Global Positioning System Reference
In-Depth Information
From these relations let us find the relation between angle
β
and
L
.Takingthe
derivative of
x
and
z
of Equation (2.24), the results are
dx
a
e
sin
βdβ
dz
=
b
e
cos
βdβ
=−
(2.26)
Thus
dx
dz
=
a
e
b
e
tan
β
1
−
e
e
tan
L
=−
tan
β
=
(
2
.
27
)
From these relationships let us find the three unknowns.
2.11 CALCULATION OF ALTITUDE
(
5
)
In the following three sections the discussion is based on reference 5. From
Figure 2.7 the height
h
can be found from the law of cosine through the triangle
OPA
as
r
2
r
0
−
h
2
r
0
+
h
2
=
2
r
0
h
cos
(π
−
D
0
)
+
=
2
r
0
h
cos
D
0
+
(
2
.
28
)
where
r
0
is the distance from the center of the earth to the point on the surface
of the earth under the user position. The amplitude of
r
can be found from
FIGURE 2.7
Altitude and latitude illustration.
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