Achievable Positioning Accuracies in a Network of GNSS Reference Stations - Global Navigation Satellite Systems: Signal,Theory and Applications - page 190

them to the RINEX from the nearest network station and to the RINEX of virtual stations,
generated by the network software close to the measurement site.

The ultimate goal of this chapter is to quantify the accuracy achievable nowadays with
geodetic and GIS receivers when they are used into a network of reference stations, as well
as to verify (or deny) the possibility that, thanks to the continuous GNSS modernization
program, the improvement of new satellite constellations and new algorithms for
computing and positioning, networks that are characterized by large distances between
reference stations can be used for high accuracy real-time positioning.

2. The network positioning concept

Between 1990 and 1995, the carrier-phase differential positioning has known an enormous
evolution due to phase ambiguity fixing method named “On The Fly” Ambiguity
Resolution (Landau & Euler, 1992). Using this technique, a cycle slip recovery, also for
moving items, was not more problematic, but positioning problems when distances
between master and rover exceed 10-15 kms were not solved. For this reasons, at the end
of the 90's, the Network Real Time Kinematic (NRTK) or, more generally, Ground Based
Augmentation Model (GBAS) was realized. (Vollath et al, 2000, Raquet & Lachapelle,
2001, Rizos, 2002).

First, to understand the network positioning concept it is necessary keep in mind some
concepts about differential positioning. To do this, it is possible to write the carrier-phase
equation in a metric form:

p p p p p p p p p

φ () i = ρ − cdT + cdt − α I + T + i + E + λ Ni + ε (1)

k k k i k k k k i k k

p
k φ term represents the carrier-phase measurement on the i -th
frequency. On the right-hand side of the equation, in addition to the geometric range p

In this equation, the ()

ρ
between the satellite p and the receiver k , it is possible to find the biases related to receiver
and satellite clocks multiply by the speed light (

p

cdT and

cdt ), the ionospheric propagation

k

p 22

1

delay α (with a known coefficient α= f f that depend by the i -th frequency), the

i k i i

p p

k

p

tropospheric propagation delay

T

, the multipath error Mi , the ephemeris error

E

, the

p

carrier-phase ambiguity multiply by the frequency length λ Ni and finally the random

i k

errors p

ε .
Single differences can be written considering two receivers ( h and k ). Neglecting multipath
error, that depends only by the rover site and therefore can not be modelled, it is possible to
write:

p p p p p p p p p

φ () i = φ () i − φ () i = ρ + λ i − cdT − α I + T + E + ε (2)

hk h k hk i hk hk i hk hk hk hk

After that, double differences equations can be written considering two receivers ( h and k )
and two satellites ( p and q ). Subtracting the single difference calculated for the satellite q
from those one calculated for the satellite p , it is possible to obtain the double differences
equation, neglecting random errors contribution:

pq p q pq pq pq pq pq pq

φ () i = φ () i − φ () i = ρ + λ i − α I + T + E + ε (3)

hk hk hk hk i hk i hk hk hk hk