Global Positioning System Reference
In-Depth Information
The following steps can be taken to improve user position accuracy.
1. From the satellite and user position the transit time
t
t
can be found as
t
t
=
(x
−
x
u
)
2
+
(y
−
y
u
)
2
+
(z
−
z
u
)
2
/c
(
4
.
48
)
where
x
,
y
,
z
,and
x
u
,
y
u
,
z
u
are the coordinates of the satellite and the
user respectively,
c
is the speed of light.
2. Use the transit time to modify the angle
er
in Equation (4.46) as
er
−
˙
ie
t
t
er
⇒
(
4
.
49
)
3. Use the new value of
er
in Equation (4.47) to calculate the position of
the satellite
x
,
y
,and
z
.
4. The above operations should be performed on every satellite. From these
values a new user position
x
u
,
y
u
,
z
u
will be calculated.
5. Repeat steps 1, 2, 3, and 4 again to obtain a new set of
x
,
y
,and
z
.When
the old and new sets are within a predetermined value, the new set can be
considered as the position of the satellite in the new coordinate system. It
usually requires calculating the
x
,
y
,and
z
values only twice.
6. These new
x
,
y
,and
z
values will be used to find the user position.
4.11 EPHEMERIS DATA
(
4-6
)
In the previous sections several constants and many ephemeris data are used in
the calculations. This section lists all these constants and the ephemeris data used
in the calculations. The details of the ephemeris data transmitted by the satellites
will be presented in the next chapter.
The constants are listed as follows:
(
4
)
=
GM
=
3
.
986005
×
10
14
meters
3
/sec
2
, which is the WGS-84 value of the
earth's universal gravitational parameter.
˙
ie
=
7
.
2921151467
×
10
−
5
rad/sec, which is the WGS-84 value of the earth's
rotational rate.
µ
π
=
3
.
1415926535898.
=
×
10
8
c
2
.
99792458
meter/sec, which is the speed of light.
Theephemerisdataare:
M
0
: mean anomaly at reference time.
n
: mean motion difference from computed value.
√
a
s
: square root of the semi-major axis of the satellite orbit.
e
s
: eccentricity of the satellite orbit.
T
GD
,
t
oc
,
a
f
0
,
a
f
1
,
a
f
2
: clock correction parameters.
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