Bernese GPS Software Version 5.0 - Bernese GNSS Software

2.3.6.3 Wide-Lane Linear Combination L5
The linear combination
L5 =
1
f1 − f2
2.3 Observation Equations
(f1 L1 − f2 L2) (2.47)
is used in the Bernese GPS Software on the double-difference level for phase observations
to fix cycle slips and to resolve ambiguities to their integer values. Using Eqns. (2.37c) and
(2.37d) and neglecting both, the ionospheric refraction I ij
kℓ and the tropospheric refraction
∆̺ ij
kℓ , we obtain
L ij
5kℓ = ̺ij
kℓ +
c
(n
f1 − f2
λ5
ij
1kℓ − nij
2kℓ )
n ij
. (2.48)
5kℓ
The formal wavelength λ5 is about 86 cm and is roughly four times larger than λ1 or λ2.
Therefore, this linear combination is called wide-lane combination and the corresponding
ambiguity
is called wide-lane ambiguity.
n ij
5kℓ = nij
1kℓ − nij
2kℓ
2.3.6.4 Melbourne-Wübbena Linear Combination L6
(2.49)
The Melbourne-Wübbena combination is a linear combination of both, carrier phase (L1
and L2) and code (P1 and P2) observables as described by [Wübbena, 1985] and [Melbourne,
1985]. This combination eliminates the effect of the ionosphere, the geometry, the clocks,
and the troposphere. The combination is given by
L6 =
1
f1 − f2
(f1 L1 − f2 L2) −
For double-difference observations, we obtain
1
f1 + f2
(f1 P1 + f2 P2) . (2.50)
L ij
6kℓ = λ5 n ij
5kℓ . (2.51)
With “good” P-code data (rms ≤ 1 m) this linear combination may be used for the resolution
of the wide-lane ambiguities n ij
5kℓ . On the zero-difference level, the same linear combination
gives
(2.52)
L i 6k = λ5 n i 5k
which means that this linear combination may be used to check zero-difference observations
for cycle slips. However, only the difference ni 1k − ni 2k can be checked in this way.
The most important linear combinations and their characteristics are summarized in Table
2.10. The specifications with respect to “noise” and “ionosphere” are based on units of
meters. L1 and L2 (expressed in meters) are assumed to be equally accurate and uncorrelated.
Note that the noise of “L6” is given relative to that of P1 and P2, respectively, since
this noise level is pre-determined exclusively by the quality of the P-code data considered
(compare also Eqn. (2.50)).
Bernese GPS Software Version 5.0 Page 41