Global Positioning System Reference
In-Depth Information
The
ν
can be found from Equations (3.37) and (3.39) and they are designated as
ν
1
and
ν
2
where
ν
1
=
cos
−
1
cos
E
−
e
s
1
−
e
s
cos
E
sin
−
1
1
−
e
s
sin
E
ν
2
=
(3.40)
1
−
e
s
cos
E
The
ν
1
value calculated from Matlab is always positive for all
E
values and
ν
2
is
positive for
E
=
0to
π
and negative for
E
=
π
to 2
π
as shown in Figure 3.8.
Thus, the true anomaly can be found as
ν
=
ν
1
sign
(ν
2
)
(
3
.
41
)
where sign
(ν
2
)
provides the sign of
ν
2
; therefore, it is either
+
1or
−
1. It
is interesting to note that to find the true anomaly only
M
and
e
s
are needed.
Although the semi-major axis
a
s
appears in the derivation, it does not appear in
the final equation.
3.13 SIGNAL STRENGTH AT USER LOCATION
(
1,8,14-16
)
In this section the signal strength at the user location will be estimated. The
signal strength can be obtained from the power of the transmitting antenna, the
FIGURE 3.8
ν
1
and
ν
2
versus
E
.
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