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 2 )
( 3 . 41 )
where sign 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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