The document proposes a new localization method called A2L (Angle to Landmark) for wireless sensor networks. A2L uses angle of arrival measurements between sensor nodes and a subset of nodes equipped with GPS (landmarks) to determine the positions of non-landmark nodes. Compared to previous methods like APS and AHLoS that also use angle and distance measurements, simulations show that A2L can locate a greater number of nodes with higher accuracy while requiring fewer connections between nodes. The method is also low-cost since it does not require each node to have GPS or other expensive equipment.

1. 1
A2L: Angle to Landmarks Based Method
Positioning for Wireless Sensor Networks
Mustapha Boushaba1 , Abderrahim Benslimane2 and Abdelhakim Hafid1
1
Network Research Laboratory, University of Montreal
CP 6128 succ Centre-Ville Montréal, QC, H3C 3J7, Canada
{boushamu, ahafid}@iro.umontreal.ca
2
Laboratoire Informatique d’Avignon - CERI
339 chemin des Meinajaries BP 1228-84911 Avignon Cedex 9
benslimane@lia.univ-avignon.fr
node location can be found by using extra hardware such as
Abstract— Thanks to recent technological progress, GPS (Global Positioning System); however, equipping each
autonomous wireless sensor networks have experienced sensor node with GPS is very expensive in terms of energy and
considerable development. Currently, they are used in the areas cost... A more acceptable solution would require only a subset
of health care, environment, military etc. Examples include:
biomedical sensor monitoring (e.g., cardiac patient monitoring),
of nodes equipped with GPS; the positions of their neighbors
habitat monitoring (e.g., animal tracking), weather monitoring are computed using techniques such as trilateration and
(temperature, humidity, etc.), vehicle detection, low-performance triangulation. It has been proven that the trilateration cannot be
seismic sensing, movement, acoustic ranging, and natural disaster used alone for node localization within a network with a very
detection/monitoring (e.g., flooding and fire). For a number of small density of GPS nodes. Most techniques use recursive
sensor-based applications, the knowledge of the positions of algorithms combining triangulation with trilateration or
sensors is required or, at least, preferable. In this paper, we
propose a new method to locate a large number of nodes in multilateration.
wireless sensor networks where only a subset of them are Some of the GPS based methods use estimated distance
landmarks (i.e., know their positions). Our method is AOA-based between pairs of neighbors. These methods are called Range-
(Angle Of Arrival) and it is called A2L (Angle to Landmark). Based Localization Schemes (in contrast with Range-Free
Compared, via simulations, to previous methods such as APS and Localization Schemes [1, 2, 3]). The most popular methods are
AHLoS, A2L considerably increases the number of located nodes
RSSI (Received Signal Strength Indicator), ToA/TDoA (Time
with accurate precision while using a smaller node degree.
of arrival / Time difference of arrival) and AOA (Angle of
Keywords: Angle of Arrival, Localization, trilateration. arrival). In RSSI, nodes measure the power of the received
signals and thus, can calculate the effective propagation loss.
I. INTRODUCTION Theoretical or empirical models are used to translate this loss
into distance. In ToA/TDoA, nodes directly translate the
Sensor networks are becoming a standard technology in
propagation time into distance if the signal propagation speed
wireless communications. The development of these networks
is known. The most basic localization system using ToA
involves many different research areas, such as
techniques is GPS [4]. In AOA, nodes estimate the angle at
communication, sensing and computing. This leads to smart
which signals are received and use simple geometric
disposable micro-sensors that can be deployed anywhere
relationships to calculate their positions. The accuracy of these
regardless of geographic limitations. Therefore, such sensors
measurements is closely related to the network environment;
may be applied widely in military, national security,
thus, the positions computed by the nodes may contain errors.
environment monitoring, traffic surveillance, medical domains.
In this paper, we propose a localization algorithm called
These networks usually use a large number of tiny sensors.
