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devices whose location is known (reference devices). Distances can be
estimated by means of several approaches [3].
Time-of-flight method estimates the distance between a moving object
and a fixed point by measuring the time a signal takes to travel between
the object and point P at a known speed. This method requires accurate
clocks, especially for radio frequency (RF) signals. In this case, a 1-┬Ás error
in timing leads to a 300-m error in distance estimation.
The attenuation approach takes into account the fact that the intensity of an
emitted RF signal decreases as the distance from the emission source increases.
Given the signal strength at the emission, it is possible to estimate the distance
from an object to some point P by measuring the signal strength at the point P .
Of course, a function correlating attenuation and distance is needed.
Once distance has been estimated, the positioning task is mainly
accomplished by the triangulation method. With this method, the position of an
object is obtained by measuring its distance from multiple reference positions.
2D triangulation algorithm requires three different measurements from three
non-collinear points, and the mobile device is located at the intersection of
three circles (Figure 1). 3D positioning requires distance estimation from four
non-coplanar points. For example, a global positioning system (GPS) receiver
needs at least four satellites for 3D position estimation.
In the case of RF signal attenuation method, the circles' radius is
evaluated on the measured strength of received signals, exploiting the
relationship between signal strength and distance. RF signals are affected by
a high degree of uncertainty (and consequently estimated distances too), and
actually measured RF signal strength define a cloud-shaped region around the
base station (Figure 2).
Figure 1: 2D positioning by triangulation.
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