Global Positioning System Reference
In-Depth Information
(
)
Subframe_Number
=+
1
MOD GPS_Time
6 5
,
(
)
(
)
Word_Number
=+
1
MOD
GPS_Time
30
×
0020
.
,
10
(
)
Bit_Number
=+
1
MOD GPS_Time, .
002
0
(9.45)
(
)
Integer_PN_Rolls
MO =
MOD GPS_Time
0001
.
(
)
Code_Phase
=
2
,
046
×
GPS_Time
×
1000 2 046
,
,
,
The equations shown in (9.45) enable the user to precisely compute the Code_Phase ,
Bit_Phase , Bit_Number , Word_Number , and Subframe_Number of the signal leav-
ing the satellite at precisely any time into the week based on a GPS_Time . Of course,
the user will observe this code phase on the ground later in time after it propagates
from the satellite to the user by the propagation time, Dtprop . Dtprop is easily com-
puted, as shown in (9.47), based on the geometric range between satellite and user
divided by the speed of light. In addition, the signal will be slipped forward or back-
ward in time an amount proportional to the satellite clock correction Tcorr to the
tune of a few milliseconds. Thus, the user will always be able to predict the code
phase to all satellites observed on the ground at any instantaneous GPS_Time by the
pseudocode:
(
)
(
)
Code_Phase_observed
=
MOD
2 046
,
×
GPS_Time+Tcorr
Dtprop
×
1000 2 046
,
,
,
where:
(
)
(
)
2
Tcorr=a
+a
×
GPS_Time
t
+
a
×
GPS_Time
t
(9.46)
f
0
f
1
oc
f
2
oc
Dtprop
=
SV_POS
USER_POS
SOL
(9.47)
a f 0 , a f 1 , a f 2 are the zeroth through second-order satellite clock correction terms from
navigation data message subframe 1, and t oc is the reference GPS time for the satellite
clock correction terms.
Likewise, all equations of (9.45) can be modified to include the user-observed
parameters as follows:
GPS_Time
Tcorr
+
Subframe_Number_observed
=+
1
MOD
65
,
Dtpro
p
GPS_Time
+
(
)
Word_Number_observed
=+
1
MOD
30
×
0020
.
,
10
Tcorr
Dtprop
GPS_Time
Tcorr
+
Bit_Number_ob
served
=+
1
MOD
,.
0020
(9.48)
Dtprop
GPS_Time
Tcorr
+
Integer_PN_Rolls_observed
=
MOD
0001
.
Dtprop
GPS
_Time
Tcorr
+
×
Code_Phase_observed
=
MOD
2046
×
1000 2 046
,
,
,
Dtprop
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