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tion of the observation site. Therefore it's usually hard to find an appropriatemodel for
it. Thus the most efficient method is to eliminate its effect by using signals in different
frequencies. This is the main reason why almost all space geodetic techniques trans-
mit signals in at least two different frequencies. Forming linear combinations with
different frequencies allows eliminating the effect of the ionosphere to a large extent.
4.2.1 Eliminating First Order Ionospheric Effects in GNSS Measurements
The fundamental observation equation for the GNSS code-pseudorange including
the frequency dependent ionospheric refraction, reads
t
S
trop
ion
L
1
b
S
P
1
=
ρ
+
c
(δ
t
R
−
δ
)
+
Δρ
+
Δρ
+
c
(
b
R
+
)
L
1
+
ε,
t
S
trop
ion
L
2
b
S
P
2
=
ρ
+
c
(δ
t
R
−
δ
)
+
Δρ
+
Δρ
+
c
(
b
R
+
)
L
2
+
ε,
(61)
where
ρ
geometric distance between receiver and satellite
t
S
δ
t
R
,δ
receiver and satellite clock offsets to the GPS time
trop
Δρ
delay of the signal due to the troposphere
ion
Δρ
frequency-dependent delay of the signal due to the ionosphere
b
S
b
R
,
frequency-dependent hardware delays of the satellite and receiver (DCB)
(in ns)
ε
random error
Further corrections like relativistic effects, phase-wind up, or antenna phase center
corrections are omitted in Eq.
61
.
The code ranges are obtained from measurements of the signals
P
1 and
P
2
modulated at the two carriers with the frequencies denoted by
L
1
and
L
2
and the
ionospheric term
ion
is equivalent to the group delay in Eq.
46
.
A linear combination is now performed by
Δρ
P
1
,
2
=
n
1
P
1
+
n
2
P
2
,
(62)
where
n
1
and
n
2
are factors to be determined in such a way that the ionospheric
refraction cancels out. Substituting Eq.
61
into Eq.
62
leads to the postulate
ion
ion
L
2
n
1
Δρ
L
1
+
n
2
Δρ
=
0
.
(63)
Assuming
n
1
and
n
2
as
f
L
1
f
L
1
−
f
L
2
f
L
1
−
n
1
=+
f
L
2
,
n
2
=−
f
L
2
.
(64)
