Global Positioning System Reference
In-Depth Information
P
1
ϕ
1
,
0
,
λ
1
,
0
,x
1
,
0
,y
1
,
0
,P
2
ϕ
2
,
0
,
λ
2
,
0
,x
2
,
0
,y
2
,
0
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
↓
s
12
,
0
,
t
12
,
0
γ
1
,
0
, d
12
,
0
,
¯
α
12
,
0
,
↓
/
1
,
-
α
12
,
0
− γ
1
,
0
−
∆
t
12
,
0
=
t
12
,
0
2
.
s
12
,
0
−
∆
s
12
,
0
=
d
12
,
0
Figure 9.12
Reducing observations for plane network adjustments.
¯
α
12
,b
=
− γ
1
,
0
− ∆
t
12
,b
t
12
,
0
(9.23)
[33
δ
213
,b
− ∆
δ
213
,b
=
t
13
,
0
+ ∆
t
12
,
0
(9.24)
Lin
—
-
——
Lon
PgE
d
12
,b
=
s
12
,b
− ∆
s
12
,
0
(9.25)
The observation equations are
dx
2
+
¯
t
12
,b
(9.26)
sin
¯
cos
¯
sin
¯
cos
¯
t
12
,
0
d
12
,
0
t
12
,
0
d
12
,
0
t
12
,
0
d
12
,
0
t
12
,
0
d
12
,
0
t
12
,
0
−
¯
v
t
=
dy
1
−
dx
1
−
dy
2
+
sin
t
13
,
0
d
13
,
0
dy
1
−
cos
t
13
,
0
d
13
,
0
dx
1
+
sin
t
12
,
0
d
12
,
0
cos
t
12
,
0
d
12
,
0
sin
t
12
,
0
d
12
,
0
[33
v
δ
=
−
−
dy
2
(9.27)
cos
t
12
,
0
d
12
,
0
sin
t
13
,
0
d
13
,
0
cos
t
13
,
0
d
13
,
0
dx
3
+
t
13
,
0
−
t
13
,b
−
dx
2
−
dy
3
+
sin
t
12
,
0
dx
2
+
t
12
,
0
−
t
12
,b
(9.28)
cos
t
12
,
0
dy
1
−
sin
t
12
,
0
dx
1
+
cos
t
12
,
0
dy
2
+
v
d
=−
The scheme in Figure 9.12 suggests that the reduction elements
s
be com-
puted from the approximate coordinates and that the GML functions be used to com-
pute the geodesic azimuth. The use of the GML type of functions can be avoided if
explicit functions for
∆
t
and
∆
∆
t
and
∆
s
are available.
9.2.5 The
∆
t
and
∆
s
Functions
Th
e literature contains functions that relate
∆
t
and
∆
s
explicitly to the geodetic
lat
itude and longitude or mapping coordinates, i.e.,
∆
t
=
t
geod
(ϕ
1
,
λ
2
,ϕ
1
,
λ
2
)
=
t
map
(x
1
,y
2
,x
1
,y
2
)
(9.29)
∆
s
=
s
geod
(ϕ
1
,
λ
2
,ϕ
1
,
λ
2
)
=
s
map
(x
1
,y
2
,x
1
,y
2
)
(9.30)
