Global Positioning System Reference
In-Depth Information
1
2
T
int
Δ
f
D
=
(
)
τ
,
f
D
Δ
f
d
θ
(
)
ˆτ,
f
D
0.5 chip
Δτ
(a)
!
Estimated Doppler Shift
Estimated Code Delay
"
!
(b)
(c)
Fig. 2. (a) Acquisition search-space; (b) Auto-correlation functions of BPSK(1) and BOC(1,1);
(c) Sinc function
signal
τ
BPSK
=
0.5 chip. However, for BOC signal, due to the appearance of side-peaks,
τ
is chosen so that the tracking stage can avoid to lock to the side-peaks. For BOC(1,1), in
order to achieve the same average correlation loss as for a BPSK signal,
τ
BOC
(
1,1
)
=
0.16
2
3
T
int
chip (Wilde et al., 2006). As for Doppler shift dimension,
f
D
=
as in (Kaplan, 2005)
1
2
T
int
as in (Misra & Enge, 2006) are often chosen concerning the trade-off between
complexity and sensitivity.
f
D
=
or
2.3 Acquisition performance parameters
When dealing with real signals, the incoming code is affected by several factors such as
propagation distortion and noise, thus resulting in a distorted correlation function. In order to
achieve an optimal detection process, the Neyman-Pearson likelihood criterion is used. In fact,
the magnitude
S
m
=
|
2
of each complex correlator output can be modeled as a random
variable with statistical features. Thus,
S
m
is compared with a predetermined threshold (
V
)
in order to decide which hypothesis between
H
0
(
S
m
R
m
|
<
>
V
) is true, where
H
0
and
H
1
respectively represent the absence or presence of the desired peak. Once the decision
V
) and
H
1
(
S
m
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