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Fig. 1.
Triangulation illustration with one, two, and three access points.
property enables us to infer the distance from an access point by considering
the loss of signal strength. By calculating the distance to two or more access
points triangulation can be used to determine user location [7]. This can be
geometrically represented as rings centered at each access point (Fig. 1). Using
the signal propagation model a device with a given signal strength can assume,
under ideal conditions, that it is a proportional distance from the access point.
This effectively places the device in a range of points formed by a circle centered
on the access point as shown in Fig. 1. If the device can be detected by two
access points then the possible locations can be reduced to the points at which
the two circles centered on the access points intersect. With the addition of three
access points the location can be determined to a single point, by calculating
where the three circles intersect.
The propagation model can best be understood by assuming an ideal radio-
frequency (RF) signal without any interference. Figure 2 represents a large open
area with three fixed access points (A, B and C). This area is assumed to exist
on a flat plane. The device shown in the figure is able to detect signals from all
three of the access points. The signal strength
2
to access point A is 5mW, to
access point B is 1mW, and to access point C is 0.23mW. Assuming all of the
access points are sending a 100mW signal we can calculate the distance of the
devices using the ideal propagation formula as shown.
sig
orig
sig
AP
AccessP oint
distance
=
(1)
A
distance
=
100
mW
5
mW
=4
.
47
B
distance
=
100
mW
1
mW
=10
C
distance
=
100
mW
0
.
23
mW
=20
.
85
2
Signal strengths are traditionally represented in dBm a logarithmic value based on
the mW. The following formula defines the relationship dBm = log(mW)
∗
10.
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