Angle to Landmark (A2L). This algorithm is based on some
Sensor nodes are low-cost, low-power, and communicate in
existing techniques such as Angle of Arrival (AOA) and
short distances. Together, they communicate in wireless mode
distance estimation for computing nodes positions. Our
and collaborate to provide information for common missions.
technique is low cost, does not require expensive infrastructure
A sensor node has generally embedded processing capabilities
and any compass. We use a fraction of landmarks allowing
and potentially has a number of sensors dedicated to sensing
each node in the network to calculate its own position.
different features such as acoustic, seismic, infrared (IR), and
Compared to some previous methods such as APS and
magnetic elements; it can also operate as imagers and micro-
AHLoS, A2L considerably increases the number of located
radar devices.
nodes with better precision.
For specific applications, some nodes must know their
The paper is organized as follows. Section 2 presents related
physical position to determine where events occur. Sensor
work. Section 3 describes the proposed A2L algorithm.

2. 2
Section 4 evaluates the performance of A2L using simulations.
Section 5 concludes the paper and presents future work.
II. RELATED WORK
A large number of existing techniques attempt to solve the
localization problem. A detailed survey can be found in [5].
We identify four categories:
Fig. 2. Sample topology: 5 nodes with 3 landmarks
- Infrastructure-based systems: They require infrastructures
like RADAR [6] or Cricket [7]. Other techniques are hybrid ones, it’s the case of the
- Robot-based systems: They use robots to locate nodes [8]. technique described in [15] where the authors combine APS
- GPS-free methods: They do not require anchors to locate with two other existing localization methods, namely MDS
nodes. The authors in [9] propose a method that builds a (Multidimensional Scanning) and SDP (Semidefinite
virtual system of coordinates, and the nodes compute their Programming). MDS calculates positions using a set of
positions in this virtual system. distances whereas SDP is a relaxation based method.
- GPS-based methods: They use the positions of anchors
(equipped with GPS) to determine estimated positions of non- In [11] authors propose an AHLoS system that produces
anchor nodes. high quality positions. It uses ultrasound and RF techniques to
The authors, in [10, 14, 2], use distance and angle deal with the ranging problem. To estimate node locations,
information to compute nodes position. APS [12] use the AHLoS uses a set of nodes initially configured as Landmarks
angle-of-arrival technique (AOA) for localization. All nodes in and defines several types of multilateration: atomic, iterative,
APS have the capability to compute orientation and position. and collaborative. Atomic multilateration can be applied as a
basic multilateration when a node has enough Landmarks
In this algorithm, nodes iteratively obtain position and
neighbors. Once at least three distances to three Landmarks are
orientation information starting from landmark nodes. When a
known, a node may compute its own location. When a node
non-positioned node knows at least three landmarks, it can
estimates its position, it becomes a Landmark. Therefore, an
apply a trilateration technique for computing its position and iterative multilateration continues until no more nodes can be
its orientation to the landmarks. This information will be localized. But in some case, even after applying these two
broadcasted to neighbors for subsequent iterations. For methods there are nodes unable to compute their positions. In
localizing an arbitrary node A (Fig. 1 [10]), it needs to have at a collaborative fashion, nodes try to estimate their locations
least two neighbors, B and C, which have estimates - angles or using beacons at two hops away.
ranges for landmark L (B and C should to be neighbors too). The disadvantage of AHLoS is that it requires high
. percentage of beacons to achieve high percentage of located
nodes. For example, to resolve 90 percent of unknown nodes
with an average degree of 6.28, AHLoS requires a density of
45% beacons.
To improve localization rate with better accuracy, using a
small set of landmarks and a small node degree, we propose
A2L that locates more nodes than existing approaches, e.g.,
A2L allows locating D and E in the topologies shown in Fig. 2
(see Section III for more details).
Fig. 1. Node A infer it’s bearing to a landmark L
III. ANGLE TO LANDMARK ALGORITHM
Let us consider the topology shown in Fig.2; nodes A, B, C
In this Section, we present a new method that allows
are landmarks and D, E are not positioned nodes. With APS,
localizing a high percentage of nodes in wireless sensor
the landmarks A, B and C start the localization mechanism. In
networks by using a minimum number of landmarks. It is
a recursive way, nodes E and D try to compute their positions
AOA-based where each node computes the difference between
and their orientations towards landmarks. Node E needs to
two AOA: incoming angle from landmark neighbors and from
have two neighbors that know the coordinates or the
non-positioned neighbors (Figure. 3). These angles are used to
orientation towards landmark C; this is not the case in the
compute distances between nodes and landmarks within two
topology shown in Fig. 2. Thus, no quadrilateral can be
hops. We assume that each node (e.g., Medusa node [13]) is
formed between node D and the landmark C; the same applies
able to measure its distance from its immediate neighbors and
for localizing node E. In this topology, APS cannot locate
has an antenna array enabling it to compute the incoming
nodes D and E.
signals angles (AOA).
