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GPS-free positioning in mobile ad hoc networks .pdf

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本文讲述了传感器网络中,传感器节点在没有GPS支持的情况下,节点间自发明确各自在网络中的位置,在WSN定位方面有兴趣的朋友,可以看看,应该会有所收获的。
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Preprint 0 (2001) ?{? 1
GPS-free p ositioning in mobile ad ho c networks
Srdjan
Capkun, Maher Hamdi, Jean-Pierre Hubaux
Institute for computer Communication and Applications (ICA)
Communication Systems Department (DSC)
Swiss Federal Institute of Technology Lausanne (EPFL)
CH-1015 Lausanne, Switzerland
(srdan.capkun, maher.hamdi, jean-pierre.hubaux)@ep.ch
We consider the problem of node positioning in ad hoc networks. We prop ose a distributed, infrastructure-
free positioning algorithm that does not rely on GPS (Global Positioning System). Instead, the algorithm uses
the distances between the nodes to build a relative coordinate system in which the no de positions are computed
in two dimensions. Despite the distance measurement errors and the motion of the no des, the algorithm provides
sucient location information and accuracy to support basic network functions. Examples of applications where
this algorithm can be used include Location Aided Routing 8] and Geodesic Packet Forwarding 7]. Another
example are sensor networks, where mobility is less of a problem. The main contribution of this work is to
dene and compute relative positions of the nodes in an ad ho c network without using GPS. We further explain
how the prop osed approach can be applied to wide area ad ho c networks.
Keywords:
ad ho c, mobile, distributed, wireless networks, p ersonal communication system, self-locating,
radio-location, GPS-free, self-organization.
1. Intro duction
The presented work is a part of the Termin-
ode pro ject, a 10 year ongoing pro ject that in-
vestigates large area, wireless, mobile ad ho c net-
works 1,19,20]. The main design points of the
pro ject are to eliminate any infrastructure and
to build a decentralized, self-organized and scal-
able network where no des perform all networking
functions (traditionally implemented in backbone
switches/routers and servers).
In this pap er, we describ e an algorithm for the
p ositioning of no des in an ad ho c network that do es
not use GPS. The algorithm provides a p osition
information to the nodes in the scenarios where an
infrastructure do es not exist and GPS cannot be
used. GPS-free p ositioning is also desirable, when
the GPS signal is to o weak (e.g., indoor), when it is
jammed, or when a GPS receiver has to b e avoided
for cost or integration reasons.
We intro duce a distributed algorithm that en-
ables the no des to nd their p ositions within the
network area using only their lo cal information.
The algorithm is referred to as the Self-Positioning
Algorithm (SPA). It uses range measurements b e-
tween the no des to build a Network Co ordinate
System (Fig 1.). The Time of Arrival (TOA)
metho d is used to obtain the range between two
mobile devices.
Despite the distance measurement errors and
the motion of the no des, the algorithm provides
sucient lo cation information and accuracy to sup-
p ort basic network functions. Examples of applica-
tions where this algorithm can b e used include Lo-
cation Aided Routing 8] and Geo desic Packet For-
warding 7], both in ad hoc and sensor networks.
In the Geo desic Packet Forwarding algorithm, the
source sends packets in the physical direction of the
destination no de. Given that the no de knows its
p osition and the p ositions of the destination no de
in the relative co ordinate system, it is able to com-

2
Capkun, Hamdi, Hubaux / GPS-freepositioning in mobile ad hoc networks
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)
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,
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.
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)
Figure 1. The algorithm uses the distances between the
nodes and builds the relative coordinate system.
pute in which direction (to which next hop no de)
to send packets.
The no des in the ad ho c networks are usually
not aware of their geographical p ositions. As GPS
is not used in our algorithm, we provide relative
p ositions of the nodes with resp ect to the network
top ology.
For the sake of simplicity, we present the algo-
rithm in two dimensions, but it can be easily ex-
tended to provide p osition information in three di-
mensions.
The paper is organized as follows. In section
2 related work in the eld of radio-lo cation tech-
niques is describ ed. In section 3 we present the
algorithm for building a Lo cal Co ordinate System
at each no de. In section 4 we describ e the means
to dene the center and the direction of the Net-
work Co ordinate System. In section 5 we discuss
the inuence of the range errors on the accuracy of
the p osition estimation. We present the simulation
results in section 6.
2. Related work
Following the release of US FCC regulations for
lo cating E911 callers, p ositioning services in mo-
bile systems have drawn much attention recently.
The new regulations intro duce stringent demands
on the accuracy of mobile phone location. The
FCC requires that by Octob er 2001, the wireless
op erators lo cate the p osition of emergency callers
with a ro ot mean square error b elow 125m 9].
Several radio-location metho ds are prop osed for
lo cating the Mobile Stations (MSs) in cellular sys-
tems 2]: the Signal Strength method, the Angle of
Arrival (AOA) metho d, the Time of Arrival (TOA)
and Time Dierence of Arrival (TDOA) metho ds.
The Time of Arrival and Signal Strength metho ds
use range measurements from the mobile device to
several base stations to obtain its p osition. Thus,
the accuracy of the estimated p osition depends on
the accuracy of the range measurements. Distance
measurements are corrupted bytwotyp es of errors:
Non-Line of Sight (NLOS) error and measuring er-
ror. The measurements in cellular systems, taken
by Nokia 3], show that NLOS error dominates the
standard measurement noise, and tends to be the
main cause of the error in range estimation. They
also show that the lo cation estimation error lin-
early increases with the distance error. Following
these measurements, Wylie and Holtzman prop ose
a metho d for the detection and correction of NLOS
errors 5]. They show that it is p ossible to de-
tect a NLOS environment by using the standard
deviation of the measurement noise and the his-
tory of the range measurements. They prop ose a
metho d for LOS reconstruction and they showthat
the correction is only p ossible if the standard mea-
surement noise dominates the NLOS error. A dif-
ferent approach is presented in 4] by Chen. Chen
shows that if the NLOS measurements are unrec-
ognizable, it is still p ossible to correct the lo cation
estimation errors, if the numb er of range measure-
ments is greater than the minimum required. The
algorithm is referred to as the Residual Weighing
Algorithm (Rwgh).
In 6] Rose and Yates give a theoretical frame-
work of the mobility and lo cation tracking in mo-
bile systems. They present a study of mobility
tracking based on user/service/host location prob-
ability distribution.
A signicant amountofwork has b een rep orted
considering context-aware computer systems. In
these systems, mobile computers automatically
congure themselves based on what was happ en-

