Precise Real-Time Positioning Using Network RTK - Global Navigation Satellite Systems: Signal,Theory and Applications - page 171

network information are broadcast separately. The method requires advanced software in
the rover receiver to do interpolation of corrections. However, unlike the VRS approach, the
user has information about error sizes, which helps in quality control and analysis of results.
The rover software decides how the network information is applied. For instance, the user
can apply the corrections at his location to mitigate observation errors and do differential
positioning with the broadcast master station data. Alternatively, the user can utilise the
network information to construct a VRS at a nearby location, or the user may apply the
Precise Point Positioning (PPP) in what is known as PPP-RTK (Teunissen et al., 2010). FKP
can apply an open message with one-directional communication (from centre to users) to
cover a certain area. In this case, no restrictions would exist on the number of users. A bi-
directional communication can also be employed.

In FKP, the residuals at the network reference stations are assumed to define a surface
which is “parallel” to the WGS-84 ellipsoid in the height of the reference station. For
baselines less than 100 km, the spatial variations of the residuals can be approximated by a
low-order surface model, e.g. a plane, using a bilinear polynomial in the form:

δr(t) = a(t) (φ − φ R ) + b(t) (λ - λ R ) + c(t) (9)

where:

a, b, c coefficients defining the plane at time (t). a and b model the trend of change of
error within the area, and c is used for modelling the station specific errors of the master
station if undifferenced observations are used or the averaged value of the station specific
errors of all the stations if double difference observations are used (Wu et al., 2009).
φ, λ geographic coordinates of the interpolated point (in radians)

φ R , λ R geographic coordinates of the reference point (in radians)

The coefficients are estimated from a weighted least squares solution from the computed
residuals at each reference station using Equations 3 or 4 and 5. For instance, for n number
of reference stations we have:

∆ ∆ 1
∆ ∆ 1

(10)

∆ ∆ 1

where Δλ R-j and Δφ R-j are the difference in latitude and longitude between the reference
station R and station j, respectively.

The least-squares estimates for the coefficients can be obtained by (Wu, 2009):

̂

(11)

Where:

∆ ∆ 1
∆ ∆ 1

and

(12)

∆ ∆ 1