Global Positioning System Reference
In-Depth Information
f
D
α
max
α
mean
Doppler-induced code-phase
(kHz) (dB)
(dB)
estimation error (chips)
-5
0.01
14.18
1.683
-2.5
2.66
18.88
0.830
0
12.77 22.48
0
2.5
2.22
18.93
-0.839
5
0.19
14.47
-1.838
=
Table 1. Peak-to-floor ratios and Doppler effect on estimated code phase,
C
/
N
0
24 dB-Hz
and
T
int
=
1s.
During the acquisition phase, if the local code is generated at the nominal chip rate
R
c
, the
correlation between local and received codes suffers a loss due to the difference with the true
received chip rate
R
c
. Furthermore, such a loss increases with the integration times. A loss
of about 8 dB in
α
mean
can be estimated at
C
/
N
0
=
=
1 s). Table 1 shows the
degradation of the correlation peak and the code-phase estimation error.
24 dB-Hz (
T
int
3.3.3 Local oscillator stability
The uncertainty on the nominal value
f
LO
of the LO frequency is usually expressed as
fractional frequency deviation (Audoin & Guinot, 2001):
)=
)
f
LO
=
(
(
)
−
)
f
LO
−
(
f
t
f
t
f
LO
f
t
y
LO
(
=
t
1
(29)
f
LO
where
f
is the true instant frequency.
y
LO
is affected by environmental conditions (e.g.
temperature, pressure), dynamic stress (e.g. acceleration, jerk, etc.), circuital tolerances, etc.
The time deviation (i.e. the time difference between the clock with the true oscillator and an
ideal clock), is given by:
(
t
)
t
(
)=
(
)
x
LO
t
y
LO
u
du
(30)
−
∞
With the zero-th order expansion
y
LO
(
t
)=
y
0
+
..., (
y
0
is a constant frequency offset), the time
deviation results:
x
LO
(
)=
+
·
t
(31)
where
x
0
is an initial synchronization error between real and ideal clocks and
t
is the time
elapsed since the initial synchronization epoch. This model can be used to evaluate the effect
of the local oscillator accuracy on both the down-conversion and the sampling stages.
t
x
0
y
0
During the down-conversion the true mixing signal (used in (25)) is:
2 cos
[
2
π
(
f
RF
−
f
IF
)(
1
+
y
0
t
)]
(32)
The true IF carrier is actually affected by an additional unpredictable shift, that prevents the
exact carrier frequency estimation, even with very accurate Doppler aiding information. By
means of (31) we can evaluate the impact of the LO on the sampling process. With the true
Search WWH ::
Custom Search