Global Positioning System Reference
In-Depth Information
Then the decision variable of GDC (Fig. 6(c)) is
i
=
1
A
i
2
M
−
1
S
GDC
(36)
Note that the CDC technique is in fact the GDC taking into account span-1
A
1
only, see
Fig. 6(b). Basically, the GDC technique can be considered as a coherent integration of the
differential combinations at different sample distances. Following the analyzes in (Ta et al.,
2012), with small
M
(e.g.
M
≤
T
b
/
T
int
), in normal circumstances with normal user dynamic
and frequency standards, the average frequency drift is small and tends to zero. Therefore,
the values of
G
m
,
f
d
m
in (6) are constant for all
m
. The signal component
A
i
∈
[
0,
M
−
1
]
of
an arbitrary span-i (
A
i
) in (35) can be represented as
M
m
=
i
G
2
e
j
2
π
i
f
d
T
int
A
i
|τ
,
f
d
=
(37)
with
f
d
=
f
d
1
=
=
...
f
d
M
=
√
2
C
(38)
G
=
G
1
=
...
=
G
M
R
[
τ
]
sinc
(
f
d
T
int
)
For the GDC technique, substituting (37) into (36),
S
GDC
is computed
i
=
1
G
2
e
j
2
π
i
f
d
T
int
2
−
M
1
2
S
GDC
=
|
|
=
D
(39)
Equation (39) shows that the residual carrier phase is still present i
n t
he
d
GDC
. This fact causes
an unpredictable loss, which depends on the specific value of
f
d
. To eliminate this loss,
Modified Generalized Differential Combination (MGDC) technique (Ta et al., 2012) can be
used, see Fig. 6(d). Following this technique, the decision variable of the MGDC technique is
M
1
i
=
1
|
A
i
|
.
−
S
MGDC
=
(40)
If the noise is neglected, (40) becomes
−
M
1
i
=
1
|
A
i
|
=
|
(
M
−
1
)
G
2
e
j
2
π
f
d
T
int
G
2
e
j
4
π
f
d
T
int
2
2
S
MGDC
=
|
+
|
(
M
−
2
)
|
+
...
(41)
M
(
M
−
1
)
G
2
e
j
2
π
(
M
−
1
)
f
d
T
int
2
G
2
G
2
G
2
G
2
+
|
|
=(
M
−
1
)
+(
M
−
2
)
+
...
+
=
2
By forming the decision variable in this way, the unpredictable loss caused by the residual
carrier phase is canceled completely. However, the non-coherent integrations between all the
spans make the noise averaging process worse than for GDC.
Note: for the GDC and MGDC techniques, the number of spans involved can vary from 1 to
M
−
−
1. By default, all (
M
1) possible spans are considered as in (40). If a different number
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