Bernese GPS Software Version 5.0 - Bernese GNSS Software

Mean Difference (in millimeters)
600
500
400
300
200
100
0
Amb. Free, Non Ecl.
Amb. Fixed, Non Ecl.
Amb. Free, Ecl.
Amb. Fixed, Ecl.
159 160 161 162 163 164 165 166
Day of Year 1995
Mean Difference (in millimeters)
1200
1100
1000
900
800
700
600
500
400
300
200
100
0
169 170 171 172
Day of Year 1995
8.2 Theory
Amb. Free, Non. Ecl
Amb. Fixed, Non Ecl.
Amb. Free, Ecl.
Amb. Fixed, Ecl.
Figure 8.2: Orbit quality estimated from discontinuities at day boundaries (eclipsing and
non-eclipsing satellites).
This last equation shows how the normal equation system changes if the ambiguities have
been resolved (fixed on their integer values). Fixing ambiguities considerably reduces the
number of parameters and the solution will get much more stable. It should be pointed
out, that usually the majority of unknown parameters actually are the ambiguities. How do
the solutions improve if the ambiguities have been resolved? The answer depends strongly
on the ratio between the number of unknown non-ambiguity parameters and the number
of measurements which are used for the estimation of these parameters (the length of the
observing sessions for static applications). Figure 8.1 shows the effect of ambiguity resolution
if only the receiver coordinates and few troposphere parameters are estimated in a regional
(European) network (for details see [Mervart, 1995]). In this case the main effect may be seen
for session length up to 4 hours. However, the second important advantage of the ambiguity
fixed solutions is the significantly reduced number of parameters which have to be stored in
the memory. This saves RAM and speeds up processing considerably. If many parameters
are estimated (orbits, Earth orientation parameters etc.) ambiguity resolution improves
also the results of much longer sessions (3-days sessions used in CODE for IGS processing).
Figure 8.2 shows the improvement in the estimated orbits (for details see [Mervart et al.,
1995]): The ambiguity fixed solution is the official IGS CODE solution since June, 1995.
8.2 Theory
There are many methods how to resolve the ambiguities. Some of them are very sophisticated,
some quite simple, but most of them consist of two steps:
Step 1: The ambiguities are estimated as real numbers together with other parameters.
Step 2: The integer values of the ambiguities are resolved using the results of Step 1 (the
real-valued ambiguities and the variance-covariance matrix). Usually statistical tests
are performed to resolve the ambiguities in a reliable way.
Bernese GPS Software Version 5.0 Page 169