In Figure 3, let us suppose that A, D, and F are the
landmarks. B, C, E and N are the non-positioned nodes. Plain
lines are the links between two immediate neighbors and

3. 3
dashed line are the links between nodes at two hops away. graph G = (NR, E), where NR represents the set of sensor
nodes and E the set of links between nodes. A link between
two nodes exists if each node is within the transmission range
of the other. We classify nodes into two sets: (1) NL: the set of
landmarks (i.e., know their positions using GPS for example);
and (2) NnL: the set of non-positioned nodes. All nodes in NL
and NnL are randomly placed in a geographic area using a
uniform distribution .
The goal of our proposed protocol is to locate a maximum
number of nodes in NnL by using a minimum of landmarks.
Our protocol requires that nodes exchange two messages
called INIT and POSITION:
Fig. 3. Localization nodes using A2L algorithm - INIT message
It is broadcasted once by NL nodes (landmarks) to their
To compute its position, node N needs to know the distances immediate neighbors (one hop). The INIT message structure is
and the coordinates of the Landmarks A, D, F and G.. When defined by two fields < idL, CoordL >, where idL is the
node N receives all useful information, it applies a identifier of the sending node and CoordL its coordinates
triangulation to compute distances to Landmarks at two hops. (x,y).
As an example, let θN be the incoming angle from node N and - POSITION Message:
θF the incoming angle from F, When the message POSITION is broadcasted, a receiver
When N knows the angle θ = | θN – θF |, it becomes easy to node K can extract information of interest from A2L records.
compute dNE distance by applying the formula: This will help a node K trying to locate itself. This message is
dNF=dNE+dEF-2.dNE.dEF.cos(θ) (2) broadcasted by each node I, in NnL, having at least one
Let us assume a 2-D space, (x,y) is the unknown position, neighboring landmark J and another neighboring node K
and (xi,yi) are the coordinate of the ith Landmark for i=1,…,n. which is not a landmark. When node K receives this message,
The coordinates and the estimated distance (di), distance it can compute its distance towards landmark J by applying the
between the ith Landmark and (x,y), are related by the triangulation mechanism using equation (2). The format of the
following set of equations: message POSITION is defined as: <idS, CoordS, A2L1, A2L3,
…, A2Ln>
( x1 − x )2 + ( y1 − y )2   d 12  where idS is the identifier of the node which broadcasts the
   
 M  = M  (3) POSITION message and CoordS are the coordinates (x,y) of
(xn − x)2 + ( yn − y )2  dn2 
    the sender node broadcasting the message POSITION., A2Lk
is defined as <idLj, idlk, CoordL, DistL, Angle>, where idLj
To resolve this set of equations, we transform (3) into a is the identifier of landmark J, idlk is the identifier of node k
linear system of equations by subtracting the nth equation (the to which the message A2L is destined, CoordL are
coordinates (x, y) of landmark J, and Angle is the angle
last line in (3)) from each other equation (lines 1 to n-1 in (3)).
between landmark J, transmitter I and the receiver K of A2L
The linear system is written in the form Ax = b, where
message. This angle will be computed by node I; it is the
difference between two AOAs (AOA from nodes J and K).
 2 ( x1 − x n ) 2 ( y1 − y n ) 
 
A =  M M , B. A2L algorithm
2( x 2 ( y n −1 − y n ) 
 n −1 − x n )  Initially, every landmark initializes A2L positioning
 x 12 − x n + y 12 − y n + d n2 − d 12
2 2
 (4) algorithm by broadcasting a message INIT. For each node, the
 
b =  M  MAC Layer can provide information for building Neighbors
x 2 2 2 2 2 2  table, called TN, shown in Fig.10. For each node I, each entry
 n −1 − x n + y n − 1 − y n + d n − d n −1 
of TN includes: (1) id: node’s identifier from incoming signal;
When range (di in (4)) measurements are noisy resolving (2) AOA: incoming angle from node id; and (3) Distance: the
different equations (lines in (4)) would not yield the same distance between node id and node I.
