Global Positioning System Reference
In-Depth Information
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TABLE 6.5
Effects of Selected Slips on the Ionospheric Phase Function
N
1
−
√
α
f
N
1
−
√
α
f
∆
N
1
∆
N
2
∆
∆
N
2
∆
N
1
∆
N
2
∆
∆
N
2
−
2
−
7
6.983
7
0
7.000
−
−
2
6
5.700
7
1
5.717
−
2
−
5
4.417
7
2
4.433
−
2
−
4
3.133
7
3
3.150
−
2
−
3
1.850
7
4
1.867
−
2
−
2
0.567
7
5
0.583
−
2
−
1
−
0.718
7
6
−
0.700
−
2
0
−
2.000
7
7
−
1.983
2
0
2.000
−
7
−
7
1.983
2
1
0.717
−
7
−
6
0.700
2
2
−
0.567
−
7
−
5
−
0.583
[22
2
3
−
1.850
−
7
−
4
−
1.867
2
4
−
3.133
−
7
−
3
−
3.150
2
5
−
4.417
−
7
−
2
−
4.433
2
6
−
5.700
−
7
−
1
−
5.717
Lin
—
-0.
——
Nor
PgE
2
7
−
6.983
−
7
0
−
7.000
Table 6.5 shows an arrangement of integers that have a practically undistinguish-
able effect on the ionospheric function. It is seen that, e.g., the impact of the combi-
nations
(
7
)
and
(
7
,
0
)
differs by only 0.02 cycle. This amount is too small to
be discovered reliably in an observation sequence. Unfortunately, there is no unique
combination of small
(
−
2
,
−
∆
N
1
,
∆
N
2
)
that smooths the ionospheric function if slips are
[22
present.
6.
6.5 Multipath Equations
The multipath equations relate a pseudorange and carrier phases of both frequencies
as follows,
− α
f
Φ
1
− Φ
2
=−λ
1
N
1
+
− α
f
λ
1
N
1
− λ
2
N
2
2
2
M
1
≡
P
1
− Φ
1
+
1
1
(6.100)
+
cT
GD
+ δ
M
1
− α
f
Φ
1
− Φ
2
=−λ
2
N
2
+
− α
f
λ
1
N
1
− λ
2
N
2
2
α
2
α
f
f
M
2
≡
P
2
− Φ
2
+
1
1
(6.101)
+
c
α
f
T
GD
+ δ
M
2
These expressions can be readily verified. Analyzing these expressions over time is
useful for initial cycle slip scanning. While these multipath functions should theoreti-
cally be constant in time, the actual variation is dominated by measurement accuracy
and multipath of the pseudoranges.
