Global Positioning System Reference
In-Depth Information
The WN is used to determine the week of YUMA data (WY) used. The DOW is
used as part of the input time. The closer the WY to the WN, the more accurate
the calculated results should be.
The hour, minute, and second should be changed to Greenwich time. For
example, to the local time in Dayton, Ohio, there is added 4 hours for daylight
saving time and 5 hours for winter time. The time is then changed to seconds. If
the WN and the YUMA week numbers are different, a correction factor is needed.
Every sidereal day and solar day is off by approximately (4 × 60 4 . 09) seconds,
and every week is off by 7 × ( 4 × 60 4 . 09 ) seconds. Thus, the overall time in
Dayton, Ohio, in the summer is obtained as
t GPS
= [DOW × 24 + (h + 4 ) × 60 + min] × 60 + sec + 7 × (W N WY)
× ( 4 × 60 4 . 09 )
(12.23)
where h, min, and sec are input time representing local time in hours, minutes,
and seconds, and ( h
4) represents the 4-hour adjustment from Dayton, Ohio,
to Greenwich time in summer. The epoch time t oe can be found as
+
t oe =
t yu +
a f 0
( 12 . 24 )
where t yu and a f 0 are from the YUMA data and t oe is the time used in the next
step of calculations.
Step2. Calculatesatelliteposition . The equations used to calculate the satel-
lite position are presented in Chapter 4. They are repeated here for convenience.
The nine quantities obtained from YUMA data are e s , t yu , i , ž , a s , , ω , M 0 ,
and a f 0 . They are used in the following equations repeated here from Chapter 4.
The constants used in these calculations are µ
10 14
m 3 /sec 2
=
3 . 986005
×
and
ž ie
10 5 rad/sec.
The mean motion is calculated as
=
7 . 2921151467
×
µ
a s
n
=
( 4 . 33 )
This equation is simplified because n is not available in the almanac data. The
mean anomaly can be found as
M
=
M 0 +
n(t GPS
t oe )
( 4 . 34 )
where time t c is replaced by T GPS and t oe can be found in Equation (12.24) The
eccentric anomaly E can be found through iteration as
E
=
M
+
e s sin E
( 4 . 35 )
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