Global Positioning System Reference
In-Depth Information
speed, one can calculate the maximum Doppler velocity
v
dm
, which is along the
horizontal direction as
v
s
r
e
r
s
3874
6368
26560
×
v
dm
=
=
≈
929 m/s
≈
2078 miles/h
(
3
.
9
)
This speed is equivalent to a high-speed military aircraft. The Doppler fre-
quency shift caused by a land vehicle is often very small, even if the motion
is directly toward the satellite to produce the highest Doppler effect. For the
L
1
frequency (
f
1575
.
42 MHz), which is modulated by the C/A signal, the
maximum Doppler frequency shift is
=
f
r
v
dm
c
1575
.
42
929
3
×
10
8
×
f
dr
=
=
≈
4
.
9kHz
(
3
.
10
)
where
c
is the speed of light. Therefore, for a stationary observer, the maximum
Doppler frequency shift is around
±
5kHz.
If a vehicle carrying a GPS receiver moves at a high speed, the Doppler effect
must be taken into consideration. To create a Doppler frequency shift of
5kHz
by the vehicle alone, the vehicle must move toward the satellite at about 2,078
miles/hr. This speed will include most high-speed aircraft. Therefore, in designing
a GPS receiver, if the receiver is used for a low-speed vehicle, the Doppler shift
can be considered as
±
5 kHz. If the receiver is used in a high-speed vehicle, it is
reasonable to assume that the maximum Doppler shift is
±
10 kHz. These values
determine the searching frequency range in the acquisition program. Both of
these values are assumed an ideal oscillator and sampling frequency and further
discussion is included in Section 6.15.
The Doppler frequency shift on the C/A code is quite small because of the low
frequency of the C/A code. The C/A code has a frequency of 1.023 MHz, which
is 1,540 (1575.42/1.023) times lower than the carrier frequency. The Doppler
frequency is
±
1
.
023
×
10
6
f
c
v
h
c
×
929
3
×
10
8
f
dc
=
=
≈
3
.
2Hz
(
3
.
11
)
If the receiver moves at high speed, this value can be doubled to 6.4 Hz. This
value is important for the tracking method (called block adjustment of synchroniz-
ing signal or BASS program), which will be discussed in Chapter 8. In the BASS
program, the input data and the locally generated data must be closely aligned.
The Doppler frequency on the C/A code can cause misalignment between the
input and the locally generated codes.
If the data is sampled at 5 MHz (referred to as the sampling frequency), each
sample is separated by 200 ns (referred to as the sampling time). In the tracking
program it is desirable to align the locally generated signal and the input signal
within half the sampling time or approximately 100 ns. Larger separation of
these two signals will lose tracking sensitivity. The chip time of the C/A code
is 977.5 ns or 1/(1
.
023
×
10
6
) sec. It takes 156.3 ms (1/6.4) to shift one cycle
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