Global Positioning System Reference
In-Depth Information
By making pseudorange measurements to four or more satellites, the user receiver
can compute its position by using one of the position determination techniques dis-
cussed in Chapter 2. Since the residual pseudorange error,
ε
um
, is generally smaller
statistically than the error of the uncorrected pseudorange, a more accurate position
solution is generally attained. Importantly, when pseudorange corrections are
applied, the clock offset produced by the position solution is the difference between
the user's clock error and the reference station clock error. For applications where
the user requires accurate time, the reference station clock offset may be estimated
using the standard position solution technique and removed from the pseudorange
corrections. Removal of the reference station clock offset is generally desirable, even
when the user does not require accurate time, since a large reference station clock
bias could result in excessively large pseudorange corrections (e.g., to fit within a
fixed-size data field in a digital message).
Because pseudorange errors vary with time, as discussed in Section 8.2, the
transmitted pseudorange correction,
[
]
()
()
()
∆ρ
i
t
=
Rt
i
−
ρ
i
t
m
m
m
m
m
m
which is an estimate of the pseudorange error with the sign inverted, is most accu-
rate at the instant of time
t
m
, for which the correction was calculated. To enable the
user receiver to compensate for pseudorange error rate, the station may also trans-
mit a pseudorange rate correction,
ρ
i
t
. The user receiver then adjusts the
pseudorange correction to correspond to the time of its own pseudorange measure-
ment,
t
, as follows:
∆&
()
()
()
( (
)
i
i
&
i
∆
ρ
t
=
∆
ρ
t
+
∆
ρ
t
t
−
t
m
m
m
m
m
m
i
The corrected user receiver pseudorange,
ρ
cor
(), for time
t
is then calculated from
()
()
()
ρ
i
t
=
ρ
i
t
+ ∆
ρ
i
t
ucorr
,
m
8.3.1.3 Performance of Code-Based LADGPS
Using the information presented in Section 8.2 on the spatial and time correlation
characteristics of GPS errors, Table 8.1 presents an error budget for a LADGPS sys-
tem in which the reference station and the user rely only on the GPS SPS (i.e., L1 C/A
code only). The values in the table assume that latency errors are negligible (e.g.,
that the pseudorange corrections are transmitted over a high-speed data link). It is
also assumed that the reference station and user are either at the same altitude or
that a tropospheric height difference correction is employed. Note that multipath is
the dominant error component over short baselines. For longer baselines, the resid-
ual ionospheric or tropospheric errors may dominate. Over very long baselines, per-
formance may be improved by applying a local tropospheric error model at both the
reference station and user locations, rather than the conventional short-baseline
design in which neither side applies a model.
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