Global Positioning System Reference
In-Depth Information
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TABLE 2.5
Partial Derivatives with Respect to Local Geodetic Coordinates
∂
α
1
∂n
1
=
sin
α
1
s
cos
β
1
∂
α
1
∂e
1
=−
cos
α
1
s
cos
β
1
a
11
=
(a)
a
12
=
(b)
∂
α
1
∂u
1
=
0
a
13
=
(c)
∂
α
1
∂n
2
=−
sin
α
1
s
cos
a
14
=
[cos
(ϕ
2
−
ϕ
1
)
+
sin
ϕ
2
sin
(
λ
2
− λ
1
)
cot
α
1
]
(d)
β
1
∂
α
1
∂e
2
=
cos
α
1
s
cos
β
1
a
15
=
[cos
(
λ
2
− λ
1
)
−
sin
ϕ
1
sin
(
λ
2
− λ
1
)
tan
α
1
]
(e)
∂
α
1
∂u
2
=
cos
α
1
cos
ϕ
2
s
cos
β
1
a
16
=
[sin
(
λ
2
− λ
1
)
+
(
sin
ϕ
1
cos
(
λ
2
− λ
1
)
−
cos
ϕ
1
tan
ϕ
2
)
tan
α
1
] (f)
[50
∂
β
1
∂n
1
=
sin
β
1
cos
α
1
s
∂
β
1
∂e
1
=
sin
β
1
sin
α
1
s
a
21
=
(g)
a
22
=
(h)
∂
β
1
∂u
1
=−
cos
β
1
s
Lin
—
*
1
——
Sho
*PgE
a
23
=
(i)
∂
β
1
∂n
2
=
−
cos
ϕ
1
sin
ϕ
2
cos
(
λ
2
− λ
1
)
+
sin
ϕ
1
cos
ϕ
2
+
sin
β
1
cos
β
2
cos
α
2
a
24
=
(j)
s
cos
β
1
∂
β
1
∂e
2
=
−
cos
ϕ
1
sin
(
λ
2
− λ
1
)
+
sin
β
1
cos
β
2
sin
α
2
s
cos
β
1
a
25
=
(k)
∂
β
1
∂u
2
=
sin
β
1
sin
β
2
+
sin
ϕ
1
sin
ϕ
2
+
cos
ϕ
1
cos
ϕ
2
cos
(
λ
2
− λ
1
)
s
cos
β
1
a
26
=
(l)
[50
∂s
∂n
1
=−
cos
β
1
cos
α
1
∂s
∂e
1
=−
cos
β
1
sin
α
1
a
31
=
(m)
a
32
=
(n)
∂s
∂u
1
=−
sin
β
1
∂s
∂n
2
=−
cos
β
2
cos
α
2
a
33
=
(o)
a
34
=
(p)
∂s
∂e
2
=−
cos
β
2
sin
α
2
∂s
∂u
2
=−
sin
β
2
a
35
=
(q)
a
36
=
(r)
•
Transforming Postadjustment Results:
If the adjustment happens to have been
carried out with the (x) parameterization, and it is, subsequently, determined
necessary to transform the result into the
(ϕ)
or (w) coordinates, then the trans-
formations (2.106) and (2.108) can be used; i.e.,
d
w
=
R
d
x
(2.111)
where