results. To solve this, we use a least-squares solution (5) which
id AOA Distance
is a technique borrowed from linear algebra that is often used
in applications that consists of over-determined system with Fig.4. Neighbors table structure
noisy measurements.
x = ( AT A) −1 AT b (5)
ˆ When a landmark’s neighbor I receives INIT messages, it
updates its landmarks table, called TL (Fig.5), and tries to
A. Message exchanges by A2L nodes resolve the corresponding trilateration system by using
We consider an adhoc network R modeled by a bidirectional equation (5). Node I must have at least three non-aligned

4. 4
landmarks in its TL table. For each node I, each entry of TL Landmarks coordinates and distances (i.e., message
includes: (1) idL: the landmark identifier; (2) Coord: POSITION). By receiving message POSITION, node N
coordinates (x,y) of landmark idL; (3) Distance: the distance computes distances dND, dNA and dNF, updates its TL and
between landmark idL and node I; it is retrieved from TN or applies a trilateration for computing its position. The TTL
computed by triangulation; and (4) nextHop: the sender of the value in this case is equal 2. When N is localized, it broadcasts
message POSITION. If its value is equal to idL then the its message POSITION containing its position and A2L fields
landmark idL is neighbor; otherwise, they are two hops away. serving nodes B, C, E to be located. Thus, all nodes are
Node I builds a list of A2L by combining the TL and TN located with TTL maximum value equal to 3.
records; the Angle in each element of the list corresponds to
the difference between the AOA landmark J and the AOA Algorithm. 1. Angle to Landmark Algorithm: process
from node K. This information allows node I to build the when node i receives a message POSITION.
POSITION message to be broadcasted toward its neighbors. Input: message POSITION
As an example, let us consider a node I (with identifier equal Output: node i coordinates and message POSITION
Variables:
to 3), that maintains two tables: (1) TN with 3 entries <4, 2.3, - nb2L is the number of landmarks at two hops from node i.
10; 5, 1.1, 12 ; 6, 3.2, 10>; and (2) TL with one entry < 5, - nbL is the number of landmarks at one hop (immediate
(850,200), 12, 5> . The information in TL means that the node neighbors for node i).
5 is a Landmark and it is one hop away from node I (3). The - TL table is a landmarks table
message POSITION will include two A2L fields: - TN table is a neighbors table
A2L4 = <5, 4, (850, 200), 12, 1.2) Functions:
- Receive (POSITION): it is used to check the A2L fields in the
A2L6 = <5, 6, (850, 200), 12, 2.1) message POSITION which are intended for node I and updates the
Thus, POSITION=<3, , A2L4, A2L6>. In this example, the Landmarks table (TL) that node i maintains.
field CoordS is null; this means that node 3 (I) cannot be - Positioning (TL): it is used to compute node position by
localized; it broadcasts its message POSITION to help nodes 4 applying a least-squares technique and builds message
and 6 to compute their location. POSITION.
- Broadcast (POSITION): it broadcasts the message POSITION to
the neighbors of node i.
idL Coord distance nextHop
---------------- Algorithm -----------------
Fig.5. Landmarks table structure
1 For (i є NnL){
2 Receive (POSITION);
Upon receipt of a POSITION message, a non-positioned 3 If (nb2L+nbL ≥ 3) {
node J checks whether the message contains A2L; if the 4 POSITION = Positioning(TL);
5 Broadcast (POSITION);
response is yes, it applies triangulation to compute the
6 If (localized) Sleep();}
distances towards other landmarks at two hop neighbors and
7}
updates its table TL. Node J consults its table TL to compute
its position. It must have at least three non aligned landmarks.
