Global Positioning System Reference
In-Depth Information
x
m
b
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
x
=
(7.94)
=
N
12
12
13
b
T
N
1
S
12
N
12
13
N
1
S
···
···
(7.95)
is
called the double-difference float solution.
Finally, the partial derivatives of triple differences follow from those of double
di
fferences by differencing
∂ϕ
pq
∂ϕ
pq
∂ϕ
pq
km
(j, i)
∂
x
m
km
(j)
∂
x
m
km
(i)
∂
x
m
=
−
(7.96)
be
cause the triple difference is the difference of two double differences. The design
m
atrix of the triple difference contains no columns for the initial ambiguities, because
th
ese parameters cancel during the differencing.
[26
Lin
—
-
——
No
PgE
7.
7.3 Independent Baselines
Th
e ordering scheme of base station and base satellite used for identifying the set of
independent double-difference observations is not the only scheme available. It has
been used here because of its simplicity. An example where the base station and base
satellite scheme requires a slight modification occurs when the base station does not
observe at a certain epoch due to temporary signal blockage or some other cause. If
station 1 does not observe, then the double difference
ϕ
pq
23
∆
can be computed for this
[26
pa
rticular epoch. Because of the relationship
ϕ
pq
23
ϕ
pq
13
ϕ
pq
12
=
−
(7.97)
th
e ambiguity
N
pq
23
is related to the base station ambiguities as
N
pq
23
N
pq
13
N
pq
12
=
−
(7.98)
In
troduction of
N
pq
23
as an additional parameter would create a singularity of the nor-
m
al matrix because of the dependency expressed in (7.98). Instead of adding this
ne
w ambiguity, the base station ambiguities
N
pq
12
and
N
pq
13
are given the coefficients
1 and
1, respectively, in the design matrix. The partial derivatives with respect
to
the station coordinates can be computed as required by (7.97) and entered di-
re
ctly into the design matrix, because the respective columns are already there. A
si
milar situation arises when the base satellite changes. The linear functions in this
ca
se are:
−
ϕ
23
km
ϕ
13
km
ϕ
12
km
=
−
(7.99)
N
23
km
N
13
km
N
12
km
=
−
(7.100)
