Global Positioning System Reference
In-Depth Information
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receiver, using double differencing and employing some ambiguity fixing technique.
Since RTK positioning is very economical, it is desirable to extend the reach of
RTK over longer baselines. Because of the high spatial correlation of troposphere,
ionosphere, and orbital errors, one expects that over a sufficiently small region the
error terms
T
km
,I
km
, and
d
p
km
depend on the distance between receivers. Wübbena
et al. (1996) took advantage of this dependency and suggested the use of reference
station networks to extend the reach of RTK.
There are two requirements at the heart of multiple reference station RTK. First,
the positions of the reference stations must be accurately known at the centimeter
level. This can be readily accomplished using postprocessing and long observation
times. The second requirement is that the single- or double-difference integer ambi-
guities for baselines between reference stations are also known. It is then possible
to compute tropospheric and ionospheric corrections and transmit these to an RTK
user, to be applied to the rover's observations. For the discussion below we assume
that the tropospheric term
T
km
ρ
[29
p
km
, which is permissible
includes the orbital error
d
ρ
ac
cording to (7.19) and (7.20).
There are several variations available regarding the practical implementation of
m
ultiple reference station RTK. Because of its prevailing use with short baselines
an
d because of the design of existing software, the initial implementation of multiple
re
ference station networks was derived from double-difference observations. Below
w
e give a general description using single differences. One could begin with the dual-
fre
quency pseudorange and carrier phase observations and use (7.33) to compute the
w
ide-lane ambiguity integers
N
km,w
Lin
—
1
——
Nor
*PgE
N
km,
2
between network reference
sta
tions and for every satellite. One could then compute the tropospheric delay
T
km
us
ing measured meteorological data, the tropospheric models such as (6.17) and
(6
.18) for the vertical dry and wet delays, and the tropospheric model mapping
fu
nction (6.22). Alternatively, a continuously running Kalman filter can be used on
th
e ionospheric-free function (7.41)
N
km,
1
−
=
[29
T
k
m
ϑ
k
−
T
m
m
ϑ
m
+
p
km,
IF
p
km,
0
R
km
Φ
− ρ
=
cd
t
km
+
(7.223)
to
estimate the vertical tropospheric delays
T
k
and
T
m
, the receiver clock difference
dt
km
, and the ambiguity constant
R
km
using observations from all satellites. A simpler
pa
rameterization
T
km
m(ϑ
k
)
or
T
km
m(ϑ
k
)
may be permissible for the relative tropo-
sp
heric correction. The subscript zero in
p
km,
0
indicates that the known reference
station coordinates are used to compute the ranges. The individual ambiguities
N
km,
1
and
N
km,
2
ρ
can then be estimated from
R
km
= β
f
λ
1
N
km,
1
− γ
f
λ
2
N
km,
2
(7.224)
N
km,w
=
N
km,
1
−
N
km,
2
(7.225)
The ionospheric term
I
km,
1
,P
can then be computed from the ionospheric function
(7.40)