IV. EXPERIMENTAL RESULTS
Therefore, to compute its position, J takes into consideration
landmarks at one hop then landmarks at two hops. This In order to evaluate the performance of A2L, we developed
technique allows node J to compute its position with a better our own JAVA-based simulator. We assume that all messages
degree of accuracy by reducing errors caused by AOA broadcasted by nodes during simulation are reliably delivered
measurement. If the least-squares system is resolved, node J to their neighbors. We generate many random sensor network
becomes a landmark and notifies its neighbors by broadcasting topologies according to the number of nodes and the number
POSITION message; it may also turns off all the circuits going of landmarks; we use a square area where nodes are randomly
into sleep mode to save energy. Otherwise, it simply placed using a uniform distribution. Landmarks are selected
broadcasts POSITION messages to help other nodes to be randomly and nodes’ degrees (average number of neighbors)
localized. The coordinates (x,y) sent by node J will help are controlled by specification of their radio range. We assume
nodes at a TTL(Time To Live) bigger than 2 computing their that each node is equipped with an AVR microcontroller [13].
positions. For our simulation, we set the radio transmission power to
Let us consider the topology shown in Fig 3 to describe the 0.24mW. The simulation results represent the average of 100
execution of the proposed algorithm (Algorithm 1). Initially, executions.
A, F, D, G broadcast their messages INIT. None of the nodes We studied the effect of TTL and the landmark rate on the
B, C, and E is located after the first iteration (TTL=1). Node E rate of nodes being positioned (percentage of non landmarks
builds a message POSITION including information: angle θˆ able to resolve their positions) and the corresponding energy
consumption. Our results were compared respectively with
ˆ ˆ ˆ
(where θ = θ N − θ F ) position F(x,y) and distance dEF and APS using AOA and AHLoS. We believe that it is preferable
broadcasts it. At the same time nodes B, C, and N compute the to limit the TTL value to 2 for better accuracy localization as
angles to Landmarks and broadcast their values with localization errors increase with TTL. However, our

5. 5
simulations covered a wide range of TTL values.
In the first set of simulations (Fig 6 and Fig 7), we consider In the third set of simulations we study the relationship
a scenario with 300 nodes and 10% of landmarks. We execute between the localization rate, the amount of landmarks
A2L and APS algorithms for various values of TTL (from 1 to required and the average node degree.
10) and various node degrees (4.2, 6.14, 10.27) With TTL Fig. 9 shows that A2L, for a 200-nodes network (average
value equal to 1; only the nodes with at least three landmarks node degree is equal to 5.36), uses only 15% of landmarks to
can apply a trilateration technique to compute theirs positions. localize 98% of the network’s nodes. These results show the
With a TTL value equal to 6, A2L improves, compared to superiority of A2L over AHLoS [12] ,which requires an
APS, the localization rate by 16%, in the case the node degree average node degree equal to 6.28 to localize 90% of the
is equal to 4.6, and by 21%, in the case the node degree is nodes with 45% of landmarks.
equal to 6.14.. In the case of a large node degree, such as
10.27, A2L locates 12% (resp. 3%) more than APS with TTL
equal to 2 (resp. 6). Further the localization improvement, A2L
converges faster than APS; indeed, ,A2L locates all the nodes
with TTL value equal to 6 while APS requires TTL value
equal to 7 (Figs. 6-7).. The force of A2L is laid in the angles
that a node forms with its neighbors and a distant landmark.
Knowing these angles, even if a node doesn’t have any
immediate landmark neighbor, it can use its two-hop landmark
neighbors and apply trilateration to compute its position; this Fig 9. Required Landmarks for localization in networks with different sizes in
is not the case for APS. Hence, A2L is more efficient than as square area 100x100
APS in uniform topologies with small or large node degree.
In the fourth set of simulations, we study the relationship
between the amount of traffic generated - during the
A2L_4,2 A2L_6,14 A2L_10,27 APS_4,2 APS_6,14 APS_10,27
localization process - by the network nodes and other
1
00 100
80
attributes, of interest, including network size, energy, etc.
