Global Positioning System Reference
In-Depth Information
Substituting these new values into Equation (4.19) will produce the desired
results.
4.8 CORRECTION OF GPS SYSTEM TIME AT TIME OF TRANSMISSION
(
5,6
)
In Equations (4.21) and (4.23) the GPS time is used, and this time is often
referred to at the time of transmission. (This section discusses only the cor-
rection of this time. The actual obtaining of the time of transmission will be
discussed in Section 9.10.) The signals from the satellites are transmitted at the
same time except for the clock error in each satellite. The time of receiving
t
u
is
the time the signal arrives at the receiver. The relation between the
t
and
t
u
is
t
u
=
+
t
ρ
i
/c
t
=
t
u
−
ρ
i
/c
(4.31)
where
ρ
i
is the pseudorange from satellite
i
to the receiver and
c
is the speed of
light. Since the pseudorange from each satellite to the receiver is different, the
time of receiving is different. However, in calculating user position, one often
uses one value for time. The time of receiving
t
u
is a reasonable selection. If
a time of receiving
t
u
is used as a reference, from the above equation the time
of transmission from various satellites is different. The time of transmission is
the receiving time minus the transit time. This time is represented by
t
and is
referred to as the time of transmission corrected for the transit time.
The
t
value must be corrected again from many other factors. However, in
order to correct
t
,the
t
value must first be known. This requirement makes the
correction process difficult. To simplify this process, let
t
c
represent the coarse
GPS system time at time of transmission corrected by transit time. The value
t
c
can be obtained from time of the week (TOW), which will be presented in
Section 5.9. For the present discussion, let us assume that the
t
c
value is already
obtained. The time
t
k
shall be the actual total time difference between the time
t
c
and the epoch time
t
oe
and must account for the beginning or end of the week
crossovers. That is, the following adjustments must be made on
t
c
:
If
t
k
=
t
c
−
t
oe
>
302
,
400 then
t
k
=
t
k
−
604
,
800 or
t
c
⇒
t
c
−
604
,
800
If
t
k
=
t
c
−
t
oe
<
−
302
,
400 then
t
k
=
t
k
+
604
,
800 or
t
c
⇒
t
c
+
604
,
800 (4.32)
where
t
oe
can be obtained from ephemeris data, 302,400 is the time of half a
week in seconds. The time of a week in seconds is 604,800 (7
×
24
×
3600).
The
following
steps
can
be
used
to
correct
the
GPS
time
t
.From
Equation (4.22), the mean motion is calculated as
µ
a
s
+
n
=
n
(
4
.
33
)
=
×
10
14
meters
3
/sec
2
where
µ
3
.
986005
is the earth's universal gravitational
parameter and is a constant,
√
a
s
and
n
are obtained from ephemeris data.
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