Global Positioning System Reference
In-Depth Information
Substituting these relations into Equation (2.52) and solving for
r
0
, the result is
cos
2
L
co
a
e
r
0
b
e
cos
2
L
co
+
a
e
(
1
−
cos
2
L
co
)
sin
2
L
co
b
e
r
0
+
=
=
1 r
a
e
b
e
a
e
b
e
b
e
r
0
=
cos
L
co
=
or
a
e
1
−
1
−
b
e
a
e
1
−
e
e
cos
L
co
b
e
1
+
1
2
e
e
cos
2
L
co
+···
r
0
=
(
2
.
54
)
Use Equation (2.23) to replace
b
e
by
a
e
, Equation (2.41) to replace
e
e
by
e
p
,and
L
to replace
L
co
because
L
≈
L
co
,andthen
e
p
)
1
e
p
cos
2
L
e
p
2
r
0
≈
a
e
(
1
−
+
−
+···
e
p
sin
2
L
≈
a
e
(
1
−
e
p
)(
1
+
e
p
−
+···
)
(2.55)
In this equation the higher order of
e
p
is neglected. The value of
r
0
can be
found as
e
p
sin
2
L)
r
0
≈
a
e
(
1
−
(
2
.
56
)
To solve for the latitude and altitude of the user, use Equation (2.51) to find
the geodetic latitude
L
first. Then use Equation (2.56) to find
r
0
, and finally, use
Equation (2.33) to find the altitude. The result is
x
u
+
e
p
sin
2
L)
h
≈
r
−
r
0
≈
y
u
+
z
u
−
a
e
(
1
−
(
2
.
57
)
2.14 SATELLITE SELECTION
(
1,8
)
A GPS receiver can simultaneously receive signals from 4 up to 11 satellites,
if the receiver is on the surface of the earth. Under this condition, there are
two approaches to solve the problem. The first one is to use all the satellites to
calculate the user position. The other approach is to choose only four satellites
from the constellation. The usual way is to utilize all the satellites to calculate
the user position, because additional measurements are used. In this section and
section 2.15 the selection of satellites will be presented. In order to focus on this
subject only the four-satellite case will be considered.
If there are more than four satellite signals that can be received by a GPS
receiver, a simple way is to choose only four satellites and utilize them to solve
for the user position. Under this condition, the question is how to select the four
satellites. Let us use a two-dimensional case to illustrate the situation, because it is
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