Coverage (%)
80
Coverage (%)
60 60 Fig. 10 shows the variation of the average number of
40 40
transmitted bytes for each network size; the number of
20 20
0 0
transmitted bytes is computed by summing the sizes of all
0 1 2 3 4 5 6 7 8 9 1
0 0 1 2 3 4 5 6 7 8 9 10
TTL TTL
INIT and POSITION messages generated/broadcasted by
landmarks and non landmarks to locate the maximum number
Fig 6. A2L Coverage in different node Fig 7. APS Coverage in different node of nodes. Fig. 11 shows the corresponding energy
degree (4.2, 6.14, 10.27) degree (4.2, 6.14, 10.27)
consumption; the transmission power of the network’s
In the second set of simulations, we set the TTL value to 2 (Medusa) nodes is set to 0.24mW.
and vary the landmarks rate in a 300-nodes topology. The Fig. 12 shows the variation of the amount of traffic
radius is set to 14. In this scenario, the average node degree is generated during the localization process with the percentage
6.14. Fig. 8 shows that A2L requires only 45% of landmarks of landmarks in the network. The Figure shows that the
(i.e., 45% of the network nodes are landmarks) to locate 63% number of transmitted bytes is inversely proportional to the
of non-localized nodes, whereas APS requires more than 70% number of Landmarks. This can be easily explained by the fact
of landmarks to achieve the same goal. APS’s problem is that that increasing the number of landmarks in the network speeds
it requires that each node should to form a quadrilateral with up the convergence with smaller values of TTL. Indeed, in this
two neighbors and a landmark. This situation usually occurs in case, most of the exchanged messages are of type INIT (rather
networks with high node degree. We conclude that A2L than POSITION) that has far smaller size than POSITION.
requires fewer landmarks than APS (using AOA) to locate the
10% 20% 10% 20%
same amount of nodes.
60 1
0,9
50
Energy per node (µj)
Bytes Transmitted
0,8
A 2L APS
0,7
(thousand)
40
0,6
100 30 0,5
0,4
80 20
o ea e %
Cv r g ( )
0,3
60 10 0,2
0,1
40 0 0
50 100 150 200 250 300 50 100 150 200 250 300
20
Network Size Network Size
0
10 15 20 25 30 35 40 45 50 55 60 65 70
Landmarks (%)
Fig.10 Traffic Vs size with 10% and Fig.11 Average energy Vs network
20% Landmarks size with 10% and 20% Landmarks
Fig 8. localized nodes rate Vs landmarks in 300 nodes network
Fig. 13 shows the variation of the amount of traffic

6. 6
generated during the localization process with the value of APS_using AoA APS_using DvDistance A2L
TTL and the percentage of localized nodes; the results are as 120
expected. For smaller values of TTL, the amount of generated 100
traffic is smaller but the percentage of localized nodes is 80
Nodes (%)
smaller too. For bigger TTL values, the amount of generated 60
traffic is bigger and the percentage of localized nodes is bigger 40
as well. 20
0
0 10 20 30 40 50 60 70 80 90 100
Bytes Transmitted Localized nodes 30
Position Error (% of the range)
Bytes Transmitted (thousand)
30 120 25
Fig. 14 Accuracy measurement in 100 nodes networks
Bytes Transmitted
Percent of Localized
25 100 20
(thousand)
20 80
15
Nodes
15 60
10 40
10
V. CONCLUSION
5
5 20
0 0 0
10 20 30 40 50 60 70 80 90
In this paper, we propose a new algorithm, called A2L, to
1 2 3 4 5 6 7 8 9
TTL
Percent of initial landmarks
locate a large number of nodes in wireless sensor networks
where only a subset of them is composed of landmarks. A2L
Fig. 13 Traffic Vs TTL Vs localized Fig 12 Traffic Vs Landmarks in 200-
nodes in 200-nodes network with nodes network makes use of landmarks coordinates and AOA to compute the
10% Landmarks distance from a node to a landmark at a maximum of 2 hops
away. Then, it uses trilateration to compute the node’s position
In the five set of simulations, like in [2, 10], a Gaussian in the case it knows at least 3 landmarks are 1 or 2 hops away
distribution error (with standard deviation as a parameter) is from it.
applied to AOA and a normal distribution error (with standard Simulations showed that A2L algorithm is more effective; it
deviation and the radio range as parameters) is applied to converges faster and locates more nodes. Compared to existing
distance measurement. Errors are normalised using the “real” techniques, such as APS and AHLoS, A2L considerably
positions of the nodes and the radio range (i.e., increases the number of located nodes with better precision
error=[Euclidian distance between the estimated position and while using a smaller node degree and fewer landmarks
the “real” position]/(radio range)). Currently, we are finalizing our study of positioning errors
Since A2L uses a Least-Squares technique, we need to introduced by A2L and techniques to minimize them.
control the consistency of the resolution of the equations (4).
