Global Positioning System Reference
In-Depth Information
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
rately because of high carrier phase resolution and the small multipath (as compared
to the one for code measurements). Unfortunately, this function alone does not per-
mit the estimation of the absolute TEC, because the initial ambiguities are not known.
Expressing (6.92) and (6.93) in units of length, we obtain the function
≡ Φ
2
− Φ
1
=
1
− α
f
I
1
,P
+
c
f
2
N
2
−
c
f
1
N
1
+ δ
Φ
,I
+
Φ
I
ε
Φ
,I
(6.99)
where
δ
Φ
,I
is a function of the carrier phase hardware delays and multipath. In
Ex
pression (6.99) we have made used of Equations (6.85) to (6.88) to convert the
io
nospheric phase delays to respective pseudorange delays. The functions
P
I
and
Φ
I
ar
e affected by the ionosphere by the same amount.
[22
6.6.4 Discriminating Small Cycle Slips
An
alysis of dual-frequency carrier phase functions requires some extra attention be-
ca
use certain combinations of slips in L1 and L2 phases generate almost identical
ef
fects. For example, consider the ionosphere-free phase observable (6.94). Unfortu-
na
tely, the ambiguities enter this function not as integers but in the combination of
β
f
N
1
− δ
f
N
2
, necessitating a search for a noninteger fraction in the residuals of the
io
nosphere-free phase. Table 6.4 lists in columns 1 and 2 small changes in the am-
bi
guities and illustrates in columns 3 and 4 their effects on the ionospheric-free and
th
e ionospheric phase functions, respectively. Certain combinations of both integers
pr
oduce almost identical changes in the ionosphere-free phase function. For example,
a
change of
(
Lin
—
2.8
——
No
PgE
−
−
9
)
causes a small change of 0.033 cycles, whereas
(
1
,
1
)
causes
a
change of 0.562 cycles, which is almost identical to the one caused by
(
8
,
10
)
.If
ps
eudorange positioning is accurate enough to resolve the ambiguities within three
to
four cycles, then these additional difficulties in identifying slip combination can
be
resolved.
7
,
[22
TABLE 6.4
Small Cycle Slips and Phase Functions
∆
N
1
−
√
α
f
∆
N
1
∆
N
2
β
f
∆
N
1
− δ
f
∆
N
2
∆
N
2
±
1
±
1
±
0
.
562
∓
0
.
283
±
2
±
2
±
1
.
124
∓
0
.
567
±
1
±
2
∓
1
.
422
∓
1
.
567
±
2
±
3
±
0
.
860
∓
1
.
850
±
3
±
4
∓
0
.
298
∓
2
.
133
±
4
±
5
±
0
.
264
∓
2
.
417
±
5
±
6
±
0
.
827
∓
2
.
700
±
6
±
7
±
1
.
389
∓
2
.
983
±
5
±
7
∓
1
.
157
∓
3
.
983
±
6
±
8
∓
0
.
595
∓
4
.
267
±
7
±
9
∓
0
.
033
∓
4
.
550
±
8
±
10
±
0
.
529
∓
4
.
833
