Geoscience Reference
In-Depth Information
Substituting these values for
n
1
and
n
2
,Eq.
63
is fulfilled and the linear combi-
nation Eq.
62
becomes:
f
L
1
f
L
1
−
f
L
2
f
L
1
−
P
1
,
2
=
P
1
−
P
2
=
P
3
.
(65)
f
L
2
f
L
2
This is the
P
3
ionospheric-free linear combination for code ranges. This linear com-
bination can be written in a more convenient expression:
1
P
3
=
(
P
1
−
γ
P
2
),
(66)
1
−
γ
where
f
L
2
γ
=
f
L
1
.
(67)
A similar ionospheric-free linear combination for carrier phase may be derived.
The carrier phase models can be written as:
t
S
trop
ion
L
1
L
1
=
ρ
+
c
(δ
t
R
−
δ
)
+
Δρ
−
Δρ
+
λ
L
1
B
L
1
+
ε,
t
S
trop
ion
L
2
L
2
=
ρ
+
c
(δ
t
R
−
δ
)
+
Δρ
−
Δρ
+
λ
L
2
B
L
2
+
ε,
(68)
where
B
at each
frequency denotes a constant bias expressed in cycles, which contains the integer
carrier phase ambiguity
N
and the phase hardware biases of satellite and receiver.
According to Schaer (
1999
) one cannot separate
N
from the hardware biases.
Now a linear combination is performed
λ
L
1
and
λ
L
2
are the wavelengths at
L
1
and
L
2
band, and the term
λ
L
1
,
2
=
n
1
L
1
+
n
2
L
2
.
(69)
With similar coefficients as in Eq.
64
, the linear combination reads:
f
L
1
f
L
1
−
f
L
2
f
L
1
−
L
1
,
2
=
L
1
−
L
2
=
L
3
.
(70)
f
L
2
f
L
2
The
L
3
ionospheric-free linear combination for phase ranges can also be expressed
as
1
L
3
=
(
L
1
−
γ
L
2
).
(71)
1
−
γ
