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
Regarding the stochastic model, we make the simplifying assumption that all carrier
phase observations are uncorrelated and are of the same accuracy. Thus the complete
RST
×
RST
cofactor matrix of the undifferenced phase observations is
ϕ
I
Q
ϕ
= σ
(7.80)
with
σ
ϕ
denoting the standard deviation of the phase measurement expressed in
cycles.
The next task is to find the complete set of independent double-difference obser-
vations. We designate one station as the base station and one satellite as the base
satellite. Without loss of generality, let station 1 be the base station, and satellite 1 be
the base satellite. The session network of
R
stations is now thought of as consisting
of
R
−
1 baselines emanating from the base station. There are
S
−
1 independent
[26
double differences for each baseline. Thus, a total of
(R
1
)
independent
double differences can be computed for the session network. On the basis of an or-
dered observation vector like (7.78), and the base station and base satellite ordering
scheme, an independent set of double differences for epoch
i
is
∆
i
=
ϕ
12
−
1
)(S
−
Lin
—
7.3
——
Nor
PgE
1
R
(i)
T
ϕ
1
S
ϕ
12
ϕ
1
S
12
(i)
···
12
(i)
···
1
R
(i)
···
(7.81)
∆
1
.
∆
T
∆
=
(7.82)
[26
Th
e transformation from undifferenced to double-differenced observations is
∆
=
D
ψ
(7.83)
w
here
D
is the
(R
−
1
)(S
−
1
)T
×
RST
double-difference coefficient matrix. If we
I
as
define the auxiliary matrix
1
10 0
10
−
I
=
10
10 0
−
(7.84)
−
1
then the pattern of
D
can be readily seen from Table 7.3. The boxes highlight the
columns and rows that refer to a specific epoch. Each additional baseline adds another
row and column to the highlighted area.
For the ordered vector of triple-difference observations, we have
∇
i
=
ϕ
12
+
1
,i)
T
ϕ
1
S
ϕ
12
ϕ
1
S
12
(i
+
1
,i)
···
12
(i
+
1
,i)
···
1
R
(i
+
1
,i)
···
1
R
(i
(7.85)
