Bernese GPS Software Version 5.0 - Bernese GNSS Software

8. Initial Phase Ambiguities and Ambiguity Resolution
Satellites
✲
time
(a) Short session and a short baseline.
Satellites
A3
A4
A1
Figure 8.3: Satellite visibility plot
A5
A2
A7
A6
A8
✲
time
(b) Long session and a long baseline.
In the Bernese GPS Software ambiguities may be resolved only if double-difference observations
are processed. Single-difference (between receivers) ambiguities are then stored in
the single-difference header files. For each session and each baseline we have to select one
single-difference bias n j
as reference and actually our estimated ambiguity parameters
are the differences
Fkℓ
n ij
Fkℓ = niFkℓ − nj
Fkℓ . (8.8)
Usually, the ambiguity with the maximum number of observations is selected as reference.
If there are N single-difference ambiguities for one session and one baseline, there are at
most N −1 linearly independent unknown ambiguity parameters. If there is an epoch when
all the single-difference phase measurements were initialized again, the session breaks up
into two parts and for each part one reference ambiguity must be selected. In that case only
N −2 ambiguity parameters may to be estimated. The set of measurements corresponding to
exactly one reference ambiguity is called an observation cluster (different from an ambiguity
cluster, see below). In the following we will assume to have only one observation cluster.
Figure 8.3(a) shows the satellite visibility plot for a short (several minutes) session. For
short sessions there is usually one (or more) satellite(s) which was(were) observed all the
time. One of these satellites may be selected as reference satellite (and the corresponding
ambiguity as reference ambiguity). For longer sessions the situation is different:
• No satellite is observed during the entire session,
• there are periods during which only few satellites were observed, for very long baselines
there may be even periods during which only one or two satellites were observed.
Typically, for long baselines and sessions we obtain a satellite visibility plot as in Figure
8.3(b). In that case the program selects (single difference) ambiguity A1 (maximum
number of observations) as a reference. After the first ambiguity resolution step (real-valued
ambiguities are estimated) a detailed inspection usually shows that the (double-difference)
ambiguities A2 − A1,A6 − A1,A7 − A1,A8 − A1 have large a posteriori rms errors. On the
other hand, the parameters A3 − A1,A4 − A1,A5 − A1 have small rms errors. This result is
a consequence of the selection of the reference ambiguity. If A2 would have been selected as
reference the parameters A6 −A2,A7 −A2,A8 −A2 would have small a posteriori rms errors
and the parameters A1 − A2,A3 − A2,A4 − A2,A5 − A2 big ones. The following conclusions
may be drawn:
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