Bernese GPS Software Version 5.0 - Bernese GNSS Software

if the real-valued ambiguities p1 ij ij
kℓ , p2kℓ ambiguities we may use the alternative (integer) values pA1 ij ij
kℓ , pA2kℓ hand site of Eqn. (8.14):
The difference
| (λ1p1 ij
kℓ
8.3 Ambiguity Resolution Algorithms
are taken into account. Instead of these real-valued
to compute the right-
λ1pA1 ij ij
kℓ − λ2pA2kℓ ij ij
− λ2p2kℓ ) − (λ1pA1kℓ ij
− λ2pA2kℓ ) |
is actually the difference between the ionosphere bias which was estimated during the initial
ambiguity-free solution and the ionosphere bias which would be the result of the alternative
ambiguity-fixed solution. The difference has to be very small (see option “Search width
for geometry-free linear combination” in panel “GPSEST 3.2.1: General Search Ambiguity Resolution
Strategy”).
It is almost mandatory to use the SEARCH strategy in rapid static mode. If both frequencies
are available (L1 and L2 measurements are processed) usually several minutes of data
are sufficient to resolve the ambiguities and achieve an accuracy of about a centimeter. If
only one frequency is processed the observation interval has to be longer (usually about
30 minutes of data are sufficient). In rapid static mode usually only short (up to several
kilometers) baselines are processed.
The disadvantage of our SEARCH strategy has to be seen in the fact, that either all the
ambiguities or none are resolved. This may cause problems if long sessions are processed
and/or very long baselines are involved (see Figure 8.3(b)).
8.3.3 SIGMA-Dependent Algorithm
Let pi, pj be two (double-difference) ambiguity parameters (relative to the same reference
ambiguity). For each parameter pi we compute the a posteriori rms error in the initial
least-squares adjustment:
mi = σ0 Qii , (8.15)
where Qii is the corresponding element of the cofactor matrix. For the difference pi −pj the
a posteriori rms error is
mij = σ0
Qii − 2 · Qij + Qjj . (8.16)
The rms errors mi and mij of every possible double-difference ambiguity (see Eqn. (8.9) and
(8.10)) are first sorted in ascending order of their rms errors. Within one iteration step the
Nmax best determined ambiguities (or differences between ambiguities) are then resolved
(rounded to nearest integers), provided
• that the corresponding a posteriori rms error mi,mij is compatible with σ0 (mi ≤ σmax
or mij ≤ σmax), and
• that within the confidence interval (pi −ξmi,pi +ξmi) or (pij −ξmij,pij +ξmij) there
is exactly one integer number.
Nmax (“Maximal number of ambiguities fixed per iteration step”), σmax (“Maximal sigma of resolvable
ambiguities”) and ξ (“Ambiguity resolvable if exactly one integer within”) are input parameters of
the program GPSEST (panel “GPSEST 3.2.2: Sigma-Dependent Ambiguity Resolution Strategy”,
Bernese GPS Software Version 5.0 Page 175