Global Positioning System Reference
In-Depth Information
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6.6.6 Generalizing the Dual-Frequency Phase Function
Th
e general linear combination of dual-frequency carrier phase observations at a
gi
ven station is,
ϕ
m,n
≡
nϕ
2
= λ
−
m,n
ρ +
mϕ
1
+
(6.102)
I
m,n,ϕ
+ λ
−
m,n
T
¯
N
m,n
−
f
m,n
d
t
+
f
m,n
d
t
+
+ δ
m,n,ϕ
+
ε
m,n,ϕ
The frequency, wavelength, ambiguity, and the ionospheric terms for the general
carrier phase function
ϕ
m,n
are
f
m,n
=
mf
1
+
nf
2
(6.103)
c
f
m,n
=
c
mf
1
+
[22
λ
m,n
=
(6.104)
nf
2
N
m,n
=
mN
1
+
nN
2
(6.105)
Lin
—
3.2
——
No
PgE
mf
2
+
nf
1
I
m,n,ϕ
=
mI
1
,ϕ
+
nI
2
,ϕ
=
I
1
,ϕ
(6.106)
f
2
I
m,n,
Φ
= λ
m,n
I
m,n,ϕ
(6.107)
Be
cause the GPS L1 and L2 frequencies are related as
f
1
/f
2
=
77
/
60, the
m
=
70
and
n
60 combination does not depend in the ionosphere. Expressed in units of
len
gth, the function (6.102) becomes
=−
[22
¯
Φ
m,n
= ρ + λ
m,n
N
m,n
−
cd
t
+
cd
t
+
I
m,n,
Φ
+
T
+ δ
m,n,
Φ
+
ε
m,n,
Φ
(6.108)
with
δ
m,n,
Φ
and
ε
m,n,
Φ
being the respective functions of the hardware delays, multi-
pa
th, and measurement noise. The ionospheric ratio with respect to the L1 carrier can
be
written as
mf
2
+
I
k,m,n,
Φ
I
k,
1
,
Φ
f
1
f
2
nf
1
=
(6.109)
mf
1
+
nf
2
In
(6.102) the distances are expressed in units of the wavelength. A change in
ϕ
m,n
by
one cycle, or a change of the ambiguity
N
m,n
by one cycle, represents a distance
change along the station-satellite direction by one wavelength of
λ
m,n
. The distance
corresponding to one wavelength is frequently called a lane. Determination of the
ambiguity
N
m,n
thus implies that the topocentric range has been resolved within the
unit of
λ
m,n
. One might, therefore, prefer transformations that give large wavelengths
and solve the respective ambiguities. The assumption is that the unmodeled errors are
small enough to allow a unique determination of these ambiguities. In a subsequent
solution, when estimating
N
1
and
N
2
, one could constrain the
N
m,n
. Unfortunately,
