
node location error based on the node’s distance to the
recursion origin. The use of the beacon structure does have
some implications on its applicability, but we believe that
the possibility of the random deployment of this structure
makes this scheme very applicable.
This work has also proposed a more generic way to
divide localization systems into three distinct components:
the distance estimation, the position calculation, and the
localization algorithm. We have shown how each of these
components can affect the final localization error and, thus,
that they should be studied and analyzed separately.
Finally, the effects of the localization errors on geo-
graphic algorithms have been analyzed using real localiza-
tion systems. We simulated two geographic algorithms that
have not been studied in the presence of real localization
errors: GEAR, a geographic routing algorithm, and GAF, a
density control algorithm. The results show the importance
of having more accurate localization systems and also the
importance of proposing geographic algorithms that con-
sider the localization inaccuracy.
ACKNOWLEDGMENTS
This work was partially supported by NSERC Grants, the
Canada Research Chairs Program, the Early Researcher
Award, the Ontario Distinguished Researcher Award, the
Brazilian Research Council (CAPES), and the Brazilian
National Council for Scientific and Technological Devel-
opment (CNPq) under processes 55.4087/2006-5, 47.4194/
2007-8, and 57.5808/2008-0.
REFERENCES
[1] I.F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cyirci,
“Wireless Sensor Networks: A Survey,” Computer Networks,
vol. 38, no. 4, pp. 393-422, Mar. 2002.
[2] A. Boukerche, “Algorithms and Protocols for Wireless Sensor
Networks,” Wiley & Sons, 2008.
[3] A. Boukerche, Handbook of Algorithms for Wireless Networking and
Mobile Computing. Chapman & Hall/CRC, 2005.
[4] S. Nikoletseas, “Models and Algorithms for Wireless Sensor
Networks (Smart Dust),” Proc. 32nd Conf. Current Trends in
Theory and Practice of Computer Science (SOFSEM ’06), pp. 64-83,
2006.
[5] M. Ilyas and I. Mahgoub, Handbook of Sensor Networks: Compact
Wireless and Wired Sensing Systems, chapter 20, CRC Press LLC,
2004.
[6] A. Boukerche, S. Nikoletseas, “Protocols for Data Propagation in
Wireless Sensor Networks,” Wireless Communication Systems and
Networks, M. Guizani, eds., Plenum Press, 2004.
[7] S. Nikoletseas and P.G. Spirakis, “Efficient Information Propaga-
tion Algorithms in Smart Dust and Nanopeer Networks,” Proc.
IST/FET Int’l Workshop Global Computing (GC ’04), pp. 127-145,
Mar. 2004.
DE OLIVEIRA ET AL.: AN EFFICIENT DIRECTED LOCALIZATION RECURSION PROTOCOL FOR WIRELESS SENSOR NETWORKS 689
Authorized licensed use limited to: Mochamad Hariadi. Downloaded on July 14, 2009 at 23:01 from IEEE Xplore. Restrictions apply.

[8] A. Sekhar, B.S. Manoj, and C.S.R. Murthy, “A Novel Solution for
Time Synchronization in Wireless Ad Hoc and Sensor Networks,”
Proc. 12th Int’l Conf. High Performance Computing (HiPC ’05),
pp. 333-342, Dec. 2005.
[9] A. Boukerche and D. Turgut, “Secure Time Synchronization
Protocols for Wireless Sensor Networks,” IEEE Wireless Comm.,
vol. 14, no. 5, pp. 64-69, Oct. 2007.
[10] A. Boukerche, H.A.B.F. de Oliveira, E.F. Nakamura, and
A.A.F. Loureiro, “A Novel Location-Free Greedy Forward
Algorithm for Wireless Sensor Networks,” Proc. IEEE Int’l
Conf. Comm., pp. 2096-2102, May 2008.
[11] A. Boukerche, H.A.B.F. de Oliveira, E.F. Nakamura, and
A.A.F. Loureiro, “A Novel Lightweight Algorithm for Time-Space
Localization in Wireless Sensor Networks,” Proc. 10th ACM-IEEE
Int’l Symp. Modeling, Analysis and Simulation of Wireless and Mobile
Systems (MSWiM ’07), pp. 336-343, Oct. 2007.
[12] A.Y. Zomaya, M. Haydock, and S. Olariu, “Some Observations on
Using Meta-Heuristics for Efficient Location Management in
Mobile Computing Networks,” J. Parallel and Distributed Comput-
ing, vol. 63, no. 1, pp. 33-44, 2003.
[13] S. Jayashree, B.S. Manoj, and C.S.R. Murthy, “A Novel Battery
Aware MAC Protocol for Ad Hoc Wireless Networks,” Proc.
11th Int’l Conf. High Performance Computing (HiPC ’04), pp. 19-29,
Dec. 2004.
