Image Processing Reference
In-Depth Information
~
B
2
(
x
2
;
y
2
)
~
~
S
(
x
;
y
)
B
1
(
x
1
;
y
1
)
α
3
~
~ ~
S
(
x
;
y
)
B
3
(
x
3
;
y
3
)
α
2
α
1
B
2
(
x
2
;
y
2
)
B
1
(
x
1
;
y
1
)
(a)
(b)
FIGURE .
Localization with (a) angulation and (b) lateration. (From Reichenbach, F., Resource aware algorithms
for exact localization in wireless sensor networks, PhD thesis, University of Rostock, Rostock, Germany, December
. With permission.)
Connecting the points
S
x
;
y
leads to a triangle, where the name of
this technique comes from. Moreover, measuring the angles α
(
)
,
B
(
x
;
y
)
and
B
(
x
;
y
)
and α
allows calculating the
○
−(
remaining angle α
with α
=
α
+
α
)
.Usingthelawofsinegivestheestimatedposition
with
B
S
B
B
sin
(
α
)
,respectively,
B
S
B
B
sin
(
α
)
.
Assuming that, instead of angles, distances are known between nodes, a position can be deter-
mined via trilateration (Figure .b). A minimum of three distances
B
S
,
B
S
,
B
S
and three beacon
positions build a system of equations:
=
=
sin
(
α
)
sin
(
α
)
B
i
S
S
S
x
y
(
)
=(
B
i
(
x
i
)−
(
))
+(
B
i
(
y
i
)−
(
))
(.)
6.3.5 Proximity-Based Techniques
6.3.5.1 Nearest Beacon
Simply choosing the nearest beacon position, for example, by determining the highest received signal
strength indication (RSSI), is a possibility to solve the localization problem. Although, this can be
achieved with minimal computation effort, the localization error may be very high. Nevertheless,
the estimated position can be used as start value for iterative methods that increase the precision
[BRBT].
6.3.5.2 Coarse-Grained Localization
Centroid localization (CL) was first published by Bulusu as “GPS-less low cost outdoor localization
for very small devices” in [Bul]. The algorithm completely avoids explicit distance measure-
ments, but assumes a grid-based beacon placement with constant distances
q
between each other as
demonstrated in Figure .. To localize nodes,
b
beacons
B
(
x
;
y
)⋯
B
b
(
x
b
;
y
b
)
are aligned in a grid.
The transmission range of beacons is assumed to be circular.
