Global Positioning System Reference
In-Depth Information
where k i =
x i +
y i . Equation 4 can be expressed in a matrix form
Hx = b
(5)
k 2
d 2 +
d 1
x 2 y 2
x 3 y 3
. .
x n y n
x m
y m
, and
k 3
d 3 +
d 1
1
2
H =
x =
b =
where
,
.
.
k n
d n +
d 1
Equation 5 represents an overdetermined system (i.e., n
2). Practically, such a system has
no exact solution. Therefore a linear least squares method is used to estimate the location of
the MS as follows:
>
1
T
T
ˆ
x =
H
H
H
b
(6)
) 1
T signifies matrix transpose and
where
(
.
)
(
.
signifies matrix inverse.
Alternative techniques, such as the maximum likelihood are reported in McGuire et al. (2003);
Wang et al. (2003).
4.1.2 TDOA data fusion
TDOA is preferable to the TOA due to the fact that TDOA does not require synchronization
between the MS and BS's, Figure 2. Instead, it takes advantage of the synchronization of the
CDMA cellular network BS's to compute the difference between the time of arrivals of the MS
MS
(x m ,y m )
d 21 =c(t 2 -t 1 )
BS 2
(x 2 ,y 2 )
d 1 =ct 1
BS 1
(x 1 ,y 1 )
d 31 =c(t 3 -t 1 )
BS 3
(x 3 ,y 3 )
Fig. 2. The TDOA localization method.
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