[14] T. Zia and A.Y. Zomaya, “Security Issues in Wireless Sensor
Networks,” Proc. Int’l Conf. Systems and Networks Comm.
(ICSNC ’06), p. 40, Oct. 2006.
[15] Y. Xu, J.S. Heidemann, and D. Estrin, “Geography-Informed
Energy Conservation for Ad Hoc Routing,” Proc. ACM
MobiCom ’01, pp. 70-84, 2001.
[16] A. Boukerche, H.A.B.F. de Oliveira, E.F. Nakamura, and
A.A.F. Loureiro, “Localization Systems for Wireless Sensor Net-
works,” IEEE Wireless Comm., special issue on wireless sensor
networks, vol. 14, no. 6, Dec. 2007.
[17] L. Doherty, K.S. Pister, and L.E. Ghaoui, “Convex Position
Estimation in Wireless Sensor Networks,” Proc. IEEE
INFOCOM ’01, vol. 3, pp. 1655-1663, Apr. 2001.
[18] A. Savvides, C.-C. Han, and M.B. Strivastava, “Dynamic Fine-
Grained Localization in Ad-Hoc Networks of Sensors,” Proc. ACM
MobiCom ’01, pp. 166-179, 2001.
[19] Y. Shang, W. Ruml, Y. Zhang, and M.P. Fromherz, “Localization
from Mere Connectivity,” Proc. ACM MobiHoc ’03, pp. 201-212,
2003.
[20] D. Niculescu and B. Nath, “Ad Hoc Positioning System (APS),”
Proc. IEEE Global Telecomm. Conf. (GLOBECOM ’01), pp. 2926-2931,
Nov. 2001.
[21] J. Albowicz, A. Chen, and L. Zhang, “Recursive Position
Estimation in Sensor Networks,” Proc. Ninth Int’l Conf. Network
Protocols (ICNP ’01), pp. 35-41, Nov. 2001.
[22] N. Bulusu, J. Heidemann, D. Estrin, and T. Tran, “Self-
Configuring Localization Systems: Design and Experimental
Evaluation,” ACM Trans. Embedded Computing Systems, vol. 3,
no. 1, pp. 24-60, Feb. 2004.
[23] A. Boukerche, H.A.B.F. de Oliveira, E.F. Nakamura, and
A.A.F Loureiro, “A Voronoi Approach for Scalable and Robust
DV-Hop Localization System for Sensor Networks,” Proc. 16th
Int’l Conf. Computer Comm. and Networks (ICCCN ’07), pp. 497-502,
2007.
[24] L. Hu and D. Evans, “Localization for Mobile Sensor Networks,”
Proc. ACM MobiCom ’04, pp. 45-57, 2004.
[25] M. Rudafshani and S. Datta, “Localization in Wireless Sensor
Networks,” Proc. Sixth Int’l Conf. Information Processing in Sensor
Networks (IPSN ’07), pp. 51-60, 2007.
[26] J. Heidemann, F. Silva, C. Intanagonwiwat, R. Govindan,
D. Estrin, and D. Ganesan, “Building Efficient Wireless Sensor
Networks with Low-Level Naming,” Proc. 18th ACM Symp.
Operating Systems Principles (SOSP ’01), pp. 146-159, 2001.
[27] C.Intanagonwiwat,R.Govindan,andD.Estrin,“Directed
Diffusion: A Scalable and Robust Communication Paradigm for
Sensor Networks,” Proc. ACM MobiCom ’00, pp. 56-67, Aug. 2000.
[28] J. Heidemann, F. Silva, and D. Estrin, “Matching Data Dissemina-
tion Algorithms to Application Requirements,” Proc. First Int’l
Conf. Embedded Networked Sensor Systems, pp. 218-229, Nov. 2003.
[29] Y. Yu, R. Govindan, and D. Estrin, “Geographical and Energy
Aware Routing: A Recursive Data Dissemination Protocol for
Wireless Sensor Networks,” Technical Report CSD-TR-01-0023,
UCLA Computer Science Dept., 2001.
[30] V. Ramadurai and M.L. Sichitiu, “Localization in Wireless Sensor
Networks: A Probabilistic Approach,” Proc. Int’l Conf. Wireless
Networks (ICWN ’03), pp. 275-281, June 2003.
[31] M.L. Sichitiu and V. Ramadurai, “Localization of Wireless
Sensor Networks with a Mobile Beacon,” Proc. First IEEE Int’l
Conf. Mobile Ad Hoc and Sensor Systems (MASS ’04), pp. 174-183,
Oct. 2004.
[32] B. Hofmann-Wellenho, H. Lichtenegger, and J. Collins, Global
Positioning System: Theory and Practice, fourth ed. Springer,
1997.