Capkun, Hamdi, Hubaux / GPS-freepositioning in mobile ad hoc networks
3
ing in the environment around them. Examples
of these systems include Active Badge 14] and
RADAR 15].
Recently, some p osition-based routing and packet
forwarding algorithms for the ad ho c networks have
been prop osed in 7,8,16{18]. In all these algo-
rithms it is assumed that the p ositions of the no des
are obtained through GPS.
To the b est of our knowledge, no algorithms have
b een prop osed for p ositioning of the nodes without
GPS in ad ho c networks.
3. Lo cal Co ordinate System
Wemake the following assumptions on our sys-
tem mo del:
the observed network is an infrastructure-
free network of mobile and wireless devices
all the devices (no des) have the same tech-
nical characteristics
all the wireless links between the nodes are
bidirectional
the no des use omnidirectional antennae
the maximum sp eed of the movement of
no des is limited to 20 m/s
In this section we show how every no de builds
its Lo cal Co ordinate System. The node becomes
the center of its own co ordinate system with the
p osition (0
0) and the positions of its neighbors
are computed accordingly. In section 4 we further
showhow the agreement on a common co ordinate
system (Network Co ordinate System) center and
direction is achieved.
If a node
j
can communicate directly (in one
hop) with no de
i
,
j
is called a one-hop neighbor
of
i
. Let
N
b e the set of all the no des in the net-
work.
8
i
2
N
, we dene
K
i
as the set of one-hop
neighb ors of
i
. Likewise,
8
i
2
N
, we dene
D
i
, as
a set of distances between
i
and eachnode
j
2
K
i
.
The neighbors can be detected by using b eacons.
After the absence of a certain numb er of successive
b eacons, it is concluded that the no de is no longer
a neighb or. The distances between the no des are
measured by some means, e.g. the Time of Arrival
metho d.
The following procedure is performed at every
no de
i
:
detect one-hop neighbors (
K
i
)
measure the distances to one-hop neighbors
(
D
i
)
send the
K
i
and
D
i
to all one-hop neighb ors
Thus, every no de knows its two-hop neighbors and
some of the distances b etween its one-hop and two-
hop neighb ors. A number of distances cannot be
obtained due to the p ower range limitations or the
obstacles between the no des. Fig. 2 shows no de
i
and its one-hop neighbors. Continuous lines repre-
sent the known distances between the no des, while
dashed lines represent the distances that cannot be
obtained.
By cho osing two no des
p q
2
K
i
such that the
distance b etween
p
and
q
(
d
pq
)isknown and larger
than zero and such that the no des
i p
and
q
do
not lie on the same line, no de
i
denes its Local
Co ordinate System. The latter is dened suchthat
no de
p
lies on the p ositive x axis of the coordinate
system and no de
q
has a positive
q
y
comp onent.
In this way, the Lo cal Co ordinate System of
i
is
uniquely dened as a function of
i p
and
q
.
Thus, the co ordinates of the no des
i
,
p
and
q
are:
i
x
=0
i
y
=0
p
x
=
d
ip
p
y
=0
q
x
=
d
iq
cos
q
y
=
d
iq
sin
(1)
where
is the angle
6
(
p i q
) and it is obtained by
using a cosines rule for triangles:
= arccos
d
2
iq
+
d
2
ip
;
d
2
pq
2
d
iq
d
ip
(2)
The positions of the no des
j
2
K
i
,
j
6
=
p q
, for
which the distances
d
ij
d
qj
andd
pj
are known, are
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- 活宝贝熊猫2012-09-20很久以前下的,东西都做完了,很有用

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