Image Processing Reference
In-Depth Information
Relative
error
r = q
f
Av
=
0.20
qf
max
=
0.48
q
2
q
2
q
A
i
0.4
q
r
0.3
q
q
q
0.2
q
0.1
q
0
0
0
0
q
2
q
0
q
2
q
FIGURE .
gridofbeacons:(a)resultingoverlapsand(b)localizationerror.(FromBlumen-
thal, J. and Timmermann, D.,
th IEEE/ACM International Conference on Distributed Computing in Sensor Systems
(DCOSS )
, pp. -, Santorini, Griechenland, June . With permission.)
Scenario with a
×
CL starts on every beacon by sending a packet including its own position and network address.
Sensor nodes within the beacon's transmission range receive corresponding packets and save its con-
tent.Attheendofthisphase,everysensornodereceived
n
packets and determines the position with
the centroid formula:
n
n
S
(
x
;
y
)=
B
j
(
x
j
;
y
j
)
(.)
j
=
If no beacon position is received, a sensor node's position cannot be estimated. Analysis in an
outdoor testbed with a quadratic sensor field of side length
a
m, four beacons at the corners
and test points resulted in an averaged localization error of
f
Av
=
=
. m with standard deviation
σ
f
Av
. m [Bul]. Additional analysis showed that the error strongly depends on the beacons
transmission range and placement [BRHT,Rei]. For that, [RBT] presents a simple equation
to determine the optimal transmission range in terms of a specific grid width. Moreover, Bulusu et
al. and Salomon suggest strategies for a better beacon placement, which also reduces the localization
error significantly [BHE,SB]. In finite sensor networks with high transmission ranges, the CL is
characterized by a very high localization error near the borderlines of the network. his error can be
reduced significantly as proposed by Blumenthal [Blu].
=
6.3.5.3 Weighted Centroid Localization
Weighted CL (WCL) is an extension of CL by including distances in form of weights in the centroid
formula. WCL was first published in [BRT] and features randomly distributed beacons opposite to
the grid alignment CL assumes.
Figure . shows a sensor node, which was localized by CL and also WCL. Four beacons are placed
at the corners of the sensor field. Whereas CL leads to a high error, WCL reduces the error, because
nearer beacons pull the sensor node's position stronger to their own position than to farer beacons.
This also works in case of noisy distance measurements. Beacons have constant and ideal concentric
transmission ranges. In a first phase, beacons send their position and network address to all sensor
nodes in range. hese nodes save this information. Contrary to CL, the distances to all beacon must
be measured by one of the techniques described in Section .. After a defined timeout, phase starts.