[33] N.B. Priyantha, A. Chakraborty, and H. Balakrishnan, “The
Cricket Location-Support System,” Proc. ACM MobiCom ’00,
pp. 32-43, Aug. 2000.
[34] L. Girod and D. Estrin, “Robust Range Estimation Using
Acoustic and Multimodal Sensing,” Proc. IEEE/RSJ Int’l Conf.
Intelligent Robots and Systems (IROS ’01), vol. 3, pp. 1312-1320,
Oct./Nov. 2001.
[35] K. Whitehouse, “The Design of Calamari: An Ad-Hoc Localization
System for Sensor Networks,” master’s thesis, Univ. of California
at Berkeley, 2002.
[36] K. Fall and K. Varadhan, The NS Manual—Notes and Doc-
umentation, The VINT Project, http://www.isi.edu/nsnam/ns/
ns-documentation.html, Dec. 2003.
[37] K. Langendoen and N. Reijers, “Distributed Localization Algo-
rithms,” Embedded Systems Handbook, R. Zurawski, ed. CRC press,
Aug. 2005.
[38] B. Karp and H.T. Kung, “GPSR: Greedy Perimeter Stateless
Routing for Wireless Networks,” Proc. ACM MobiCom ’00,
pp. 243-254, 2000.
[39] A. Boukerche, H.A.B.F. de Oliveira, E.F. Nakamura, and
A.A.F. Loureiro, “Towards an Integrated Solution for Node
Localization and Data Routing in Sensor Networks,” Proc. 12th
IEEE Symp. Computers and Comm. (ISCC ’07), July 2007.
[40] K. Seada, A. Helmy, and R. Govindan, “On the Effect of
Localization Errors on Geographic Face Routing in Sensor
Networks,” Proc. Third Int’l Symp. Information Processing in Sensor
Networks (IPSN ’04), pp. 71-80, 2004.
[41] J.C. Navas and T. Imielinski, “Geocast—Geographic Addressing
and Routing,” Proc. ACM MobiCom ’97, pp. 66-76, 1997.
[42] N. Bulusu, J. Heidemann, and D. Estrin, “GPS-Less Low Cost
Outdoor Localization for Very Small Devices,” IEEE Personal
Comm. Magazine, vol. 7, no. 5, pp. 28-34, Oct. 2000.
[43] D.K. Goldenberg, P. Bihler, M. Cao, J. Fang, B.D.O. Anderson,
A.S. Morse, and Y.R. Yang, “Localization in Sparse Networks
Using Sweeps,” Proc. ACM MobiCom ’06, pp. 110-121, 2006.
[44] S. Capkun, M. Hamdi, and J.-P. Hubaux, “GPS-Free Positioning in
Mobile Ad Hoc Networks,” Cluster Computing, vol. 5, no. 2,
pp. 157-167, 2002.
[45] T. He, C. Huang, B.M. Blum, J.A. Stankovic, and T. Abdelzaher,
“Range-Free Localization Schemes for Large Scale Sensor Net-
works,” Proc. ACM MobiCom ’03, pp. 81-95, 2003.
Horacio Antonio Braga Fernandes de Oliveira
received the PhD degree in Computer Science
from the Federal University of Minas Gerais,
Brazil, with a partial doctoral fellowship at
University of Ottawa, Canada, in 2007 and
2008. He is currently an associate professor of
computer science in the Department of Compu-
ter Science, Federal University of Amazonas
(UFAM), Manaus, Brazil. He is also with the
PARADISE Research Laboratory, School of
Information Technology and Engineering (SITE), University of Ottawa,
and with the Department of Computer Science, Federal University of
Minas Gerais, Belo Horizonte, Brazil. His research interests include
localization and synchronization algorithms, distributed algorithms, and
wireless ad hoc, vehicular, and sensor networks. He is the author of
several papers in the different areas of his research interests. He was the
corecipient of the Best Paper Award at ICC 2008.
690 IEEE TRANSACTIONS ON COMPUTERS, VOL. 58, NO. 5, MAY 2009
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Azzedine Boukerche is a full professor and
holds a Canada Research Chair position at the
University of Ottawa (uOttawa). He is the
founding director of the PARADISE Research
Laboratory, School of Information Technology
and Engineering (SITE), Ottawa. Prior to this, he
held a faculty position at the University of North
Texas, and he was a senior scientist at the
Simulation Sciences Division, Metron Corp., San
Diego. He was also employed as a faculty
member in the School of Computer Science, McGill University, and
taught at the Polytechnic of Montreal. He spent a year at the JPL/NASA-
California Institute of Technology, where he contributed to a project
centered about the specification and verification of the software used to
control interplanetary spacecraft operated by JPL/NASA Laboratory. His
current research interests include wireless ad hoc and sensor networks,
wireless networks, mobile and pervasive computing, wireless multi-
media, QoS service provisioning, performance evaluation and modeling
of large-scale distributed systems, distributed computing, large-scale
distributed interactive simulation, and parallel discrete-event simulation.
