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
which yields the following parameters and covariance matrix
N
1
]
T
z
=
[
ρ + ∆
I
1
,P
N
w
≡
N
1
−
N
2
(7.29)
x
Z
T
Σ
=
Σ
Z
(7.30)
z
=
σ
1
,
Φ
=
U
sing again the numerical values
k
154 and
0
.
002 m, the standard devia-
tio
ns and the correlation matrix become
σ
ρ+∆
,
σ
1
,N
=
0
.
99 m
,
0
.
77 m
,
0
.
28 cycL
w
,
9
.
22 cycL
1
(7.31)
σ
I
,
σ
w
,
1
−
0
.
9697
−
0
.
1230
−
0
.
9942
[24
1
0
.
1230
0
.
9904
C
z
=
(7.32)
1
0
.
0154
Lin
—
3.7
——
Nor
PgE
sym
1
The third parameter in (7.29) is the wide-lane ambiguity. We observed that there is
little correlation between the wide-lane and L1 ambiguities. Furthermore, the corre-
lations between the wide-lane ambiguity and both the topocentric distance and the
ionospheric parameter have been reduced dramatically. Considering the small stan-
dard deviation for the wide-lane ambiguity in (7.31) and its low correlations with
the other parameters, it should be possible to estimate the wide-lane ambiguity from
ep
och solutions. The semiaxes of the ellipse of standard deviation for the ambiguities
ar
e 9.22 and 0.28, respectively, and an orientation of 89.97° for the semimajor axis,
i.e
., the ellipse is elongated along the
N
1
direction. The correlation matrix (7.32) still
sh
ows high correlations between
N
1
, the ionosphere, and the topocentric distance.
If
we consider the square root of the determinant of the covariance matrix to be a
sin
gle number that measures correlation, then
(
[24
)
1
/
2
|
|
|
|
≈
C
z
/
C
x
33 implies a major
de
correlation of the epoch parameters.
The solution (7.29) is also obtained if we express the carrier phases (7.19) in cycles
an
d then multiply with
Z
from the left. In fact, the following popular expressions can
be
readily verified,
f
1
P
1
+
f
2
P
2
N
w
=
ϕ
w
−
λ
w
+
f(
δ
1
,P
,
δ
2
,P
,
δ
1
,ϕ
,
δ
2
,ϕ
)
(f
1
+
f
2
)
(7.33)
≈
ϕ
w
−
0
.
65
P
1
−
0
.
51
P
2
+···
ϕ
w
=
ϕ
1
−
ϕ
2
(7.34)
c
f
w
=
c
f
1
−
λ
w
=
f
2
≈
0.86 m
(7.35)
