Global Positioning System Reference
In-Depth Information
8.3.1.2 Pseudorange Domain Corrections
In most operational LADGPS systems, instead of determining position coordinate
errors, the reference station determines and disseminates pseudorange corrections
for each visible satellite. The process is explained in the following mathematical
treatment.
In order for the user receiver to determine its position accurately with respect to
the Earth (i.e., for absolute DGPS applications), the reference station must have
accurate knowledge of its own position in ECEF coordinates. Given that the
reported position of the
i
th satellite is (
x
i
,
y
i
,
z
i
) and the position of the reference sta-
tion is known through a survey to be at position (
x
m
,
y
m
,
z
m
), the computed geometric
distance,
R
i
, from the reference station to the satellite is
(
)
(
)
(
)
2
2
2
i
Rxx
−
+
yy
−
+
z
−
z
m
i
m
i
m
i
m
ρ
i
, to the
i
th
satellite. This measurement contains the range to the satellite, along with the errors
discussed in Chapter 7 and Section 8.2:
The reference station then makes a pseudorange measurement,
i
i
ρ
=+ +
Rct
δ
ε
(8.5)
m
m
mm
where
ε
m
are the pseudorange errors and
c
δ
t
m
represents the reference station clock
offset from GPS time.
The reference station differences the computed geometric range,
R
i
, with the
pseudorange measurement to form the differential correction
i
i
i
∆ρ
=−=− −
R
ρ
c t
δ
ε
m
m
m
mm
This correction, which may be a positive or negative quantity, is broadcast to
the user receiver, where it is added to the user receiver's pseudorange measurement
to the same satellite
i
i
i
ρ
+
∆
ρ
=
Rct
ct
+
δ
+
ε
u
m
u
u
u
(
)
+−
δ
−
ε
mm
To a significant extent, the user receiver's pseudorange error components will be
common to those experienced by the reference station with the exception of
multipath and receiver noise. The corrected pseudorange can be expressed as
ρ
i
=+ +
R
i
ε
c t
δ
(8.6)
ucor
,
u
um
m
where
ε
um
= ε
u
− ε
m
represents residual pseudorange errors and
δ
t
um
is the difference in
user and reference station clock offsets,
δ
t
u
− δ
t
m
.
In Cartesian coordinates (8.6) becomes
(
)
2
(
)
2
(
)
2
ρ
i
=
xx
−
+−
yy
+−
zz
+ +
ε
ct
δ
(8.7)
ucor
,
i
u
i
u
i
u
um
um
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