He has published several research papers in these areas. He served as
a guest editor for the Journal of Parallel and Distributed Computing
(special issue for routing for mobile ad hoc, special issue for wireless
communication and mobile computing, and special issue for mobile
ad hoc networking and computing), ACM/Kluwer Wireless Networks,
ACM/Kluwer Mobile Networks Applications, and Journal of Wireless
Communication and Mobile Computing. He serves as an Associate
Editor of IEEE Transactions on Parallel and Distributed systems,IEEE
Transactions on Vehicular Technology,Elsevier Ad Hoc Networks,Wiley
International Journal of Wireless Communication and Mobile Computing,
Wiley’s Security and Communication Network Journal,Elsevier Perva-
sive and Mobile Computing Journal,IEEE Wireless Communication
Magazine,Elsevier’s Journal of Parallel and Distributed Computing, and
SCS Transactions on Simulation. He was the recipient of the Best
Research Paper Award at IEEE/ACM PADS 1997 and ACM Mobi-
Wac 2006, ICC 2008, and the recipient of the Third National Award for
Telecommunication Software in 1999 for his work on a distributed
security systems on mobile phone operations. He has been nominated
for the Best Paper Award at the IEEE/ACM PADS 1999 and
ACM MSWiM 2001. He is a recipient of an Ontario Early Research
Excellence Award (previously known as Premier of Ontario Research
Excellence Award), Ontario Distinguished Researcher Award, and
Glinski Research Excellence Award. He is a cofounder of the QShine
International Conference on Quality of Service for Wireless/Wired
Heterogeneous Networks (QShine 2004). He served as the general
chair for the Eighth ACM/IEEE Symposium on Modeling, Analysis and
Simulation of Wireless and Mobile Systems, and the Ninth ACM/IEEE
Symposium on Distributed Simulation and Real-Time Application
(DS-RT), the program chair for the ACM Workshop on QoS and Security
for Wireless and Mobile Networks, ACM/IFIPS Europar 2002 Con-
ference, IEEE/SCS Annual Simulation Symposium (ANNS 2002),
ACM WWW 2002, IEEE MWCN 2002, IEEE/ACM MASCOTS 2002,
IEEE Wireless Local Networks WLN 03-04; IEEE WMAN 04-05, and
ACM MSWiM 98-99, and a TPC member of numerous IEEE and ACM
sponsored conferences. He served as the vice general chair for the Third
IEEE Distributed Computing for Sensor Networks (DCOSS) Conference
in 2007, as the program cochair for GLOBECOM 2007-2008 Symposium
on Wireless Ad Hoc and Sensor Networks, and for the 14th IEEE
ISCC 2009 Symposium on Computer and Commmunication Sympo-
sium, and as the finance chair for ACM Multimedia 2008. He also serves
as a Steering Committee chair for the ACM Modeling, Analysis and
Simulation for Wireless and Mobile Systems Conference, the ACM
Symposium on Performance Evaluation of Wireless Ad Hoc, Sensor,
and Ubiquitous Networks, and IEEE/ACM DS-RT.
Eduardo Freire Nakamura received the PhD
degree in computer science from the Federal
University of Minas Gerais, Brazil, in 2007. He
is currently a researcher and a full professor
with the Center of Analysis, Research and
Technological Innovation Foundation (FUCA-
PI), Manaus, Brazil. His research interests
include data/information fusion, distributed al-
gorithms, localization algorithms, wireless ad
hoc and sensor networks, mobile and pervasive
computing. He has published several papers in the area of wireless
sensor networks, and has served as a TPC member of the Second
Latin American Autonomic Computing Symposium, supported by the
IEEE Computer Society. He was the co-recipient of the Best Research
Paper Award at ICC 2008
Antonio Alfredo Ferreira Loureiro received
the BSc and MSc degrees in computer science
from the Federal University of Minas Gerais
(UFMG), Belo Horizonte, Brazil, and the PhD
degree in computer science from the University
of British Columbia, Canada. Currently, he is a
full professor of computer science at UFMG,
where he leads the research group in wireless
sensor networks. His main research areas are
wireless sensor networks, mobile computing,
and distributed algorithms. He was the co-recipient of the Best Research
Paper Award at ICC 2008
.For more information on this or any other computing topic,
please visit our Digital Library at www.computer.org/publications/dlib.
DE OLIVEIRA ET AL.: AN EFFICIENT DIRECTED LOCALIZATION RECURSION PROTOCOL FOR WIRELESS SENSOR NETWORKS 691
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