Image Processing Reference
In-Depth Information
In the end, the localization process is important for network protocols. Sensor networks with-
out position information are difficult to organize and waste valuable energy for, e.g., neighborhood
discovery tasks.
Intuitively, every sensor node is equipped with an available positioning system like the global
positioning system (GPS) as described in addition to in Section ... ...The resource requirements of
these localization systems, e.g., energy consumption, size, or price, are in contradiction to the limited
resources in sensor networks. Hence, positioning systems are not applicable on every sensor node.
As an alternative, positions can be estimated relative to a randomly chosen sensor node using a
Cartesian coordinate system (Section ..). Unfortunately, the localization error accumulates with
an increasing distance to that sensor node. A subsequent conversion to absolute coordinates requires
additional computation overhead.
The second alternative dominating the literature uses a small number of sensor nodes equipped
with a positioning system. Depending on the literature these nodes are called landmarks, anchors,
reference nodes, or beacons. In the following, they are defined as beacons abbreviated with
B
i
.On
basis of absolute distances or angles to these beacons and their positions, any sensor node
S
i
is able
to estimate its own position with an adequate localization algorithm.
Since centuries, efficient and well-deined mathematical methods have been known to estimate an
unknown position with at least three beacon positions and distances to them (Section .).
. Triangulation assumes exact angle measurements. However, measuring angles is difficult
in sensor nodes, due to the additional hardware overhead (Section ..).
. More adequate in sensor networks is trilateration which requires exact distance measure-
ments. Otherwise, imprecise distance measurements strongly degrade the precision of the
trilateration. This can lead from erroneous to completely useless results and makes this
techniqueunreliableandthusunfavorableforsensornetworks.
. Increasing the trilateration process by more input data, respectively more beacon posi-
tions with distance information, reduces the localization error significantly. Particularly,
stochastic errors are decreased. Further, outliers can be detected and, thus, eliminated.
As sensor networks consist of many nodes, this approach seems to be well suited. Never-
theless, an increasing amount of input data leads to a higher complexity and thus to high
resource demands.
6.2 Distance Estimation
Localization requires information about the interrelation between a node and its environment. his
information may comprise knowledge about neighboring nodes, connectivity metrics, positions of
reference nodes, the gradient and rotation of the node, and other data. Most localization algorithms
require distances between nodes and beacons in a Cartesian coordinate system.
Usually, distances cannot be measured directly. herefore, a lot of methods have been developed
to determine a distance out of other conditions. They can be divided at least into three different
typesofmethods(Figure.).Inthefollowing,themostcommonmethodstoestimateadistanceare
described.
6.2.1 Time of Arrival
In vacuum, a transmitted radio signal of an isotropic source propagates circularly with the speed
of light at
c
Vacuum
=
, km
/
s. In matter, the speed decreases significantly due to the mate-
rial properties permittivity
e
=
e
⋅
e
r
and permeability µ
=
µ
⋅
µ
r
.Inair,thespeedoflightequals
