Global Positioning System Reference
In-Depth Information
It is observed that the pseudorange
ρ
is:
[
]
(
)
(
)
ρ
=
cT t
′ +
−
T
+
δ
t
u
u
s
(
)
(
)
=′ ++ −
=
cT
T
ct
δ
t
u
s
u
(
)
(
)
cT
+
δ
t
−
T
+
ct
−
δ
t
u
s
u
D
(
)
=
r
+
ct
−
δδ
t
+
t
u
D
(
)
where
r
is the geometric range,
.
A similar expression can be derived for the carrier-phase measurement when the
raw measurement (see Section 5.7.3), usually computed in units of cycles, is con-
verted to units of meters by multiplying by the carrier wavelength in meters. As
noted earlier, the error terms are in general different for the carrier-phase measure-
ment. Further, as discussed in Section 5.7.3, the carrier-phase measurement includes
an ambiguity that is an integer multiple of a wavelength. Elaboration on the
pseudorange and carrier-phase error sources, including relativistic effects, is
provided in the following sections.
rcT T
=
−
=
ct
∆
u
S
7.2.1 Satellite Clock Error
As discussed in Chapter 3, the satellites contain atomic clocks that control all
onboard timing operations, including broadcast signal generation. Although these
clocks are highly stable, the clock correction fields in the navigation data message
are sized such that the deviation between SV time and GPS time may be as large as 1
ms [4]. (An offset of 1 ms translates to a 300-km pseudorange error.) The MCS
determines and transmits clock correction parameters to the satellites for
rebroadcast in the navigation message (see Section 3.1.2). These correction parame-
ters are implemented by the receiver using the second-order polynomial [4]:
(
)
(
)
2
δ
t
=+
a
a
t
− +
t
a
t
−
t
+
∆
t
(7.3)
clk
f
0
f
1
oc
f
2
oc
r
where:
a
f
0
=
clock bias (s)
a
f
1
=
clock drift (s/s)
frequency drift (i.e., aging) (s/s
2
)
a
f
2
=
t
oc
=
clock data reference time (s)
t
=
current time epoch (s)
∆
t
r
=
correction due to relativistic effects (s)
t
r
compensates for one of three GPS-related relativistic effects dis-
cussed in Section 7.2.3.
Since these parameters are computed using a curve-fit to predicted estimates of
the actual satellite clock errors, some residual error remains. This residual clock
error,
The correction
∆
δ
t
, results in ranging errors that typically vary from 0.3-4m, depending on the
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