Thus, we compute the residue [16]: ACKNOWLEDGMENT
∑
n 2 2
i =1
ˆ ˆ
(xi - x) + ( yi − y ) − di We would like to thank Dragos Niculescu and Badri Nath
Residue = for providing us APS code.
n
ˆ ˆ
Where ( x, y ) is the position estimate.. A large residue
REFERENCES
means that the set of equations used in the least-square is
[1] Tian He, Chengdu Huang, Brian M. Blum, John A. Stankovic,and Tarek
inconsistent. For achieving a high accuracy, we use a small Abdelzaher. Range-free localization and its impact on large scale sensor
threshold (i.e., if the residue exceeds the threshold, the networks. IEEE Personal Communications Magazine, 2005
position estimate is rejected) and we increase the TTL value. [2] Dragos Niculescu and Badri Nath. Dv based positioning in ad hoc
networks. Journal of Telecommunication Systems, 2003
We consider a network of 100 nodes in square area of [3] Nirupama Bulusu, John Heidemann, and Deborah Estrin. Gps-less low
100x100; we set, the value of the Gaussian distribution cost outdoor localization for very small devices. IEEE Personal
parameter to 5%, the values of the Normal distribution to 5% Communications Magazine, 2000
[4] B. Parkinson et al. Global positioning system: Theory and application.
and, 14 and the rate of landmarks to 10%. A2L presents a Progress in Astronomics and Aeronotics, volume I, 1996
very good performance compared to APS (Fig. 14). A2L [5] Jeffrey Hightower and Gaetano Borriello. Location systems for
makes it possible to locate up to 75% of the nodes with 10% ubiquitous computing. IEEE Computer 34(8) pp. 57-66, August 2001.
[6] Paramvir Bahl and Venkata N. Padmanabhan. Radar: An in-building rf-
position error contrary to APS which locates 36% using DV- based user location and tracking system. in: INFOCOM 2000 pp.775-
Distance [2] technique and 8% using AOA technique. A2L 784, 2000.
locates 99% of the nodes with a position error lower than 20%. [7] Nissanka B. Priyantha, Anit Chakraborty, and Hari Balakrishnan. The
APS, using DV-Distance, locates 99% of nodes but with a cricket location-support system. International Conference on Mobile
Computing and Networking, Boston, 2000.
position error of 40% which may be not acceptable for a [8] Nirupama Bulusu, John Heidemann, and Deborah Estrin. Adaptative
number of applications. Thus, A2L is definitively more precise beacon placement. The Twenty First International Conference on
than APS. Distributed Computing Systems, Phoenix, 2001.
[9] Srdan Capkun, Maher Hamdi, and Jean-Pierre Hubaux. Gps-free
More details about the techniques we used and more positioning in mobile ad-hoc networks. in Proceedings of the 34th
simulations results will be published in another paper. Hawaii International Conference on System Sciences, 2001.
[10] D. Niculescu and B. Nath, Ad hoc positioning system (APS) using AoA,
In Proceedings of the 20st Annual Joint Conference of the IEEE
Computer and Communications Societies (INFOCOM-22), April 2003.

7. 7
[11] Savvides A., Han C., Strivastava B., « Dynamic Fine-Grained
Localization in Ad-Hoc Networks of Sensors », rapport, 2000,
Department of Electrical Engineering.
[12] E. K. Wesel, Wireless Multimedia Communications: Networking
Video, Voice and Data. Addition-Wesley, One Jacob Way, Reading
Massachusetts 01867 USA, 1998.
[13] http://nesl.ee.ucla.edu/projects/ahlos/hardware.htm
[14] A. Basu, J. Gao, J. Mitchell, G. Sabhnani, Distributed Localization
Using Noisy Distance and Angle Information, 7th ACM International
Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc),
2006
[15] Ahmed, A.A. Hongchi Shi Yi Shang, A New Hybrid Wireless Sensor
Network Localization System, 2006 ACS/IEEE International
Conference on Pervasive Services June 2006
[16] K. Langendoen and N. Reijers. Distributed localization in wireless
networks: A quantitative comparison. Computer Networks, no 43, pp.
500-518, 2003