Precise Real-Time Positioning Using Network RTK - Global Navigation Satellite Systems: Signal,Theory and Applications - page 174

P P ∆R δ∆r

I δ∆r ∆T

(21)

One characteristic of the Mac approach is that its data are sent to the user at the same
ambiguity level. This can be explained as follows. In the Mac method the carrier phase
ambiguities are determined with respect to fixed single difference ambiguity values.
However, ambiguity fixing is more reliably performed using a double difference approach.
Thus, the ambiguities from the satellite s can be determined from that of the reference
satellite q and their double difference as follows:

N N N ,

(22)

Therefore, the ambiguity bias, which is the difference between the true ambiguity and the
estimated ambiguity for the reference satellite, usually known as the ambiguity level, should
be estimated. It is common to all estimated ambiguities of satellites observed from one
baseline and cancels out in double differencing.

After receiving the Mac information, the rover software is free to decide the method of
interpolating the corrections at its location. The processing centre can do the interpolation if
needed (individualised I-Max). The rover software is also free on how the Mac information
be used to determine its position. For instance, the rover can apply double differencing with
the Master reference station as the base. It can also do that after removing the errors from
both the Master reference station and its position.

6. PPP- RTK

A more recent direction of NRTK implementation is its integration with the precise point
positioning (PPP) technique, Wübbena et al. , 2005. In a standalone PPP mode, undifferenced
observations are used and the satellite related errors are mitigated by using satellite clock
corrections and utilising precise orbits to avoid the orbital errors associated with the use of
broadcast ephemeris. These satellite products are typically provided from a processing
centre analysing global data such as the International GNSS Service (IGS). Since only one
receiver is used in PPP, the ambiguities are solved as part of the unknowns with real
numbers and not fixed. As a result, several minutes of data are needed when processing to
achieve a reliable convergence of the solution. As the ambiguities are solved as real
numbers, only accuracy at the sub-decimetre, at best, is achievable from PPP. However, it is
possible to integrate PPP and NRTK into a seamless positioning service, which can provide
an accuracy of a few centimetres (Li et al., 2011). The concept of PPP-RTK is to augment PPP
estimation with precise un-differenced atmospheric corrections and satellite clock
corrections from a reference network, so that instantaneous ambiguity fixing is achievable
for users within the network coverage.

A few techniques have been yet proposed for PPP-RTK. In the method presented in
Teunissen et al., 2010, un-differenced observation equations for the network stations are
used, and thus the design matrix of the network will show a rank defect. This rank defect is
eliminated through an appropriate reparametrization (i.e. reduction and redefinition of the
unknown parameters). This results in redefined satellite clocks and ambiguities. The
tropospheric delay is lumped with the phase and pseudo range satellite clock errors and the
ambiguity becomes a between receiver single-differenced ambiguity. Eventually, a full-rank
system of observations can be obtained.