Image Processing Reference
In-Depth Information
B
4
(
x
4
;
y
4
)
B
3
(
x
3
;
y
3
)
d
3
d
4
Centroid
~
~~
S
(
x
;
y
)
S
(
x
;
y
)
d
1
d
2
~
~~
Weighted centroid
S
(
x
;
y
)
B
1
(
x
1
;
y
1
)
B
2
(
x
2
;
y
2
)
FIGURE .
WCL compared to CL. (From Reichenbach, F., Resource aware algorithms for exact localization in
wireless sensor networks, PhD thesis, University of Rostock, Rostock, Germany, December . With permission.)
This implies calculating the position at every sensor node by a weighted centroid determination:
n
(
w
ij
⋅
B
j
)
j
=
S
i
(
x
i
;
y
i
)=
(.)
n
w
ij
j
=
In Equation ., the parameter
w
ij
represents the weight between sensor node
i
and beacon
j
.
To achieve the above-mentioned characteristics, the weight can be calculated by the inverse of the
distance.
d
ij
w
ij
(
d
ij
)=
(.)
In Equation ., a new parameter was introduced—the degree
g
,whichampliiesshorter
distances to beacons.
Simulation results illustrated in Figure . show the localization error with several minima
depending on the ratio between transmission range and degree. In terms of minimal energy con-
sumption, all sensor nodes can estimate a position if
r
is greater than
r
min
=
.
q
using a weight
function
w
.
q
(critical area) not all sensor nodes are able to estimate a posi-
tion, because not enough beacons are in range. However, if high precision instead of minimal energy
consumption is demanded, then the optimum exists at
r
opt
=
/
d
.If
r
<
r
min
=
=
.
q
, because there, the smallest
localization error is achieved. Although a degree of
g
yields in the best results, it is highly
fluctuating and thus critical to apply. Higher degrees are more stable, which may be better in practice.
In conclusion, WCL is very resource aware, because every beacon sends only one short packet.
Further on, a sensor node must receive
n
packets, measures the distance and executes a calculation
with a time complexity of
=
O(
n
−
)
.
