Global Positioning System Reference
In-Depth Information
estimate given that it shares relative spatial information with nearby nodes (e.g., other vehicles
or mobile network towers).
4.1 Radio signal measurement data fusion
Radio localization methods have been studied extensively for cellular networks in a wide
range of applications (e.g., for CDMA networks see Al-Jazzar & Caffery (2004); Caffery &
Stuber (1994; 1998); Caffery (2000); Le et al. (2003); McGuire et al. (2003); Porretta et al. (2008);
Sayed et al. (2005); Venkatraman et al. (2002); Wang et al. (2003); Wylie & Holtzman (1996)
and for GSM networks see Chen et al. (2006)). An example of these systems is a localization
system that estimates the locations of emergency calls initiated by cellular phones. The system
operates on the principle that measurements from different Base Stations (BS's) are combined
in order to compute the location of a Mobile Station (MS). The BS's typically have different
levels of uncertainty in their measurements, which are minimized as a result of the fusion
process. The relative spatial information in this system is based on the measurements from
radio signals, such as Time of Arrival (TOA), Time Difference of Arrival (TDOA), Angel
of Arrival (AOA), Received Signal Strength (RSS). In some of these GPS-less approaches, a
mix of two or more different types of radio signal measurements is utilized in order to relax
constraints such as the synchronization of the BS's.
In the following subsections detailed models for some of these techniques are given.
(
x
m
,
y
m
)
signifies the MS location. The locations of
n
base stations:
(
BS
1
,BS
2
,BS
3
,...,BS
n
)
are denoted
{
(
)
(
)
(
)
(
)
}
by
, respectively. For simplicity and without loss of
generality, locations are represented by two coordinates,
x
and
y
, in the Cartesian coordinate
system.
x
1
,
y
1
,
x
2
,
y
2
,
x
3
,
y
3
,...,
x
n
,
y
n
4.1.1 TOA data fusion
Time of arrival measurements are based on the time of flight of a signal as it travels between
a source and a destination. Since the signal travels at the speed of light
(
)
c
, it is possible to
compute the distance between the two points as follows:
d
i
=(
t
i
−
)
t
m
c
(1)
where
t
m
signifies the signal sending time from the MS,
t
i
signifies the signal arrival time at
the BS
i
, and
i
signifies the BS's index (i.e.,
i
=
{
1, 2, . . . ,
n
}
).
According to Caffery & Stuber (1998), the TOA technique can be employed using three BS's,
the minimum number of reference points in two dimensions (Figure 1), in order to estimate
the MS location by computing the distances between each BS and the MS (i.e.,
d
1
,
d
2
,
d
3
), as
per Equation 1, and then formulating the following optimization problem:
d
i
2
2
3
i
=
1
2
x
m
,
y
m
=
−
(
−
)
+ (
−
)
arg
min
x
m
,
y
m
x
i
x
m
y
i
y
m
(2)
Nevertheless, due to possible NLOS propagation conditions, the actual Euclidean distances
between the MS and the BS
i
is less than or equal to
(
t
i
−
)
c
. This inequality creates more
than one solution for the optimization problem in 2, all of which reside in a bounded area,
as shown in Figure 1. A constrained version of the optimization problem in 2 is proposed in
Caffery (1999); Porretta et al. (2008) in order to increase the localization accuracy; however, the
t
m
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