Global Positioning System Reference
In-Depth Information
where
µ
=
9386005
×
10
8
m
3
/s
2
is the earth's universal gravitational parameter,
a
s
is the semi-major axis of the satellite orbit obtained from subframe 2 in bits
227 - 234 and 241 - 264, and
n
is the mean motion difference obtained from
subframe 2 in bits 91 - 106.
As discussed in Section 4.8, the correction of GPS time at time of transmission
(
t
c
) must be performed first. The correction can be made from Equation (4.32)
as follows:
if
t
c
−
t
oe
>
302400
then
t
c
⇒
t
c
−
604800
if
t
c
−
t
oe
<
−
302400
then
t
c
⇒
t
c
+
604800
(9.8)
where
t
c
is obtained from Equation (9.6) and
t
oe
(subframe 2, bits 271 - 286) is
the reference time ephemeris obtained from navigation data.
Once the GPS system time at time of transmission (
t
c
) is found, the mean
anomaly can be found from Equation (4.34)
M
=
M
0
+
n(t
c
−
t
oe
)
(
9
.
9
)
where
M
0
is the mean anomaly at reference time obtained from subframe
2
bits
107 - 114,
121 - 144.
The
eccentric
anomaly
E
can
be
found
from
Equation (4.35) as
E
=
M
+
e
s
sin
E
(
9
.
10
)
where
e
s
is the eccentricity of satellite orbit obtained from subframe 2 bits
167 - 174 and 181 - 204. Since this equation is nonlinear, the iteration method
will be used to obtain
E
.
The relativistic correction term can be obtained from Equation (4.37)
Fe
s
√
a
s
sin
E
t
r
=
(
9
.
11
)
10
−
10
sec/m
1
/
2
is a constant,
e
s
,
a
s
,and
E
are men-
tioned in Equations (9.7) and (9.10). The overall time correction term is shown
in Equation (4.38) as
where
F
=−
4
.
442807633
×
t
=
a
f
0
+
a
f
1
(t
c
−
t
oc
)
+
a
f
2
(t
c
−
t
oc
)
+
t
r
−
T
GD
(
9
.
12
)
where
a
f
0
(271 - 292),
a
f
1
(249 - 264),
a
f
2
(241 - 248),
t
oc
(219 - 234) are satellite
clock corrections,
t
GD
(197 - 204) is the estimated group delay differential, and
all are obtained from subframe 1.
The
GPS
time
at
time
of
transmission
can
be
corrected
again
from
Equation (4.39) as
t
=
t
c
−
t
(
9
.
13
)
Search WWH ::
Custom Search