Image Processing Reference
In-Depth Information
Theoretical PIT
Outside
Inside
(b)
Practical PIT
Triangle surface
Outside
Inside
(a)
(c)
FIGURE .
(a) Overlapping of triangles are basis of APIT, (b) theoretical PIT test with distances and a moveable
sensor node, and (c) practical PIT test with neighbors and RSSI values. (From Reichenbach, F., Born, A., Bill, R., and
Timmermann, D., Lokalisierung in Ad Hoc Geosensornetzwerken mittels geodatischer Ausgleichungstechnik,
GIS:
Zeitschrift für Geo Informationssysteme
,ABCVerlagGmbH,Heidelberg,Germany,,pp.-.Withpermission;
Reichenbach, F., Resource aware algorithms for exact localization in wireless sensor networks, PhD thesis, University
of Rostock, Rostock, Germany, December . With permission.)
node checks if all four neighboring RSSI are higher or lower simultaneously. This is similar to the
theoretical PIT test and avoids absolute distances as well as moving capabilities.
6.3.5.5 Bounding Box Algorithm
The bounding box algorithm was published in [SS] and is also based upon beacons. In this al-
gorithm, beacons transmit their position with a specific transmission power, respectively within a
well-defined transmission range
r
. Next, sensor nodes receive beacon packets and determine dis-
tances to beacons by one of the measurement techniques described in Section .. ..Then, each sensor
node calculates a quadratic surface
A
i
including every
B
i
is the
middle of the square (Figure .a). By comparing the minimal and maximal coordinates (Equation
.) of all resulting squares
A
i
, sensor nodes narrow down the surface on which they are placed.
This remaining square
A
S
is called bounding box (Figure .b). hese rough position estimates can
laterbeusedforiterativeapproaches.
=(
d
ij
)
(
x
i
;
y
i
)
,where
B
i
(
x
i
;
y
i
)
x
min
=
max
(
x
i
−
d
ij
)≤
x
j
≤
min
(
x
i
−
d
ij
)=
x
max
(.)
y
min
=
max
(
y
i
−
d
ij
)≤
y
j
≤
min
(
y
i
−
d
ij
)=
y
max
A disadvantage of the bounding box algorithm is that a small localization error can only be
achieved if
S
j
is placed within a convex, by beacons limited, hull
A
S
. Otherwise, the bounding box,
and therefore the localization error, increases as shown in Figure .c. Moreover, the algorithm
behaves instable if distance measurements are very noisy, because probably overlapping surfaces are
missed.
