Global Positioning System Reference
In-Depth Information
From the above equations, one can see that positioning accuracy from GNSS phase
observations is limited by two types of errors: the distance dependent errors, which include
orbit, ionosphere and troposphere errors, and station dependent errors, which include
multipath, antenna phase centre variation, and receiver hardware biases. The network
estimation methodology uses the known information of the antennae and site to reduce
station related errors and focuses on estimating the distance-dependent errors.
For the station-dependent errors, multipath can be minimised using choke rings and
modelling the site specific multipath pattern taking advantage of the fixed reflector to
antenna geometry at reference stations and of the daily repeatability of multipath. This can
be done utilizing techniques such as the Hilbert Huang transformation to decompose the
time-shifted post-fit GPS phase signal residuals (Hsieh and Wu, 2008). Another approach is
to include multipath error in the network estimation process, which will average out the
uncorrelated multipath errors. To minimise the antenna phase centre variation, the
definition of the network reference stations antennae has always to be consistent. This can
be done by using the same antenna model type for all reference stations and unifying
antenna orientation. To eliminate the phase centre variation, an absolute calibration of each
antenna is recommended. However, most current networks only apply relative calibration
of the antennae, which is a standard calibration process that can be applied for the type of
antenna used, determined relative to a reference antenna (typically a Dome Margolin Model
T with choke ring).
The distance dependent errors can be separated into a dispersive component (i.e. frequency
dependent), which is the error induced by the ionosphere, and a non-dispersive component,
that include orbital and tropospheric errors. Estimation of the dispersive and non-dispersive
errors at the network reference stations can be performed in several ways. In one approach
the state of individual GPS errors in real time can be estimated by processing all stations of
the network simultaneously using un-differenced observables (Wübbena and Willgalis,
2001, Zebhauser et al., 2002, Wübbena et al., 2005). Then, the state vector (
X
G
) at station j
reads:
G
G
(
)
T
s
s
s
s
s
s
X= N, t, t, r, T, r , M
δδδ δ δ δ
(3)
j
j
j
j I
j
The orbital and tropospheric errors are combined to form the geometric (non-dispersive)
error δ
r
, the ionospheric dispersive error
δr
I
(replacing the terms
j
Iand
j
s
δ and in
Equations 1 and 2). The state space approach has some advantages; the main one is its
ability to constrain each bias by specific models (Wübbena and Willgalis, 2001). Also, a
change in the network configuration caused by the breakdown of one of the reference
stations can be compensated without much effort. Moreover, in the case of irregular
conditions of one of the state parameters, warnings can be issued to the users.
Another popular method for estimation of network errors is using single difference linear
combination of observations. The dispersive and non-dispersive components are
determined for satellite
s
and between the reference stations
j
and
k
, using dual-frequency
receivers of L1 and L2, as follows:
δ∆r
L
δ∆r
δ∆r
L
(4)
I,
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