Bernese GPS Software Version 5.0 - Bernese GNSS Software

8. Initial Phase Ambiguities and Ambiguity Resolution
p = (p1,... ,pu) ⊤ , the part of the solution vector consisting of all real-valued (doubledifference)
ambiguities, where u is the number of double-difference ambiguities,
Q the corresponding cofactor matrix, and
σ 2 0 the a posteriori variance factor.
From the a posteriori variance factor and the corresponding cofactor matrix the standard
deviation mi for the ambiguity parameter pi or the standard deviation mij for the difference
pij between two ambiguity parameters pi, pj may be computed:
mi = σ0 Qii , mij = σ0 Qii − 2 · Qij + Qjj . (8.11)
Choosing a confidence level α and using Student’s distribution we compute the upper and
lower range-width ξ for the integer valued alternative parameter pAi or for the difference
pAij between two such parameters. Thus
pi − ξ · mi ≤ pAi ≤ pi + ξ · mi , i = 1,2,... ,u (8.12)
pij − ξ · mij ≤ pAij ≤ pij + ξ · mij , i,j = 1,2,... ,u , i = j . (8.13)
All possible combinations of integer values which meet the conditions (8.12) and (8.13) are
used to form alternative ambiguity vectors
p Ah, h = 1,... ,N
to the initial ambiguity estimate p. These alternatives are generated in forming all possible
combinations of vector components using the integer values within corresponding confidence
ranges. Each of these alternative vectors is introduced into a subsequent adjustment. The
integer ambiguities are treated in these adjustments as known quantities. The resulting
standard deviations
σh, h = 1,... ,N
are indicators for the success of the process: the integer vector p h yielding the smallest
standard deviation is selected as the final solution, unless
(1) its standard deviation is not compatible with the standard deviation σ0 of the
ambiguity-free solution (the fraction σh/σ0 is too high), or
(2) there is another vector p q yielding an almost identical standard deviation (fraction
σq / σh ≈ 1).
The maximum allowed fraction (σh/σ0)max (“Maximum allowed rms ratio re fixed to float”) and
the minimum discrimination fraction (σq/σh)min (“Minimum allowed rms ratio re 2nd best to
best”) are input options in panel “GPSEST 3.2.1: General Search Ambiguity Resolution Strategy”
(see Figure 8.6). In order to reduce the computation time and decrease the number of
alternative vectors one more condition is introduced if both frequencies (L1 and L2) are
processed. Using the geometry-free linear combination (see Section 2.3) we may write
L4 ij
kℓ + Iij
kℓ
1 − f2 1
f 2 2
= λ1p1 ij ij
kℓ − λ2p2kℓ , (8.14)
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