Bernese GPS Software Version 5.0 - Bernese GNSS Software

2. Fundamentals
2.3.6.1 Ionosphere-Free Linear Combination L3
The linear combination
L3 =
1
f2 1 − f2 (f
2
2 1 L1 − f 2 2 L2) (2.41)
is often called “ionosphere-free” because the ionospheric path delay is virtually eliminated.
The same is true for the corresponding combination of code measurements
P3 =
1
f2 1 − f2 (f
2
2 1 P1 − f 2 2 P2) . (2.42)
Taking into account the double-difference phase measurements and neglecting tropospheric
refraction ∆̺ ij
kℓ in Eqns. (2.37c) and (2.37d), the ionosphere-free linear combination has the
form
where the ionosphere-free bias B ij
3kℓ may be written as
B ij
3kℓ =
L ij
3kℓ = ̺ij
kℓ + Bij
3kℓ , (2.43)
1
f 2 1 − f2 2
This bias cannot be expressed in the form λ3 n ij
3kℓ
we know the difference n ij
5kℓ
= nij
1kℓ
− nij
2kℓ
however, the ionosphere-free bias B ij
3kℓ
B ij
3kℓ = c
f 2 ij
1λ1n1kℓ − f2
ij
2λ2n2kℓ . (2.44)
, where nij
3kℓ is an integer ambiguity1 . If
(the so-called wide-lane ambiguity — see below),
may be written as
f2
f 2 1 − f2 2
n ij
5kℓ +
c
f1 + f2
λ3
n ij
1kℓ , (2.45)
where the first term on the right-hand side is known. The formal wavelength λ3 is only
approximately 11 cm. Therefore, the unknown ambiguity n ij
1kℓ in Eqn. (2.45) is often called
narrow-lane ambiguity.
2.3.6.2 Geometry-Free Linear Combination L4
The linear combination
L4 = L1 − L2
(2.46)
is independent of receiver clocks, satellite clocks and geometry (orbits, station coordinates).
It only contains the ionospheric delay and the initial phase ambiguities and may be used
for the estimation of ionosphere models. The same linear combination may be formed using
the code observations, too.
1 The ionosphere-free bias may be written as a multiple of a wavelength of 6 mm which has, in fact, no
practical application
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